Create a blog describing what you have learned about Algebra so far.  You must include the following:
  • What are variables
  • Why do we need order of operations
  • Why is it necessary to classify numbers
Your blog must be 5 paragraphs long.  This blog is due on Thursday, October 4th, by midnight.  You may use my starter blog for ideas.
 


Comments

Mrs. Deonarine
09/26/2012 6:27pm

If you can read and write then learning algebra will be very easy for you. I say this because algebra is just like a language. There are words which are called variables and grammar rules which are called order of operations. There is even a way to describe numbers, like adjectives, only in math we call it classifying numbers.

The language of algebra starts with variables. Variables are.....

Without grammar rules it would be difficult to understand what a person is talking about. Likewise, without order of operations...

If you were unable to describe a lost object it would be difficult for someone to help you find it. The same goes for numbers....

Math is all around us. It is a universal language. Engineers, pharmacist, doctors etc. are all mathematicians...

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Sheila Chiu
10/01/2012 2:52pm

Algebra is a language and to learn it well you must learn about these
different topics. Expressions, equations, and variables. You need to know the order of operation, PEMDAS. You also need to classify your numbers.

Expressions are mathematical phrases that can include numbers, variables, and operations symbols. Equations are similar to expressions only it has an equal sign. Either side of the equation has the same value. Variables are included in both expressions and equations. It is usually a letter symbolizing a number.

Order of operations is very important in solving equations because it gives you a specific order to solving the problem so you end up with one correct answer. PEMDAS is the order to solving an equation, starting with parenthesis, exponent, multiplication, division, addition, and subtraction. Even though multiplication comes before division, whenever division is shown before multiplication you must divide first because an equation should be solved from left to right. The same goes for addition and subtraction because it is done from left to right. Therefore, following PEMDAS will get you the right answer otherwise you will receive the wrong answer.

Classifying numbers is important as well because you should be able to tell what kind of numbers you are working with. For instance, there are natural numbers, whole numbers, integers, irrational, and rational numbers. Natural numbers are any number that starts from 1 that is not zero or negative and whole numbers are any number that is not a fraction or decimal starting from zero. Integers are any number that includes negatives and zero. Rational numbers are numbers that can be written as fractions and/or decimal. Irrational numbers are numbers that cannot be written as a fraction or decimal, such as pi and square root of 7 which does not have an end and keeps going.

These are three topics you should know to be well versed in algebra. You need to know what are expressions, equations, and variables. You must be familiar with the order of operation to obtain the right answer. It is also necessary to be able to classify your numbers. Therefore, these are the three topics to acquire in order to do well in algebra.

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Ana Naumovska
10/01/2012 10:12pm

In order to be able to do more complex problems in math, first you must learn the basics. These basics include things like expressions, equations and variables. There are also order of operations (PEMDAS) and classifying numbers.
First, variables are like elements which represent one or more unknown number. Common variables are represented by letters like x, y or z. Variables are used in expressions which are a verbal form of equations. For example, a number increased by two is an expression. An equation for instance is the algebraic version of an expression. For instance, x+2 are an equation for the expression “a number increased by two”. The variable in this situation is x.
Another basic you must know is order of operations. Often this is known as PEMDAS. PEMDAS stands for parenthesis, exponents, multiplication, division, addition and subtraction. This means that whenever an equation is given, you must follow the correct order in order to get the right answer. For example, 6(2+3), first you must do what’s in the parenthesis (2+3) =5, then multiply 6x5=30. In some cases you will get a problem like 6/2x5. In that equation you have both division and multiplication but you must divide before you multiply since it’s the first things from the left. The same goes if a problem with both addition and subtraction is given.
Lastly, the classification of numbers is also an important topic. Classifying numbers is a group of whole numbers, integers, irrational and rational numbers. Whole numbers are natural numbers from 0 and up. Negative numbers go under integers but they’re still whole numbers (-1,-2,-3). Some whole numbers can be also rational numbers as long as they can be put in a fraction and have an end. Irrational numbers on the other hand are numbers that don’t have an end like pi or the square root of 2.
Algebra is like a language and in order to speak it well you must follow the rules. Some of algebras most important rules are expressions, equations, variables, order of operations and classifying numbers. Once you know these, you will be able to solve more complicated questions and learn many more things algebra has to offer.

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Yosrick Alvarez Avalos
10/02/2012 2:48pm

Algebra 1 is a language and in order to speak it you must follow the rules. This statement might seem crazy in the beginning but as you progress through the unit you start to see how learning a language is like algebra. The three main subtopics for algebra is variables, orders of operations, and classifying numbers. In order to do well in these topics you have to study and practice. (like a language)
Variables is a symbol that usually is a letter that represents a number. Variables are used in equations and expressions, the difference between an equation and expression is and equation has an equal sign. An equation is a mathematical equation that has an equal sign, an expression is a mathematical phrase that can include variables, numbers, and operation symbols. An example of an equation is 3y+2x=13, an expression is 2(4y+6x).
Order of operations plays a big role on expression and equations, it can evaluate or simplify an equation or expression. Simplify means a numerical expression that can replace it with the simplest name. Evaluate is an algebraic expression by substituting a number for each variable. Order of operations uses exponents which tells you how many times a number,a base, is used. To remember how evaluate and simplify you can use PEMDAS, its a way to remember how to simplify and evaluate, parenthesis, exponents, multiplication, division, add, and subtract, is what PEMDAS stands for.
Classifying numbers is a way to categorize a set of numbers in certain words that describe numbers such as whole number, integers, natural numbers, irrational, rational, and real numbers. Rational number is any number that can be written in an a/b form, but also numbers that repeat. Irrational number cannot be expressed as a/b form, where a and b are integers. An example of classifying numbers is 4 is a whole number, integer, natural number, and rational number.
In conclusion algebra consist of three subtopics variables, order of operation, and classifying numbers. In order to understand algebra 1 you must practice and study it, and that's exactly what I did, and now I understand it as if it were a third language.

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Becky Chan
10/02/2012 3:04pm

There are different kinds of ways math can be solved by. There are variables, expressions, equations, order of operations, and classifying numbers.

Algebra is like a language because its like having to learn the rules and follow them. Mathematicians needs to be organized and neat so they won't mess up. Variables are symbols(usually a letter) represents one or more numbers, for example 12-y. Algebraic expression is a mathematical phrase that includes numbers, variables, and operation symbols. An equation is a mathematical sentence that uses equal signs. An open sentence contains one or more variable.

Doing order of operations, is following PEMDAS, for example
6-(2+7). It is important to follow the order of PEMDAS so there won't be any mistakes, for example 5+(2+4). First, do what's in the parenthesis. Next, figure out exponents. Then, do the multiplications and division according to which comes first, that also goes for adding and subtraction. Simplify, is a numerical expression and replacing it with its simplest form. Exponent is how many times of a number base, is used s factor. Power has two parts, a base and exponent. Evaluate, means that a algebraic expression is by substituting a given number for each variable.

Classifying numbers can be like classifying food. It can be like how people eat red meat and pork which is rational. Some people are vegetarian, which is negative. People who doesn't eat meat, those are whole foods. There are people who eat icky foods like snails and insects, that is classified as irrational. Whole numbers are numbers 0 and up. Integers are negative numbers. Irrational numbers cannot be expressed in form a/b. These numbers can go on forever and you can't quote it. Real numbers are rational and irrational numbers. Inequality is a mathematical sentence that compares 2 expressions and uses symbols.

Math includes variables, expressions, equations, order operations, and classifying number. Variables are symbols that is usually a letter. Expressions is a mathematical phrase. Equations are problems that has an equal sign. Order of operations is solving the equations and expressions using PEMDAS. Classifying numbers consist of rational, negative, whole, irrational, and integer number.

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Gabe Quinones
10/03/2012 8:21am

Math is a universal language and like all languages there is a proper way to "speak" it. People around the world can be asked the same question and for once get the same answer, and there is only 1 correct answer. In order to understand math however you must know the vocabulary. Expressions and variables are huge parts of the math language and world, in order to read a math sentence "properly" you must follow PEM/DA/S. It is the order of operations that makes a "grammatically" correct "sentence." In order to even understand math to begin with however you need to know how to classify numbers like classifying nouns, verbs, and other necessities to a sentence.
Expressions are numerical sentences without an answer. Sort of like a question in English. Variables and other components of an expression are easy to identify and even easier to unfold, All expressions are like a piece of paper folded in such a complex way that you have to go in the right order to unfold the piece of paper. If you mess up one spot you will not unfold it correctly and may even end up ripping it.
The order of operations is extremely important with out it questions would have completely different answers and would be very complex. The order is parentheses, exponents, then it goes multiplication or division next depending on which one comes first when reading the expression from left to right, same goes for addition and subtraction.
Classifying numbers is a large topic but has some connections within it. A whole number ranges from 0+ but wont go into negatives. Natural numbers range from 1+ but never go to 0, Integers can be both negatives and positives. Irrational numbers never end (6.66666666787789803940934) rational numbers do end. Opposite numbers are numbers like -8 and +8.
The language of math maybe universal but that doesnt mean it isnt difficult. There are many components to this complex language and you must know them all in order to understand it.

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Cindy Lian
10/03/2012 2:52pm

Math is a language that can only be used correctly if understood and used in the right time and place. Variables/expressions/equations, P.E.M.D.A.S, and classifying numbers are parts of math.

A variable is a symbol, usually a letter, that represents one or more numbers. A variable is used as a replacement for another number. In an equation there can contain one or more variables. A variable is used in both equations and expressions. An equation contains an equal sign and expression does not.

The order of operation is important in order to do math correctly. To do a long problems with different signs you will have to use P.E.M.D.A.S. The P stands for parenthesis. The E stands for exponents. The M and the D stands for multiplication and division (you do which one comes first). The A and the S stands for addition and subtraction (you do which one comes first). If you do not follow these steps you won't be able to get the correct answer of a math problem.

The classification of numbers are also very important in the math world. If you do not classify numbers correctly you would get all mixed up when solving a problem. If you classify numbers you would know what numbers belong in which group. You would know which ones are negative or positive numbers. Whole numbers and fractions are also in a group and you would also be able to tell irrational numbers from rational numbers.

These three parts of math are important and we use them everyday. We use these all the time. They will help out with everyday life and make our lives easier.

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Tess Dreizen
10/03/2012 4:27pm

Algebra is a language and in order to understand it, all of its concepts must be applied. Variables, expressions and equations are used in algebra as a way to express numbers and represent quantities.  Order of operations is used to be precise when solving equations and it tells you the order to solve the equation. Classifying numbers is used to understand the number system and the concept classifying objects based on its kind. All of these forms of algebra are used to in order to have a better understanding of the language as a whole.
 
Variables, expressions, and equations are used to represent quantities. A variable is a symbol that represents a number. An expression is a mathematical phrase that may include numbers, variables and operation symbols. Lastly equations, they are also mathematical phrases, but including an equal sign. An example of an expression is “t minus 15” which is equivalent to “t-15”. An example of an equation is “cost of h CDs, CDs raised to $15, equals 15h=C.

Order of operations is used to be able to communicate algebraically. Order of operations uses P.E.M.D.A.S. and it stands for parentheses, exponents, multiplication, division, addition, and subtraction. When solving expressions or equations, the order of P.E.M.D.A.S. is required. Depending on the expression or equation, division and multiplication, whatever comes first determines how the problem will be solved. If multiplication comes first in a problem, that means you will solve multiplication first and visa versa. The same goes for addition and subtraction. An example of order of operations is “2*5-3+2*8=24”. Lastly, to simplify means to replace a numerical value with its lowest form.

Classifying numbers is the way to understand the number system. It is also a way to sort out numbers into their own categories. Natural numbers are the numbers “1,2,3...”. Whole numbers are natural numbers that include zero. Integers are whole numbers that include negative numbers as well. Rational numbers are any number you can write in a/b, where b does not equal 0. Irrational numbers are anything that cannot be written as a simple fraction. An example of a rational number is “4/5”. An example of an irrational number is ”0.333...”. The classification of numbers is key to understanding the importance of each number and the types of numbers that exist.

Algebra is a way to express numbers and how different concepts can be applied to different problems, including real life situations. Variables, expressions, equations, order of operations and the classification of numbers all make up algebra at it’s most basic. When these parts of algebra are used with all the other types of algebra it completes the language. In order to begin to understand this language one must understand these topics above.

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Krystal Waheed
10/03/2012 6:33pm

There are many different languages and many different ways of writing. of course we think of global languages like Spanish, Chinese and many more. but one language you may not have thought of is Algebra. but before you start speaking or writing algebra there's a couple of things you must know.
A variable is a symbol or letter that represents a number for example 9x - 53 the variable in that expression is x. the reason why i said expression instead of equation is because expression lacks an equal sign while equations always have one. also! with an equation each side of the equal sign are equivalent. An algebraic expression includes numbers,symbols and variables for example : m - 4n is an algebraic expression
GEMDAS stands for Grouping, Exponents, Multiplication, Division, Addition and Subtraction. GEMDAS is also known as order of operations. lets say you have this problem : 3 x 4 + 8 - 9 you would first do the multiplication and get 12 then add 8 to get 20 then subtract 9 to get 11. something to remember is with multiplication and division and addition and subtraction, you do whichever operation comes first in the equation from left to right.
Numbers also fall into different categories natural numbers are counting numbers like 1 2 3 4 etc... Whole numbers are non-negative numbers. Integers are whole numbers and there opposites (meaning they are also negative numbers) rational numbers are real numbers, that can be written as a ratio of two numbers when there decimals they are terminating or repeating. 1.75 is a rational number and a integer. Irrational numbers yup, you guessed it there the opposite of rational numbers the can't be written as a ratio as a decimal they are non - terminating and non - repeating. Pi is an example of an irrational number because its never ending. Real numbers are either rational or irrational.
a lot of information i know, but to sum it all up variables represent a number. the difference between an equation and an expression is that expression dont have equal signs and GEMDAS means Grouping, Exponents, Multiplication, Division, Addition and Subtraction. As long as you know all the information in this essay you will be fluent in Algebra.

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Vincenzo Acquaviva
10/03/2012 6:55pm

Math is language that most people know. This past month, I have learned a lot in math. I learned about variables/expressions/equations, the order of operation, and classifying numbers.
An equation is a mathematical statement that two expressions are equal. An example of an equation would be 1+1=2. Variables are commonplace in equations. A variable is a symbol (usually a letter) that represents a number. For example, if a variable was used in the previous equation, it would become 1+X=2. Variables can also be found in expressions. An expression is essentially a number sentence that has no equal sign. For example, 1+1 is an expression. If a variable was put into that expression it would become 1+X. The main difference between expressions and equations is the fact that equations are equivalent to something while variables are not. Basically, equations have an equal sign while expressions have none.
The order of operations is the specific order in which mathematicians use to solve equations with multiple steps. PEMDAS is an acronym used to remember the order in which problems are solved. The “P” stands of parenthesis; anything in parenthesis in an equation is solved first. “E” stands for exponents, which are solved second. “M” and “D” stand for multiplication and division which are completed third (depending on which comes first in the equation, multiplication or division). “A” and “S” stand for addition and subtraction, and are completed last (like multiplication and division, they are done depending on which comes first). So, if there was a problem that went “(1+2)/3*2+3”, the first step would be to add 1+2 in the parenthesis since parenthesis comes first which would come out to 3. The 3 would then be divided by 3 and multiplied by 2, ending with 2. That two would then be added to 2 and the grand total would be 5.
Mathematicians give names to numbers in order to group them. This is known as the classification of numbers. The groups in which numbers are placed into are rational numbers, irrational numbers, real numbers, whole numbers, and integers. A rational number is a number that can written as a simple fraction (1.5 is rational because it can be written as ¼). An irrational number is a number that cannot be written as a simple fraction (pi cannot be written as a simple fraction, therefore it has to be irrational). A real number is essentially any number there is. A whole number is any number above zero (that is not a decimal or fraction). An integer is the same as a whole number but it includes negative numbers (same rules still apply however, no decimals or fractions).
I have learned a lot this past month in math. So far, I have learned how to classify numbers, about equations and expressions, and the order of operations. I hope to continue learning about math this year.

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Elena Clemente
10/03/2012 8:04pm

Algebra is a language and learning how to use it is complex and fascinating. The first thing I learned was variables/equations/expressions, which is learning how to write sentences in math. The next thing I learned was Order of operations which is learning the order you have to use to solve the equations. The last thing I learned was classifying numbers which is learning what each number is.

Expressions in Algebra are like sentences in English. With expressions we use a letter to represent a number we don't know, like 5x. This is 5 times an unknown number.

Order of operations is the order we use to solve expressions so we do them correctly. The right order is as follows:
Parentheses ([x+1])
Exponents x to the 5th power
Multiplication (2x2)
Division (9/3)
Addition (1+1)
Subtraction (8-2)

Classifying numbers is learning all the different types of numbers used in math, just like the kind of words in English. The types are as follows:
Whole numbers: 0 and all positive numbers 0,1,2,3...
Natural numbers: all positive numbers 1,2,3...
Integers: any negative and whole number with a value -2, -1, 0, 1, 2...
Rational numbers: any number that can be expressed in a/b format
Irrational numbers: cannot be expressed in a/b format
Real numbers: all rational and irrational numbers.

These three subjects are what I've learned so far in Algebra and all are extremely helpful in my further understanding of math.

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Logan McIntyre
10/04/2012 12:55pm

Algebra blog

 The language of algebra is a language with many rules. To understand it you must understand some things beforehand. The first is Variables, expressions, and equations. The second is the order of operations. The last is classifying numbers.
The first is variables, expressions, and equations. A variable is symbol most commonly represented as a letter that represents one or more numbers. Most of the time a variable is used in two ways. The first is to represent an unknown. For example
5+X= 10
In this case the variable is X is a variable be cause we don't know what it is. This is just one way that a variable is used. The next common use a variable is to show a changing number. This will be used in equations. There is an independent variable which we will represent with Y. Y is a number that is changing by its self it is not effected by another variable. Then there is the dependent variable which we will represent with X. X will change depending on what Y does. So in the equation
2Y=X
If Y is 2 then by X is 4. As you can see the dependent variable(X) is directly effected by independent variable(Y).
The second idea is expressions. An expression is a series of numbers, variables, and mathematical symbols (+-*/. Ext) The one thing an expression can’t have is an equal sign(=). If it does have an equal symbol it is an equation. An equation is the same as an expression the only difference being an equation has an equal sign.
The second idea you should learn is the order of operations. The order of operations is the guidelines on how you solve algebraic expressions/equations. The order of operations can be summed up in an acronym P.E.M.D.A.S.
P-parentheses (4+9)
E-exponents ten to the power of five
M-multiplication 8*8
D-division 8/8
A-addition 8+8
S-subtraction 8-8
Parenthesis are used to separate parts of the equation to do first that way have otherwise been done in a later step.
Example: 4*4(3+2) because of the parenthesis you do 3+2 first instead of the other way around.
Exponents are used to show how many times the number is multiplied by its self.
Example 5*5*5*5*5 this could be shown as 5 to the 5th power. Because 5 is being multiplied by 5, 5 times.
Multiplication/Division ether of these can come before the other you read the equation left to right. The one closest to the left will be first
Example: 4*4+6/6
4*4 will be done first because it is first from left to right.
Addition/Subtraction the same rule applies to this as it does with multiplication and division it is whatever is first.
The last idea is number classification. There is one category and four subcategories.
Category #1-Real Numbers
-This consist of all numbers
Subcategory #1-Rational Numbers
Consists of all numbers that can be represented in fraction form. In case of decimals it must repeat or terminate.
Subcategory #2-Integers
-Consist of all numbers positive and negative. There can’t be fraction of decimal
Subcategory #3-Whole numbers
-Consists of all positive numbers. No fractions of decimals
Subcategory #4-Irrational numbers.
-All decimals that do not repeat or are just odd. Such as
The square root of 7 or pi.

All of these topics variables and expressions, order of operations and classifying numbers is all things you must know to speak the language of algebra.

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Abigail Austin
10/04/2012 2:48pm

Algebra is a language. It is a language spoken by doctors and architects when they're working; without it, all the work would be absolutely wrong. The words are the variables and numbers used to make it 'grammatically' correct. Of course there are different parts of Algebra, which includes the following:
Equation
Expressions
Variables
Order of Operations (PEMDAS)
Classifying Numbers
Lets talk about the first two; Equations and Expressions. Now, there is a HUGE difference, so don't get them mixed up! Well, big difference. Well, not so big difference. Well...small difference, but it is still a kind of difference. The difference between Equations and Expressions is that Expressions do not have Equal Signs. An Expression is used to express a mathematical sentence including one variable or more, numbers, and operation symbols. An Equation does have the Equal sign (hence the name) and express and Expression including the answer.
Variables are letters or symbols representing an unknown value. In an Expression, you'd probably replace the variable with a proper number while in an Equation, you're more likely to have to find the missing number through the answer and operation symbols.
Another thing you need to know is how to do Order of Operations. This includes PEMDAS (Parenthesis, Exponent, Multiplecation, Division, Addition, Subtraction). Despite being show before Division, if they are placed next to each other or Division is behind Parenthesis, Multiplication will always come after, or else the answer would be all screwed up. Also, even though Addition and Subtraction or shown separate, they can be done in any order as long as they are beside one another.
You must be able to Classify Number. No exceptions for those who don't. You must know the difference between Real Numbers and Integers, and you must know the difference between Real and Whole Numbers. And you must must MUST know the difference between Rational and Irrational Numbers. A Whole number is any existing, possible, physical number, such as one or two. It begins from one and and continues up. Then there are Integers, which are all full numbers (-1, 0, 1, ETC.) including negatives and Zero. Rational Numbers are numbers that can be written in simple fractions but not ongoing decimals. Unlike Rational Numbers, Irrational Numbers never end, such as pi or the square root of two, and cannot be written down as a fraction or decimal.
I actually worked harder on this than I thought...anyway, that's really all you need to know for anything Algebra related. Just ask your local doctor, or architect, or engineers. You'll that they all have two jobs; the second: a mathematician.

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Noah Langberg
10/04/2012 3:09pm

Algebra is a unique language, although it may not seem like one at all. Variables are the words and order of operations are the grammar rules of this special language. There are also adjectives, or classifying numbers.

The basics of algebra starts with variables. A variable is a letter or symbol that takes the place of a number in and algebraic expression or equation, which is like a sentence. Equations and expressions can be used in everyday life. Say you had 15 pears you were going to sell, and you sold 3 (obviously you have to work on your business). You want to know how many you have left (most people doing algebra should already know 15 - 3). You could say l is the amount of pears you have left, and the expression would be 15 -3 = l.

You are going to have to marshal those "words" into sentences using grammar rules, or order of operations. Order of operations is a unique way to solve equations. You use PEMDAS.
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction. You solve the smaller problems within the big one using this formula. Say you had 7 + 5 x (3 - 6) / 1(to the second power). P comes first, so you solve 3 - 6, which is -3. Next is exponents, which means one to the second power, which is one. Then multiplication/division (you solve the problem left to right, so if a division problem comes before a multiplication problem, you actually solve that one first. The same applies for addition and subtraction). You do 5 x -3, which is -15. Then you do -15 / 1, which is -15. The last thing you do is 7 + -15, which translates to 7 - 15, or -8. This is the final and only answer.

There are always different words in a sentence, like adjectives or nouns. The classification of numbers are the different words in the algebraic language. Here are the classifications:
Natural number: 1, 2, 3...
Whole number: 0, 1, 2, 3...
Integer: ...-2, -1, 0, 1, 2...
Rational number: -4.8, 9.35
Irrational number: The square root of 7, 3.14159265358979323846264...
Real number: All of the above.

Algebra is a unique language that only a few people can speak. It helps a lot with life, not just in math class though. There are a lot of real world situations that don't need algebra, but could be used in the scenario.

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Luis Zapata
10/04/2012 3:33pm

Algebra is a language and to learn it well you must learn about these
different topics. Expressions, equations, and variables. You need to know the order of operation, PEMDAS. You also need to classify your numbers.

The language of algebra starts with variables. Variables are numbers represented by a letter.Expression are mathematical phrases that include variables, numbers,and operation symbols. Equation are the same as expressions only if it had an equal sign. Variables are in both expressions and equations.

Order of operations are a key to solving an equation because it gives you a step by step way of solving and getting the correct answer to an equation. PEMDAS is the order in which you solve the equation you are given P is Parenthesis,E is for exponents,M is for multiplication,D is for division,A is for addition,and S is for subtraction. With the steps given to you , you will always get the correct answer. PEMDAS to me is basically a cheat sheet that is legal.

Classifying are also important, Well the biggest reason is so that we can talk about general rules for numbers that apply to some categories such as Whole numbers,Rational numbers,Integers,Irrational numbers and natural numbers. Natural numbers are any number that starts from 1 that is not zero or negative. Whole numbers are any number that is not a decimal or a fraction. Integers are any number that includes negatives and zero. Rational numbers are numbers that can be written as decimals and fractions. Irrational numbers are numbers that cannot be written as a decimal or a fraction. Irrational numbers are the most confusing and can be very tricky

Math is all around us. It is a universal language. Engineers, pharmacist, doctors etc. are all mathematicians. Without mathematicians computers phones wouldn't be invented . All this math we use is also used in the creation of certain programs,calculators. Knowing all this math made our civilization improve logically and architecturally. The simple steps of PEMDAS help students in answering equations , Classifying numbers are important for talking about general rules for numbers.All these topics are used for the language of algebra. Without math our civilization would have never advanced to the creation of the phones,computers,and calculators

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Timmy Chan
10/04/2012 4:41pm

Algebra is a language that uses order of operations to communicate algebraically. To communicate algebraically you need to use variables, expressions, equations, and being able to classify numbers.

Variables are symbols usually for more than one numbers. An expression is a math phrase that includes numbers. An equation consist of a mathematical sentence that has a equal sign. Mathematics needs to be precise because there can be only be one number. Algebra is a language because instead of talking you use numbers to communicate.

Order of operations consists of PEMDAS. P stands for parenthesis, E stands for exponent, M stands for multiplication, D is for division, A id for addition, and S is for subtraction. You use these rules for solving an equation or expression. These rules don't apply when multiplication and division because in this case, you do the equation or expression from left to right. The same applies with multiplication and subtraction.

Whole numbers and negative numbers are rational numbers. Irrational numbers are numbers that cannot be counted such as pie. Whole numbers are 0 and greater. Negative numbers are he opposite of the whole numbers.

A few things you may learn while taking Algebra 1 are variables, equations, expressions, order of operations, and being able to classify numbers.

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Kaya Youmans
10/04/2012 6:07pm

Math is not everyone's strong suite but once you dig into it and get inside of each nook and cranie it becomes as simple as 1,2,3. I got the chance to study variables, expressions, equations, order of operations, and how to classify numbers. I know you are probably how can you study all of these topics so closely in such a short amount of time well I am here to show you just how I did it.

Variables, expressions, and equations was a topic that I personally had no problem with this was because my previous study with these topics prepared me to do some exercises and then take a diagnostic on it. Variables, expressions, and equations was a topic that was based on defining symbols in equations in order to get what the x value was. This topic also helped to solve algebraic expressions. An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. I also studied variables. Variables are symbols which are usually represented by a letter that represents 1 or more numbers. I even studies equations. Equations are mathematical sentences that uses an equal sign. The topic I also studied was open sentences. Open sentences are equations that contain 1 or more variables. Some examples for an equation is 4x+128=32.

Order of operations was another topic that I easily understood because it was very straight forward. Order of operations is a acronym called PEMDAS (Parenthesis, Exponents, Multiplication, Division, Add, and Subtract) this is the order in which you are supposed to do an equation. In order to do operations you must know how to do PEMDAS of course and a couple of other things. You must know how to simplify. Simplifying is when you replace a numerical expression with its simplest name. You must also know the definition of exponent. An exponent tells you how many times a number is used as a factor. The base of an exponent is the number that gets factored. Another big part of order of operations is evaluation, evaluations is when you substitute a given number for each variable. Order of operations is a very easy topic once you understand and can comprehend all of the words used in the order of operations.

Classifying numbers was a topic that I needed a little bit of extra help with because it was harder than the other topics in my opinion. Classifying numbers was when you places certain types of numbers in groups by Real, Rational, Irrational, Integer, and Whole numbers. These are the categories that numbers can be sorted into. Integers are whole numbers that are not fractions. Rational numbers are all numbers with an end to it, for example the square root of 5 is an ongoing number this is a irrational number. A real number is a number either negative or positive a whole number can only be a positive number. I have just the hang of how to classify numbers I hope to get stronger as the school year progresses.

All and all variables, expressions, equations, order of operations, and classifying numbers is no easy topic, but once you figure out what everything is as a part once it comes together as a whole it is very simple!

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Shirley Lee
10/04/2012 6:39pm

For the past few weeks, I have so far learned about algebra. Algebra includes expressions, equations, variables, order of operations, and classifying numbers.

Equation is a mathematical sentence that uses an equal sign. For example, x+5=3x-7 is an equation. In that equation, x is the variable. Variables are a symbol that represents on ore more numbers. Throughout this topic, i learned that numbers are like words/sentences that could be expressed in many ways.

The next sub-topic is order of operations. Order of operations is a way to perform any operation(s) inside grouping symbols. Its an operation where you need to follow the steps of P.E.M.D.A.S. P.E.M.D.A.S. is p=parenthesis, e=exponent, m= multiplication, d=division, a-addition, and s=subtractions. This sub-topic is probably the easiest for me because i learned about this so many times.

Classifying numbers is the sub-topic. There are many different kinds of numbers out there. There are rational, irrational, real, whole, negative, positive and many other different kinds of numbers. Throughout this subject, i learned that there are names for each number and people can give different names to each other.

The topic algebra which contains expressions, equations, variables, order of operations, and classifying numbers is pretty easy to learn because they are basically almost all a review. Sometimes, some of the problems could get hard, but solving it step by step would help.

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francisco leon
10/04/2012 8:38pm

We have learned alot in math. But some of the important topic i will be sticking to are expresions and variables and equations we will be talking about order of operations and. Last but no least. Classifing numbers
An expression can includede any variable. Sign and any symblol and that they both have an equal sign. And if u flip. The whole equation. The equation has to equal. To the same as the first equation. Order of operations is like a. A way that shows u to the answer. Because. In the use of pemdas the p is perenthisis and the e is exponents. The m is multipication the d is division the a is addition and the s is subtration. And if u dont fallow this you will not get the aswer right and you will get it wrong. Clasifying numbers. Is a gruop that. Some type of numbers can go. There a rational and irational. Integers and whole nubers and natural numbers. . A rational nuber is a nuber that can be witten in a /b and. Irational can not be put in a/b form. A. Are intregers. One number that can be used in. Many groups is 4 because it is a. Whole nuber a natrual number and a integer. And a rational nuber. Some numer have loof groups and some have only one. In. Cuncusion some of the topics u need. Nooo u need!!!!!! To know. To. Do algebra. Are expressions variables and equation u also have ro know order of operations and classifying nubers to pass math and get algebra if u dont do this u. Will just be cunfused in algebra and not even know a single way to solve probloms these ar the thing thast will pass u the grade

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Andrea Garcia
10/04/2012 8:53pm

Although we may not know it, we are surrounded by math. In fact, many of the things we use (and take for granted) are products of seemingly endless years of research, testing and formulation. A very important stem of math is algebra. While there is much to know concerning algebra, to understand it, we must start at the basics, just like we would with a language. Algebra's most important basics are: Expressions (accompanied by equations and variables), Order of Operations, and the classification of numbers. Algebra is a language, and in order to comprehend and know it, we must first know the basics I have mentioned above.

Expressions are very common in algebra. Though they may seem easy at first, they are actually complex and require concentration, and awareness of order. Many math students are sometimes confused by these seemingly harmless combinations of numbers and letters, due to the fact that they are very similar to a close algebra basic: equations. They are often confused for eachother due to their likeness. One reason might be, the very alike way that these two forms of problems are written, both using numbers, variables: symbols, usually letters that represent one or more numbers; and operation symbols. In reality, an equation is a mathematical sentence that uses an equal sign.
Equation:
3+7=?
Expression:
3(x+7)
Expressions, also much like equations, can be written using verbal phrases. An example of this would be: Three times the sum of a number and seven. These verbal phrases can be translated, and often times, you will be asked to define a variable.
Verbal Phrase: 5 times the product of a number and 6
Defining a variable: x= a number (the variable can be anything you want, but remember to define it)
Translation: 5(6x)
Algebraic expressions can be tricky because, also like equations, they only have ONE correct answer. The only way to solve them may be through the Order of Operations, better known as PEMDAS.
Order of Operations is a process used to solve algebraic expressions. The order is as follows:
P-Parentheses
E-Exponents
M-Multiplication
D-Division
A-Addition
S-Subtraction.
It may seem overwhelming, but the order is actually very easy. First, you would have to solve anything in parentheses, next exponents, multiplication, division, etc. If the order is correctly followed, you should get the right answer.

6[3+3(x-y)] if X=5 and Y= 3- 1. First solve what's in the brackets ([ ]), by following the order, meaning I would solve x-y.
6[3+3x2] 2. Multiply 3 by 2.
6[3+6] 3. Since we are still in brackets, we will add 3+6.
6x9 4. Multiply
The answer is: 54
Despite how they are listed, Multiplication and Division, as well as Addition and Subtraction are on the same level, so if you are presented with a division problem before multiplication, remember that you have to solve from left to right.
The Order of operations is important for solving algebraic expressions that often represent real-world situations. The question is: how do we know if certain numbers are appropriate for these situations? That is what the classification of numbers is for.

Classifying numbers is important because as I mentioned above, it helps us determine which sets of numbers are appropriate for real-world situations.
The groups that numbers can be classified into are: natural numbers, whole numbers, integers, rational, irrational, and real numbers. Natural numbers are the counting numbers; Whole numbers are the non-negative integers, while integers are are whole numbers and their opposites. Rational numbers are real numbers that can be written as a ratio of two integers; rational numbers in decimal form are terminating or repeating, while irrational numbers are the complete opposite (they can not be written as a ratio of two integers; in decimals they are non-terminating and non-repeating). Real numbers are either rational or irrational.
Most of these sets are written on number lines, where terms like opposites and absolute value come in. Opposites are two numbers that are the same distance from zero on a number line, but lie in opposite directions.
Absolute value is a number's distance from 0 on a number line. Absolute value is important since it can also be used in algebraic expressions.

There's much still left to learn in algebra, but these three topics are some of the most important things to know, as they are the basics and are necessary to know if I want to continue learning as a student of algebra, a form of math, but also a language.



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Mandy Lau
09/29/2012 8:25pm

Algebra is a language to understand in math. Expressions & variables, order of operation, and classifying numbers is the start to understanding algebra.
The first thing i learned when I came to algebra one is expressions and variables. Algebra is a language and in order to become well you must learn abut different topics and classifications. Expressions and variables, to me it means numbers put into an equation to find the simplest form. Variables are factors that are vary to change or I call them plug in numbers. Why? Because I need to find a number for that letter to solve the equation. A variable can be represented in many ways that means it can be plugged in.
The second thing I learned was order of operations. This always goes back to my careless mistakes but since I used the PEMDAS rule it doesn’t get me as much careless as I do. Now I double check my work, so I don’t get any mistakes. Simplifying one by one is the simplest to a defined answer.
Classifying numbers was the hardest thing for me out of the two things that I learned. Irrational and rational numbers was confusing until Ms.D told me about shoe sizes to tell the difference. Integers are easy to tell because they are always negative.
To be honest this is a review for me and its a good because it gets me back on track ready to learn more. Expressions and variables, order of operation, and classifying numbers are the start of algebra. I hope to learn more!

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Jasmina Mujevic
09/30/2012 12:30pm

There are three sub-topics in the huge topic of algebra. Those sub topics are expressions and variables, order of operations, and classifying numbers.

The first topic we went over is expressions and variables. To understand this subtopic you need to know a few definitions. You need to know what a variable is , the definition of a variable is that it is a symbol (letter) that represents one or more numbers. Another important term is knowing what an open sentence is. An open sentence is an equation that contains one or more variables. Also you need to know the difference between an equation and expression. A equation is a mathematical sentence that uses an equal sign. An algebraic expression is a math phrase that includes variables operations and symbols.

The second topic is order of operations. We need order of operations so it could help us simplify harder equations that include many operations. To understand you need to know what simplify means, simplify means to replace a numerical expression with its simplest form. An exponent is how many times a number by the base, the base is the factor. A power is 2 parts, the base and the exponent. In order of operations you get a long equation with many operations, and to solve it you use PEMDAS.

The third topic is classifying numbers. To understand this subtopic you need to know the four definitions for the classification of numbers. Classifying numbers are important because there are general rules for those numbers, and those groups of numbers apply to some groups but not all. The four definitions to classify numbers are natural numbers - which are numbers like 1,2,3. Irrational number - which is a number that can not be expressed in a form of a/b where a/b are integers. Rational numbers - are numbers that can be written in the form of a/b, and real numbers are rational/irrational numbers that come from a set of real numbers.

Overall, to fully understand the language of algebra you have to fully understand the three subtopics which are expressions and variables, order of operations, and classifying numbers.

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Nilou Mahboubian
10/01/2012 4:54pm

Algebra is a language and in order to speak it well, you must follow the rules. So far in Algebra, I've learned all about Expressions, Equations, Variables, Order of Operations, Classifying Numbers, and more. In this essay I will be explaining all of these topics.

An expression is a mathematical phrase that can include numbers, variables, and operation symbols. An equation is a mathematical sentence that uses and equal sign; if an equation is true, than the two expressions on either side of the equal sign represent the same value. The difference between an expression and an equation is that an equation has an equals sign in it. A variable is a symbol, usual a letter, that represents one or more numbers. One example of an expression is 3n+ 2. The "n" is the variable. One example of an equation is 3n+2=17. The "n" is the variable in the equation. If you solve the equation, n=5

The order of operations is a series of rules that is used to solve an equation or expression with more than one operation. An acronym to easily remember the rules is: PEM/DA/S. This stands for 1.Parenthesis
2.Exponents
3.Multiplication/Division (whichever comes first left to right)
4.Addition/Subtraction (whichever comes first left to right)
It is important to use PEM/DA/S because if you don't you could get a totally different answer, which is wrong. An example of that is:
6+3x5 Without using order of operations and just solving it left to right, the answer is 45. But, if you use order of operations, you will see that 21 is the correct answer.

Classifying numbers is important because it is a way to organize different types of numbers. One category is whole numbers. Whole numbers are any positive, non-fraction numbers, plus zero 0 or 6. Another category is integers. Integers are all whole numbers, plus negative numbers like 12 or -5. One more category is rational numbers. A rational number is any number that can be put into fraction form like 4 or .25. One last category is irrational numbers. An irrational number is a fraction that doesn't have an end like pi or square root of 2.

This shows that Algebra is just like a language. Variables are words, order of operations are grammar rules, and classifying numbers are adjectives. Algebra is a lot easier to learn when you compare it to things you already know well.

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Sahib Uddin
10/01/2012 6:47pm

Mathematics is a one-way-to-solve system that cannot be done any other way, except the proper way. As a student progresses in schoolwork and moves on to different and more advanced grades of school, that person will have to memorize a lot of more proper procedures in math. Going into high school, in the ninth grade, would sometimes mean that the student will start to learn algebra, and be put in an algebra 1 class. In at least one month, that person could learn a lot of things, or be retaught things, and have the potential to write at least a five paragraph essay. I have learned at least 3 things my algebra 1 class that are very important and useful to learn in an algebra 1 class.
One topic my class and I went over was expressions and equations. These are two very similar number sentences with a very slight difference. The difference of the two number sentences are that equations have an equal sign (hence the first part of the name) and expressions do not have an equal sign visible in the number sentence. There is also the possibility of turning both these number sentences into verbal statements. An example of this with an equation would be eight plus x equals t. Mathematically, it would represent 8+x=t. An expression would be written as 8 plus x. There is no need or even want for an equal sign in an expression, so it would be mathematically written as 8+x.
Another topic that my teacher went over with me and my class is order of operations and P.E.M.D.A.S. Order of operations are mainly used for equations, P.E.M.D.A.S. is mainly used for expressions. Both of these rules mean the same thing, but it is logical to specify what you will be using it for. The letters in P.E.M.D.A.S., have different meanings. P. stands for parentheses, E. stands for exponent, M. and D. stand for multiplication or division, and A. and S. stand for addition and subtraction. To work with P.E.M.D.A.S. or order of operations in a number sentence, you have to work with the rules of P.E.M.D.A.S. from left to right, following each letter of P.E.M.D.A.S. from left to right. There is also the chance of having variables in an expression or equation. Variables are an unknown quantity that is represented by a letter. With unsolved variables, it will be impossible to give yourself, a single, independent number answer. But, there is no need to simplify an equation to a single raw number, there is an exception, if there remains an impossible to solve variable.
We have also learned the different classifications of numbers. The first classification of numbers would be natural numbers. These numbers are all the numbers past the number zero, and cannot be either a decimal or fraction. There are also whole numbers which, in short, are every single natural number, but include the number zero. Then there are integers, which are every single whole number, but include negative numbers. Integers, like whole and real numbers cannot contain fractions and decimals. Rational numbers are all numbers, except decimals that have an uncommon sequence of numbers like pi, rational numbers must have an end with the number 0. Rational numbers also cannot be the exact number of zero, like real numbers. Irrational are the opposite of rational numbers. Irrational numbers include the numbers of pi and uncommon sequence of numbers in a decimal, but like real and rational numbers, it cannot be zero, and cannot also be a whole number. Real numbers are both irrational and rational numbers, so they are all numbers, except for the number zero.
Mathematical equations and expressions can only be solved in one way. The only difference between equations and expressions are the use of equal signs for equations only. P.E.M.D.A.S. is mainly used for expressions, while order of operations are used for equations. Each number within an equation or an expression has a different classification in the number line. There is no end to learning new procedures of doing math, so people remain a student their whole life if they wish to. Mathematics are a single procedure to solve system that will never change its ways.

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Jia Min Liu
10/01/2012 7:04pm

What I learn about algebra is that, although it is just all numbers; variables; expressions; equations; and order of operations, it can also happen in real life as well. Such as an equation, the equation “2x+28=38” can represent something. Let’s say that you were visiting a market. The “2x” represents a coupon (the 2 is the number of coupons and the “x” is the amount of money of the coupon). The “+28” is the amount of money of the item you are getting. You will learn all the subtopics of algebra, so you can understand what they mean, for they can help you in the real world.

Variables are a symbol, but it is normally a letter that means one more numbers. An example is “Z, X, A, B, etc ”. Expressions are a mathematical phrase that has numbers, variables, but no equal sign. An example is “6+n”, it means “Six plus n”. Equations are a mathematical phrase that has an equal sign. An example is “9+2n=20”, it means “Nine plus two times n equals twenty”. The difference between an equation and expression is that an equation has an equal sign and an expression doesn’t.

Order of operation can be with an equation with parenthesis, exponents, multiplication, division, addition, and subtraction. The acronym PEMDAS stands for parenthesis, exponents, multiplication, division, addition, and subtraction. For example, the equation “6÷2x5” is solved by looking from your left to your right since it has the operations division and multiplication. Since you can’t just solve which ever part of the equation you like, if you don’t know which part to solve first. First you do 6 divided by 2, which is 3 and 3 time 5 is 15. Another example is “4-2+3” and you also look from your left to your right. Since you can’t just solve which ever part of the equation you like if you don’t know which part to solve first. First, you do 4 minus 2 which is 2, 2 plus 3 is 5. The reason you look from your left to your right only for multiplication/division and addition/subtraction is so that it is solved correctly.

Classifying numbers is when you define natural, whole, integer, rational, irrational, real numbers, counterexample, inequality, and opposites. A natural number is counting numbers, for example “1, 2, 3, 4, 5 and etc”. A whole number is nonnegative integers, for example “1, 2, 3, 4, 5, and etc”. An integer is whole numbers and their opposites, for example “1, -1, 2, -2, and etc”. A irrational number is numbers with a decimal form that terminates and repeats, for example “3.1415926..., 9 /7, √2 and etc”. An rational number is a nonterminating and nonrepeating number, for example 5.35747474, √4, 4/2 and etc”. A real number is a number that is rational or irrational, for example “8.3739563…, 4/3, 2.323232, 9/3, and etc”. A counterexample is an example that makes a statement false, for example” The statement: all even numbers time odd numbers is always an odd number. The real answer was all even numbers time odd numbers is always an even number”. An inequality is a mathematical sentence that compares the value of expressions using an inequality sign, for example “7≤16, 32≥27, and etc”. An opposite is a number that is the distance from zero as the other number, for example “|-8|=8, |3|=3, and etc”.

Now that you have learned algebra, you can use them in the real world with your new knowledge. Again, algebra subtopics are “variables, expressions, equations, order of operations, and classifying numbers”. Let say one day you were hungry and you got two five dollars and you were with your friend. You want to split the two five dollars so your friend can get something to eat. However, only your friend spent it and you didn’t. As you keep on walking you meet another friend that kindly gives you back the five dollars that you gave them. Now you have $10 dollars to spend on something. This can be translated as “10-5+5” and the answer would be 10. This is why math comes in handy if you learn them good enough.

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Dorian Hoxha
10/01/2012 9:13pm

What is algebra? Algebra is a part of math that makes symbol like letters of the alphabet, stand for numbers.Instead of calling something a number it is used as a variable.A variable is a symbol for a number we don't know yet.It is usually a letter like x or y.This method of solving problems is called Algebra.
An expression is a mathematical statement that can use numbers, variables, or a combination of the two.sometimes, there are operations but there is never an equal sign.an equation says that two things are the same, using a equal sign.An example of an expression is a + b – c. An example of an Equation is 5+5=10.
A verbal expression is a math expression written in words.so if your homework says 5+x then the verbal expression would be "five more than a number x". These are easy to translate, you have to work your way backwards.So if your homework says "n less than 5" you have to do 5 - n,
The order of operations is the rules of which calculation comes first in an expression.A tool used to help understand the order of operations is "PEMDAS". "PEMDAS" stands for parenthesis,exponents,multiplication,division,addition,subtraction. When you are doing a order of operations problem, you need to do it based on that order.For example"4+8/2" You divide 8 and 2 first because division comes before addition. then you get 4, you add both and get 8.Sometimes you need to follow the "PEMDAS" rule differently. When its multiplication and division you have to do it from left to right, so now the tool is "P,E,MD,AS".If multiplication comes first you have to do it before division.
Classifying topics is when you can differentiate each real number.
An irrational number is a number that can be written as a decimal, but not as a fraction.An rational number is a number that can be written as a fraction where the numerator and denominator are both whole numbers.Wholes Numbers are numbers without fractions;integers.Integers are numbers that are not fractions;whole numbers,that can also be negative.Irrational numbers include: π, √3. Rational numbers include:3/4,0.125. Rational numbers end and can also be fractions but irrational numbers dont end and cant be fractions.Integers include:-1,-2,1,2.Whole numbers include:1,2,3,4. Whole numbers cant be negative and integers can but both can have 0 as classified.

There are many types of algebra but the order of operations,expressions and variables and equations, and the real number system are key things for mathematicians to learn and understand. The basic rules and operations of algebra are one of the main branches of mathematics



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Dana Nonas
10/02/2012 4:12am

Algebra is a language, and in order to speak it well, you need to use the rules. Things we have learned have been, expressions/equations, order of operations and classifying numbers.

First, the definition of an equation is a mathematical sentence that uses an equal sign, and an expression is the same but without an equal sign, thats the difference between the two. Also, a variable is a symbol using a letter, that represents one or more numbers. An example of an expression is: 5 + 6 – (3 + 2) ... an equation without an equal sign. And an equation: (5+6) - 5 = 6.

Order of an operations, a very important strategy to keep in mind when you are doing equations that you do it in the right order or you could end up getting the wrong answer. PEMDAS; standing for Parenthesis, Exponents, Multiply, Divide, Add, Subtract. For example: 4+ (8/2) + 6x2 .. First you would do what is in parethesis, which is 8/2= 4 so now the equation is 4+4+6x4 then next you would do multiply so 6x4 which is 24 and then the addition is 8, so 24+8= 32, and that is the correct answer. If I did the addition first, and the multiplication last I probably wouldn't have gotten the same answer because I'm not using the order of operations right.

Classifying numbers. It's important to know the 4 definitions of this topic because they are general definitions for all numbers. The first one is natural numbers which is 1,2,3.. and so on. Whole numbers are from 0, to 1,2,3.. and so on. Irrational numbers cannot be expressed in the form a/b where and b are integers. That is different from rational numbers because it is any number that can be made from one integer by another.

So basically in order to "speak the language right" you need to understand these three subtopics; expressions/ equations and variables, order of operation (PEMDAS) and classifying numbers.

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Madison Jean Philippe
10/02/2012 3:30pm

Algebra is a language and in order to speak it well you must follow the rules. You must know the distinct difference between an expression and an equation, what P.E.M.D.A.S stands for and how to solve 6÷2×5 and 4-2+3, and All of the number classification and what’s the difference between whole, integers, rational and irrational numbers. If you know how to read and write algebra will be very easy but you just will have to follow the rules. Mathematicians have to be precise and organized that will lead to success in algebra.

There is a distinct difference between an equation and an expression. For example an equation has an equal sign and an expression does not have an equal sign. Another difference is you simplify an expression but the expression can have multiple variables when in simplest form whereas an equation only has one answer. An expression shows a math relationship and an equation equates two expressions.

P.E.M.D.A.S stands for parenthesis, exponents, multiplication, division, addition and subtraction. In order to successfully solve an equation or expression you must eliminate each part of pemdas in either of those in order. When it comes down to multiplication and division you do which ever operation comes first from left to right in the expression or equation and the same thing for addition and subtraction. So in order to solve 6÷2×5 you must divide 6 and 2 because division comes first in pemdas then multiply the quotient of 6 and 2 by 5 and you get 15. So in order to solve 4-2+3 you must subtract 2 from 4 and increase the difference of 4 and 2 by 3 and you get 5.

The number classifications are whole, integers, rational, and irrational numbers. A whole number can only be a whole number and never a fraction, decimal or negative number. An integer is a whole number or a negative number. A rational number is a number that can be written as a ratio of two integers and a terminating or repeating decimal. Irrational numbers is a number that cannot be written as a ratio of two integers and are non-terminating and non-repeating decimals.

Therefore, Algebra is a language and in order to speak it well you must follow the rules. You must know the distinct difference between an expression and an equation, what P.E.M.D.A.S stands for and how to solve 6÷2×5 and 4-2+3, and All of the number classification and what’s the difference between whole, integers, rational and irrational numbers. Algebra is very easy if you are a precise and organized mathematician. You must follow rules and learn why those rules apply to certain situations and how to properly execute problems.

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jade
10/02/2012 3:52pm

Variables is a symbole ugually a letter that represent one or more numbers for example :
n+7 n is a variable
the diffrence between equation a sentence that use the equal sign and expression can include letters and dosn't need a equal sign

division multiplicationin between prenthasis they must be answred first before other equation order of operation tells us what order must be used when evaluating a nummerical expression PEMDAS meen prentesis equations multiplication division addition and substraction example:
(2x3):4+3

the nerest number to 0 is the smallest and the farthest from 0 in the 2 ways <__(-) 0 (+)___> classifying numbers meen to put them in a way that makes sense ex:
-4,-3,-2,-1,0,1,2,3,4.....

now if you understood the 3 subtopic you will easilly understand the algebric language.

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Chloe Smith
10/02/2012 4:07pm

In case you haven't noticed we use math everyday. We use it on the train, buying lunch etc ... Some important skills in math that we use would be expressions/equations, order of operations and we classify numbers. When we do these things we deepen our mindset on how we use math everyday.

We use expressions and equations a lot. The difference between expressions and equations is very simple. Equations have equal signs and expressions don't. There is also one thing in common though, variables. A variable is a symbol usually a letter that represents one or more numbers. Variables can be anything such as numbers and examples. For example, the equation two less that seven times a number can be expressed as the variable n to represent the number.

To help solve complex problems we always use Order of Operations. To use Order of Operations the easy way would be P.E.M/D.A/S. this stands for (Parenthesis, Exponents, Multiplication/Division, Addition/Subtraction). For example, to solve 6/2*5 we use P.E.M/D.A/S to get an answer of 15.

Lastly we classify numbers by grouping them into three parts (whole, rational and irrational numbers). A whole number consists of positive numbers. An irrational number consists of numbers that go to infinity and higher such as 3.14159... and also the square root of 7. A rational number includes negatives and integers such as -1,-2,-3 etc...

As you can see we use math everyday. Whether if we are walking to school or buying lunch. We are all Mathematicians in our own way. We use expressions/equations, order of operations and we classify numbers. This can deepen our understanding of math skills and really help us in the long run.

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Gabriel Esclozas
10/02/2012 5:08pm

We all Started algebra in First grade(I think so); it was the big evolution of being at school, because we could learn something. We started to learn numbers, how to add them, how to multiply and how to use algebra in Sentences (the boring part). Algebra can be used in the entire world, it will always be numbers and never change. Without knowing, we all use algebra everyday: When we count the hours that we slept, when we bought food or when you’re in math class ;-).

From what we learned, Algebra comport three topic :
-Expression/Equation/variables
-Order of Operation
-Classifying numbers

Expression and Equation can both be write into Sentences. The only difference between an Expression and an Equation is that an Equation had an equal sign when an Expression has none. On an Equation, both sides should be equal or it means that the Equation is wrong. Expression and Equation had number, variables and symbols (-, +, ×, ÷). A Variable is a letter that we use to describe a number that we need to find with an Equation , and just change it with the number that it’s equals in an Expression.

Order of Operation is the rule that tells us by what we need to start solving in an Expression and Equation. This rule is describing in one word: PEDMAS. PEMDAS is the entire rule in the order of operation, it describe Parentheses, Exponents, Multiplication, Division, Addition and Subtraction. This means that in an Expression and an Equation, we need to solve first the Parentheses then the Exponents. After the Parentheses and Exponents solve, you need to do the Multiplication and Division. But Multiplication and Division are equals this means that in an operation and division, you won’t start by multiplying or dividing, but from left to right. It will be the same for Addition and Subtraction, you will just start from left to right. This paragraph means that you can write PEMDAS like This:
PEM=DA=S. To have a correct answer, the technic PEMDAS MUST be used.

Classifying numbers can be a plus but you need to know the basics. Here’s the list:
-Natural Numbers:
It includes all numbers that are not negative or 0, it starts by 1.
-Whole Numbers:
It includes all numbers that are not negative, it starts by 0.
-Integers:
It’s all numbers, even 0 and Negative number.
-Rational Numbers:
It’s all numbers that can be written as a fraction. It can be either terminating: 4.8, or repeating: 9.999999… . A Rational number can’t be divide by 0.
-Irrational Numbers:
It’s a number that cannot be express as a fraction (The total opposite of Rational numbers). An Irrational Number can’t be repeated. Example: 0.101001000 or √10
-Real Number:
The mixed of all Irrational Numbers and Rational Numbers form Real Numbers. (This means that real numbers are all numbers)
-Opposites Numbers:
Opposites number are numbers that had the same distance from O but lie in opposites direction.
-Absolute Value:
An absolute value is shown as |a| it takes a negative number and put it into positive. It works only in one way, Negative > Positive.

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Grace Barstow-Christopher
10/02/2012 6:17pm

Algebra is like a language, without learning the rules you can not speak it. There are three main rules we have learned about so far, they are order of operations, expressions vs. equations, and classifying numbers.
Order of operations, or PEMDAS, is the order in which you do things in a problem.
P-parenthesis
E-exponenets
M/D-multiplication and division (whichever comes first)
A/S-addition and subtraction (whichever comes first)
Say you have 37+2x3, because multiplication comes first in PEMDAS you do 2x3 first. But if the equation (see next paragraph) (37+2)x3 then you do 37+2 first because it is in perenthesis, which comes before multiplication in PEMDAS.
In algebra there are equations and expressions. You can think of these as full sentences and incomplete sentences. An equation would look something like this, 3+4=7, because it has the equal signe it is an equation and a "full sentence." An expression would look like this,3+4, there are no equal signes in expressions, there for they are "incomplete sentences."
And finally classifying numbers, all numbers fall under the category real numbers. But there are groups within the main group that break the numbers up. We have rational numbers, these are numbers like 1/2 that can be expressed as a fraction. There are also irrational numbers, these are numbers that can not be expressed with a fraction (.34728357925...). Rational numbers contain the category integers, integers are numbers like -2,-1,0,1,2, they do not include decimals. Even in the category integers there is another smaller category, whole numbers, these are non-decimal numbers from 0 up.
Algebra is a language and in order to understand it you must understand the basic rules, order of operations, equations vs. expressions, and classifying numbers.

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Angella Romero
10/02/2012 6:30pm

Everyone has their own definition of what Algebra is. For me, Algebra, is a language that everyone can speak. Part of this language includes variables and expression. They make up a rule called Order of Operation. Order of Operation is a big part of the language of Algebra. Without it, Algebra wouldn't exist. It wouldn't exist because Order of Operation is the base of it, keeping order. Without order, there can't be classification. Classifying numbers groups together everything we need to understand the language of Algebra.
Expressions and variables are part of Algebra. A variable is a symbol, that will represent one or more numbers. For example, when the expression t minus 10 is written, t is a variable because it is representing a number in the expression. Variables and expressions go together because a variable usually goes along side an expression. An expression is a mathematical phrase that combines numbers or variables using an operation symbol. An expression could be 2x+3, x being the variable. They, variable and expressions, play a major role on what Algebra consists of.
Without Order of Operation, no one could or would be able to understand Algebra. We need Order of Operation to keep everything in order. Basically what it is, is PEMDAS. What PEMDAS is and what it does, is when you have to simplify an algebraic expression you do what PEMDAS says. Which is parenthesis (P) first, exponents (E) second, multiplication and division in the order of which it is at (MD), and finally addition and subtraction in the order that it is in (AD). If no one followed this rule no one would be able to figure out anything in Algebra. Algebra consists of order, without Order of Operation everything would be chaos. Order of Operation gives off its own definition, it is the order of which an operation should be solved.
The final step to understand the language of Algebra, is to know what and why we need to know about classifying numbers. Classifying numbers is basically knowing where numbers stand. For example, if the number is rational, irrational, an integer, real, whole, etc. Natural numbers being 1,2,3....whole numbers are 0,1,2,3... integers are -1,0,1,2,3.... and so on. Classifying numbers tells you what those numbers are, it is like their own definition. Algebra is all about classification, if you don't classify no one will understand you.
In conclusion, Algebra is a language and in order for you to fully understand it and have people understand you; you need to know every aspect of it. Variables, expressions, Order of Operation, classifying numbers, and many other things make up Algebra. If there were no variables then expressions wouldn't exist, without Order of Operation nothing would ever be solved. And, without knowing how to classify numbers, you are basically saying you know nothing about Algebra. Anyone can learn how to properly use Algebra, as long as you know its different topics.

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Lisa Riegert
10/02/2012 8:22pm

Algebra is like a language and in order to understand it you must understand the subtopics that make up algebra which are expressions/variables/equations, order of operations and classifying numbers.

The first topic to understanding algebra is expressions/variables/equations there is a difference between expressions and equations, expressions contain no equal sign and an equation does contain and equal sign. An algebraic expression is a mathematical phrase that has numbers, operations signs and variables, variables are a symbol usually a letter that represents one or more numbers. An example of an algebraic expression would be:
3x + 5.

The second topic to understanding algebra is the order of operations, when using the order of operations you have to use PEMDAS, which stands for P being Parenthesis, E being Exponents, and M/D being Multiplication and Division and lastly A/S being Addition and Subtraction. In order of operations you are basically simplifying the equation which means to have a numeral expression and to put it into its simplest form. When solving an equation like (5+2)x3^2+1x8 You first need to solve whatever is in the parenthesis which is (7)x3^2+1x8 and then you have to solve the exponents since it’s next in PEMDAS. Which is going to be 7x9+1x8, next in PEMDAS it’s M/D and you’re going to have to do which ever comes first starting on the left, which is going to be 63+8. Lastly your going to add up all the leftover numbers which is going to be 71 your final answer.

The third topic of understanding algebra is classifying numbers, when classifying numbers you have to determine if a number is rational or irrational and the difference between the two, is rational numbers you can put into the form or a/b and their fractions and decimals. While irrational numbers are like pie that continues going on. Also whole numbers are 0,1,2,3,4,5 and negatives which are -1,-2,-3,-4,-5. Another could also be absolute value which is like |15| being 15 and |-15| being 15 also. Real numbers are also rational and irrational.

Algebra is very much like a language because to understand it there are very important subtopics like expressions/equations/variables, order of operations and classifying numbers that you need to learn to fully understand what algebra is.


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Anderson Alleyne
10/02/2012 8:50pm

Algebra is a language and they are a few things you must know. Such as variables,order of operations, and classifying numbers. It is one of key components to learning algebra. Like ingredients to recipe.
Variables is a symbol usually a letter, that represents one or more number. For example 5x+2=12. The variable is X. Another example is 9 less than a number. The expression would be n-9. N stands for number which is the variable.
Order of operations is important because it helps you undertand the promblem. Order of operations is PEMDAS which stands for parentheis,exponents,multiplicatin,division,addition,and subtraction. Multiplication and division is equal and you go from left to right. Also for addition and subtraction.
It is necessary to classify numbers to know which category it is in. Such as whole numbers numbers and irrational numbers. They are two different things. Whole such are numbers such as 0,1,2,3,4. Irrational numbers are numbers that never have an ending. Such as the square root of 5.
Algebra is language and their are a few things you must know. Variables,order of operations, and classifying numbers.

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Karen Avila
10/03/2012 9:23am

Variables, expressions, and equations are all about representing a quantity in terms of its context. Its important to know the difference between an equation and an expression which is the equal sign. Important vocabulary to know are variables, algebraic expression, equation, and open sentence. Some examples of an algebraic expression is t-15=t minus 15. Meanwhile, an equation is 3+5=n, n being 8 resulting in 3+5=8.
Order of operations consists of Algebra being used as a language. And in order to speak it well, you must follow the rules. All of the order of operations can be sumed up into a simple acronym named PEMDAS. PEMDAS stands for parenthesis, exponents, multiplication, division, addition, and subtraction. Some of the vocabulary needed for this subtopic are simplify, exponent, base, power, and evaluate. Some uses of order of operations is 6-10/5 which equals to 4. Another example is 3*6-4^2/2 which results in 10. It is extremely important to solve all algebraic equations according to PEMDAS.
The last and final topic I would like to discuss is classifying numbers. One needs to understand that the number system is just a way to classify numbers just like we classify food, birds, music, and other things. Some important vocabulary is natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, counter example, inequalities, opposites, and absolute value. Some examples of classifying numbers would be for example, classifying -12 as a real, rational, and integer. Pi can also be classified as an irrational number.
Overall, variables, expressions, equations, order of operations, and classifying numbers are all the 3 major subtopics and basics/fundamental lessons to further advance in math. To master more experienced units you must first master these.

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Gabriela Breton
10/03/2012 11:10am

http://gabrielak.weebly.com/

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Anastasia Krasilnikova
10/03/2012 1:45pm

So far I learned so many things I did not know before. But the main thing I have learned is that the Algebra is a language and in order to speak and understand it you should follow the rules
The first topic we learned was about Expressions, Variables and Equations. In order to learn something new you should review things you learned already. For example, the difference between expression and equation is that the equation has a equal sign in it, but the expression does not. Also I learned how to change sentences in English into Math expressions, for instance, 6 less than a is a - 6. There is a little trick here "less than" means when you see is you have to switch the variables. In both expressions and equation there are variables. Variable is a symbol, usually the letter, that represents one or more numbers.
The second topic is Order of Operations. It seems to be easy and basic but it is very important topic. Whole math is based on this rule:parenthesis, exponents, multiplication, division, addition, and subtraction (PEMDAS). This rule shows in what order you should solve every math problem. For example, 5+6/2, the first thing we should do according to the PEMDAS is to divide and then add so the correct answers is 8.
Classification is the third topic I have learned so far. It is very important topic for me because I did not know it before. My old teacher did not taught us what whole numbers,integers,rational and irrational are. However I learned them very fast. Example of whole numbers are 0,1,2,3..., integers are ...-2,-1,0,1,2...Rational numbers are everything you can write as a fraction and irrational numbers are √2 and Pi.
In this unit I learned a lot of things which are very important. Of course it was an easy unit but without these 3 topics we would nor be able to solve any math problems.

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Nora Carden
10/03/2012 2:08pm

It's really important that mathematicians be precise and organized. A variable is a symbol, usually a letter that represents one or more numbers. ie: x-2=20. An equation and expression are two very different things. An equation uses an equals sign (ie: 2x=5) and an expression doesn't (ie: 6-t). A lot of words like quotient and sum are used when solving an equation.

PEMDAS is used a lot in order of operations, it helps people solve problems with order of operations. P stands for Parenthesis, you solve all things in parenthesis first, if there are none, you move on. E stands for exponents, same as parenthesis you solve all exponents. M and D stand for multiplication and division, the order in these two doesn't matter. Same with A and S which stand for addition and subtraction.

A natural number is a number that isn't negative or have any decimals (ie: 1,2,3...). A whole number doesn't have decimals and isn't negative (ie 0,1,2,3...). An integer can be any number as long as it isn't a decimal or have one (ie: -2,-1,0,1...) A rational number is a number you can have in the form a/b where a and b are integers and b≠0. Real numbers are rational and irrational numbers. Counterexample is any example that proves a statement false. An inequality is a mathematical sentence that compares the value of two expressions using an inequality symbol. Opposites are two numbers that are the same distance from zero on a number line but lie in opposite directions. An absolute value is a number that it's distance from 0 on a number line. The main topics in this essay are variables, expressions, and equations, order of operations, and classifying numbers.

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Sincere Davis
10/03/2012 2:19pm

Algebra is a language, to understand this language you must understand things like; Expressions & Variables; Order of Operations; and Classifying Numbers.

Variables are words in the context of math and we use these variables to make "sentences" which would be our expressions and equations. For example 3x would be an expression. Why not a equation you ask, because a equation contains an equal sign, =. For example 3x"="6. I guess this would still be an expression since the variable isn't yet found. The variable would be 2.

Order of Operations is like using correct in a equation and/or expression. There is a easy way or remembering this method. Its called PEMDAS. Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. You have to solve the equation in this order. For example, (9+1)%2. We would do 9+1 first because its in parentheses and that would be 10. Then divide that by 2 and your answer is 5.

Classifying numbers is like defining a number in an equation and/or expression. There are many types of numbers, The basic ones are called whole numbers, these have no decimals, fractions, negatives, etc. Those other types of numbers all fall under rational or irrational numbers. All of those categories fall under Real Numbers.

Algebra is one of many languages, but to understand you just need to know how to use and solve Equations/Expressions.

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Brandon Melendez
10/03/2012 2:31pm

Algebra is a language and to understand it you must first understand the rules of it. Some of things tha must be learned to understand algebra would be variables, expresions, equations, order of operations (PEMDAS) and classification of numbers.

Variables is a symbol usually a letter, that represents one or more number/ value(s). For example 8x+9y. The variables in the example is/ would be X and Y. Expressions and equations are very alike, for they both are mathmatical sentences that have/ could have variable, numbers and operation symbols. the only difference between the two would be that equations have equal signs while expressions dont. An example of a expression and equation would be 8x+12 and 5n+14=y. Because the first mathematical sentence (8x+12) doesnt have a equal sign, that makes it a expression, making the second mathmatical sentence (5n+14=y) a equation because it has a equal sign.

Order of operations or PEMDAS, as it is commonly refered to, is the order of which you complete a mathmatical sentence when there is two or more mathmatical symbols. For those who dont know, PEMDAS stands for:
-Parentheses
-Exponents
-Multipication
-Division
-Addition
-Subtraction
When faced with a mathematical equation with two or more mathmatical symbols, this is the order of which you follow to get the correct answer, usually.

Classifying numbers is when you define natural, whole, integer, rational, irrational, real numbers, counterexample, inequality, and opposites. Natural Numbers includes all numbers that are positive, not including 0. Whole Numbers includes all numbers positive, including 0. Integers includes ever number within the number system. Rational Numbers includes all numbers that can be written as a fraction. A Rational number can’t be divide by 0, and can be a/ is every whole, natural numbers, and/or intger. Irrational Numbers are numbers that cannot be express as a fraction (The total opposite of Rational numbers). An Irrational Number can’t be repeated.For example: 0.606006060060600... . Real Numbers are/is the mixed of all Irrational Numbers and Rational Numbers formulated into Real Numbers. (This means that real numbers are all numbers). Opposites Numbers are opposites number are numbers that had the same distance from O but lie in opposites direction. Absolute Value is the distance a number is from 0. Absolute Value will always be positive and usually looks like one line on each side of a number (example: l-38l).

Algebra is a language and in order to understand it , you must understand its rules. these rules are important to both algebra and math and without them, math would make very much sense.

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Isobel Connelly
10/03/2012 3:31pm

Algebra is a language and in to order to speak any language you have to start with the basics, the building blocks if you will, so that’s so far what we’ve been studying in math, “learning the language of algebra” so this is what we’ve done so far.

Variables: are symbols usually letters that represent one or more numbers in an equation or expression (a+2x), they are essential for algebra. Variables make up your equation or expression, though expressions and equations have very different characteristics, being that equations have equals signs and expressions do not (expression: b+4c. equation: m=4+2x)

In order to figure out the answer to an equation or an expression, you will most likely be presented with exponents, and parentheses. {m+2(x3+3) + (n-8)} And there is an order in which you will do them. These steps are vitally important because they determine what answer you will get. So for this we use the order operations or P.E.M.D.A.S. (parenthesis, exponents, multiplication, division, addition and subtraction) these are very important to follow, because they enable you to correctly answer the question. For instance

Finally classifying numbers, giving groups of numbers names. (Integers: positive and negative whole numbers, no decimals or fractions: -3, -2, -1, 1, 2, 3. Rational numbers: numbers that can be expressed at ½ or decimals and that doesn’t end or repeats: 1.14, √2.Irrational numbers: numbers that cant be expressed as ½ ‘s or decimals that repeat or end. Whole numbers: positive numbers that are whole with no decimals or fractions: 1, 2, 3) Doing this is very important in several are senses. One, classifying numbers organizes things, making it easier to understand and make sense of. Secondly classifying numbers helps us, make up equations, because what the numbers are and what they do, from their classification.

To sum all this up, we have just finished the introduction to algebra. With our newfound knowledge will be able to tackle more complex and difficult problems. And a good introduction to anything in life is what sets the tone for the rest of it. So with math good understanding of an introduction will make the next thing easier to understand and undertake.


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JasmineRivera Flatiron
10/03/2012 3:52pm

What is variables? Variables is a symbol, usually a letter that represents one or more number. You must be wondering "what does a variable looks like?" Well then I will show you a example of what a variable can look like: T - 15. Since a variable is usually a letter, the variable in T - 15 is the T. Sometime the most common variable used is X or Y.
There are many math topic that use variables like Algebraic expression, Equation, and Open sentence. But first we must know the definition of each topic.

Algebraic expression- a mathematical phrase that can include numbers, variables, and operation symbols. For example: the sum of twice a number and 31. What we will do is try to write this phrase into a algebra expression, by doing that we will try to see if there are clues on what to put in the algebra expression. Sum can be use in the expression because sum means to add, another clue we can use is twice. Twice means to multiply a number two times. The variable in this phrase has to be A since A represents one or more number that needed to be multiply twice and add by 31. The algebra expression for the phrase will be 31 + 2a.
Equation- a mathematical sentence that uses an equal sign. For example: x + 3 = 5.
Open sentence- An equation that contains one or more variables. An open sentence can be either true or false depending what values are used.For example: 3y=4x+2
Variable, Algebraic expression, Equation, and Open sentence are all algebra.

What are the order of operations?
The order of operations is P.E.M.D.A.S. Each letter has a meaning on what they do.
P- Parentheses
E- Exponents
M- Multiplication
D- Division
A- Addition
S- Subtraction

Why do we need order of operations?
We need order of operations because order of operations are sets of rules that we used to follow to avoid getting confuse what to do when simplifying mathematical expressions or equations. Without the order of operation, people wouldn't be able to know what they're doing and not be able to check they're work. But remember for M/D either way can go which ever come first. Same goes for A/S.
Why is it necessary to classify numbers?
It is SUPER important to classify numbers because we classify everything in our life's almost every day. In math we classify whole numbers, natural numbers,integers, rational, or fractional numbers. We classify numbers because there are general rules for each numbers, and there are groups of numbers that apply to some groups but not all.
In the end all of these topic fits in with algebra. Algebra is also is consider to be a language because we read it and understand it, even without words. It's almost like learning a new language but by using math instead.

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Jamie Goldenberg
10/03/2012 3:57pm

Algebra is considered a language because you can read it as a problem. What I learned so far in algebra is variables, expressions,equations, order of operations, and how to classify numbers.

A variable is a symbol usually a letter that represents one or more numbers. For example, 3x is a variable. An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. Algebraic expressions are sometimes called variable expressions. For example, 4+2x. An equation is a mathematical sentence that uses an equal sign. For example, 5+5=10. The difference between a equation and a expression is that a equation has a equal sign and a expression does not. An open sentence is an equation that contains one or more variables. For example, 5x+2x.

To simplify a expression you replace it with its simplest name. An exponent tells how many times a number the base is used as a factor. A power has two parts a base and a exponent. For example, 5^2 5 is the base and 2 is the exponent. You evaluate an algebraic expression by substituting a given number for each variable. Then simplify the numerical expression using the order of operations. PEMDAS stands for parenthesis, exponents, multiply, divide, add, subtract. You solve 6/2x5 by dividing 6 by 2 and getting 3 and then multiplying 3 and 5. You solve 4-2+3 by adding 2+3 and then 4-5.

A rational number is any number that you can write in the form a/b. A rational number in decimal form is either terminating or repeating. For example, 8.222... An irrational number cannot be expressed in the form a/b. For example pi. Together rational numbers and irrational numbers form real numbers. The absolute value of a number is its distance from 0 on a number line. For example -5 absolute value is 5. The difference between a whole number and a integer is that whole numbers aren't negative. The difference between rational and irruption is ration are fractions and irrational go on forever.

What I learned in algrebra so far is variables, expressions, equations, order of operations, and how to classify numbers.

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Emily Cheung
10/03/2012 4:09pm

Algebra is like a language except it is just numbers. It is like a language in math. In algebra so far I learned variables, expressions, equations, order of operations and classifying numbers.
This topic is about variables, expression and equation. Variable is usually a letter/symbol that represents one or more number. A expression have no equal sign but includes variables and numbers. So a equation have a equal and numbers and variables. Example for a expression is 6n+5 but a equation is 6n+5=_. For example 6x the x is the variable because it is a number and symbol. There can be one sentence in a expression and equation. One sentence is when it contains one or more variable.
This topic is about order of operation. In order of operation you also have variables, expression, and equation. In order of operation you will also have to simplify and evaluate. Simplifying is making the equation or expression shorter by adding, subtracting, multiplying or diving the math that looks alike. For example 3n+5n+6xsquare it will be 8n+6xsquare because 5 and 3 are both numbers and they have the same variable. Evaluating is a given number for a variable where you have to put the number in the variable. For example n=3 and y=10 so the equation is 6n+y it will be 6(3)+10 because you are putting the number in the variable. In order of operation there is something called pemdas, that stands for something. The p is
parentheses, e for exponent, m is for multiplying, d for division, a for adding, and s for subtracting. We have that as a order to do algebra.For example if we have 5÷2(6n+5y)+4squarex 10-6+4=, we would have to do the parentheses first because it is the first one in the list in pemdas. Then we do 4square because exponent is next then 5÷2 because in the equation division came first. When we do orders of operation for mdas which is multiplying, dividing, adding and subtracting we just look to see if multiplying and dividing is first then we do that first. You look from left to right and do the same thing for adding and subtracting but multiplying and division you have to go first. Then we do the multiplying 10 and then subtract 6 and add 4 and we will get the answer. But remember to evaluate the answer for that one to solve the answer.
This is the topic about classifying numbers is finding out where the numbers belong in. A rational number is numbers that are common and don't have to think much.Like a fraction and decimal is also a rational number. For example 1/2 or 6.5. A irrational number is a number that can not be a fraction. For example 6 is a irrational number. Also a negative number is a integer. For example -2.5 is a integer. For example a vegetarian might hate eating meat, so they will find it negative, so it will be integers. Another example will be if you think a food is disgusting or it looks bad then it will be irrational way to eat. A rational number you can think of money in coins or half shoe size.
In conclusion what I learned from algebra is variables, expression, equation, order of operation and classifying numbers. Remember variables are letters and expression have no equal sign but equation does. Also order of operation has a order pemdas. Last remember classifying numbers is finding where the numbers belong. This is what I learned in algebra.

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Dandre Winn
10/03/2012 4:17pm

What have I learned so far? I have learned how to interpret expressions that represent a quantity in terms of its context meaning learned how to solve a variable which is a symbol usually that represents one or more numbers like n can represent 2 in something called and equation which would be something like this 2n+5 n being it is like a language in order to speak it well you must understand it. I have also learned how to do order of operations which helps you to solve questions like 6x2+5 and 4-2+3 so you can use pemdas which stands for parenthesis,exponents,multiplication,division, addition,and subtraction. Their are different classification of numbers such as rational numbers, integers,and irrational numbers rational numbers are just regular every day numbers such as 12345 and integers are negative numbers for example -1,-2,-3,-4.
We have learned a lot in math such as order of operations and variables but as i said algrebra is like a language in order to understand it you must speak it well.

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Khalid Jn-Baptiste
10/03/2012 4:25pm

Algebra is a language. In order to speak it well, you need to use the rules.The things I've have learned have been, expressions/equations, order of operations and classifying numbers.

Expressions is a mathematical phrase that can include number, variables and operation symbols. For example 7 less than a number is x-7. Equations is a mathematical sentence that uses an equal sign. For example 7 plus 5 equals 12, so 7+5=11. Variable is a symbol, mostly a letter that can represent any number. For example "x" can be any number. The difference between expressions and equations, is that equations has to be solved and expressions has to be simply but not solved.

Order of operations is the order of which you add, subtract, multiply, divide and squaring. Order of operations is mostly knew better as PEMDAS. P=Parentheses(). E=Exponents. M=Multiply. D=Divide. A=Add. S=Subtract. For example

7+(6*5^2+3)
6*25+3
7+153
160

Classifying numbers is when making a number specific or labeling a number. Like 2 can be the number of boys and 3 can be the number of girls.

Algebra is like a way to talk, because you have formal and informal ways to talk. People have different ways of solving problems in math. Expressions is a way to include numbers and variables together. Order of operations is a way to solve a problem formal.

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Osvaldo sanchez
10/03/2012 4:30pm

Algebra is like a language and in order to speak it well you must follow the rules. The three main subtopics about learning this language are; Expression and Variables, order of operations, and classifying numbers. In this essay I’ll be talking about these topics.
Expressions are mathematical phrases that can have numbers, addition, subtraction, multiplication, division, and variables. Just like in any language you can express yourself. In math you can express yourself with numbers. An equation is like an expression but with an equal sign. A variable is a symbol that can represent one or more numbers using a letter. An example of an equation is 9L+3=21. This equation has a variable, which is the “L”. To solve for L you must follow PEMDAS.
What is PEMDAS and what does it stand for? Pemdas stands for P= parenthesis, E= exponents, M= multiplication, A= addition, and S=subtraction. You must follow this the way it is written; if you do not then I guarantee you that you will not get the right answer. Using order of operations or (pemdas) helps you determine or solve for the variable, which in this case is “L” in the equation; 9L+3=21. If you follow pemdas you will get the “L”= 2.
Classifying numbers is basically organizing number into different categories. The categories are; whole numbers, integers, rational number, and irrational numbers. Whole numbers are any number that is above 0 on a number line (basically positive numbers), and numbers that are fractions only when you reduce it, the outcome is a whole number. An example of a whole number is the number 9 or 6/3. Rational numbers are numbers that can be written as a fraction for example 3 can be written as a fraction; 3/1. Is a number that you cannot write as a fraction or whole number. Pi is a famous irrational number. Pi is π = 3.14159265358979… etc it continues and it cannot be written as a simple fraction. Integers are any negative or positive whole numbers. For example 9 and -27 are both integers.
Math is like a language because expressions can be the way you express yourself but with numbers. Variables are words just like in any other language. Classifying numbers are like categories you can use to organize words. Order of operations is basically grammar rules you have to follow in order for your math work to be right and to make your sentences make sense. This shows that math is like a language once you know the subtopics.

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Jewel Harrison
10/03/2012 4:50pm

What Have I Learned in Algebra So Far...
For the first term I have been learning that Algebra is a language. Algebra is a language, an easy language if you know the three main subtopics, Variables/Expressions/Equations, Order of Operations (PEMDAS), and Classifying Numbers. If your read this guide, by the end you should know the true meaning of what is Algebra.
Algebra: the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers. Meaning the subtopics(PEMDAS,Classifying,Variables,Expressions and Equations)
What does every language has? Words and symbols. What are variables?
Variables: a symbol usually a letter that represents one or more numbers. The most common variables are used by letters mostly, x, y n, z etc.
For example: z=6 and y= 2
= 4y+2(z)
= 4(2)+ 2(6) Substitute the variables for their chosen number
= 8+12 Add
= 20
"Jewel what's an algebraic expression?"
" Let me explain...," Algebraic Expression: a mathematical phrase that can include numbers, variables, and operation symbols.
"Jewel if that's an expression, what's an equation?"
" An equation is basically....," Equation: an expression but has an equal sign, or a mathematical sentence.
Here's some examples below:
1. n+7= " More than" indicates addition. Add the first number 7 to the second number n.
2. n-7= "Difference" indicates subtraction. Begin with the first number n, then subtract it by the second number.
3. the product of seven and n= "Product" indicates multiplication. Multiply the first number 7 by the second number n.
4. the quotient of n and seven= "Quotient" indicates division. Divide the first number by the second number 7.
"Jewel, how do we classify numbers?"
" Well numbers come in many forms, not just 1, 2, 3 you know. Let me explain."
There's rational numbers, natural numbers, whole numbers, and integers.
Rational Numbers: is any number that you can write in a form of a fraction, where the numerator and denominator are integers, and the denominator can't equal 0. Also can be in decimal form is either terminating, such as 6.27, or repeating such as 8.2222....
Natural Numbers: The counting numbers 1...2...3
Whole Numbers: The non-negative integers 0,1,2,3
Integers: Whole numbers and their opposites
Simplifying an Expression
2[(13-7) /3 ]First simplify 12+3[18-5(16-3)]
2(6/3)Divide within 12+3[18-5-13]
2(2)Multiply 12+3 [13-13]
15
4
Let's move this one is my favorite!
"Jewel, what is it?"
"P.E.M.D.A.S. Order of Operations!"
'What's does P.E.M.D.A.S stand for?"
Let me explain, the P is parentheses, the E is exponents, the M is multiplication, the D is division, the A is addition, and the S is subtraction. The rule is for PEMDAS, is do what comes first, if division comes before multiplication, you divide first, and if subtraction comes before addition, subtract first. For example,
Do things in the parentheses first,
6 × (5 + 3) not 6 × (5 + 3)
6 x (8) 30+ 3
48 33
How do you solve 6/2 x 5 and 4-2+3
6/2 x 5 and 4-2+ 3
3x5 2+3
15 5
"Jewel this is all the functions for the language of algebra?"
" Do you understand now?"
" Thanks for the help!"
" No problem!"

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Emma Todd
10/03/2012 4:55pm

Variables, expressions, equations, order of operations, and classifying numbers are the things that i have learned in Algebra 1 so far.
A variable is a symbol, usually a letter that represents one or more numbers. Algebraic expressions are mathematical phrases that can include numbers, variables, and operating symbols. An equation is a mathematical sentence that uses a equal sign. For example of a variable is 6-n, 4+8=12 is an example of a equation.

Order of operations helps you when you are looking at a problem that has many components. Simplify is when you a numerical expression, you replace it with its simplest form. And Exponent tells you how many times the number/base is used as a factor. Base is used as a factor, Powers has two parts the base and an exponent. When you Evaluate you look at an algebraic expression by substituting a given number for each variable. PEMDAS is an example of order of operations, it stands for Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction. You follow the order of the acronym, for example (8*4)* 6 + (9*7) you would multiply 8 and 4 because they are in parenthesis then do the same for 9 and 7, multiply 32 and 6 and last add 63 and you get 255.
It would not be possible to write any equation or math problem without real numbers. Real numbers are irrational and rational numbers together. Natural numbers are numbers like 1,2,3. Whole numbers consist of 0,1,2,3 integers are numbers that are negative and positive whole numbers such as -2,-1,0,1,2. Rational numbers are any number that you can write in the form where A and B are irrational numbers. Irrational numbers can not be expressed when a/b and a and b are integers. You cannot solve or even write a mathematical equation without all of these items. For example 2+2=4 you used real, whole numbers and integers to complete this problem. 1.5 is rational, because it can be written as the ratio 3/2 that is an example of rational are irrational numbers.
This is what I have learned in Algebra so far. Variables, expressions, equations, order of operations and classifying numbers.

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Yue Jiao Jiang
10/03/2012 4:55pm

Everyone has some kind of different experience with algebra. Even with our different experiences, some of us uses the same language everyday. Just like in a language you may have certain things that you don't know, there are also certain grammar related rules that you need and there are numbers that can be different in each language. This in algebra can be looked as variables/expressions/equations, orders of operation and classifying numbers.

Variables are letters that are suppose to represent an unknown number. Expressions are number sentences without the equal sign. Equations are just how number sentences with equal signs. An example of both equations and variables is that if you have 3x-5=16, it would be an equation because it has an equal sign. The x would be the variable. If you were to translate a verbal expression to an algebraic one, you can take 4 less than 6 times a number. If you were to turn it into a algebraic one, you would get 6n-4.

Order of operations is the order of which you can use PEMDAS to solve expressions and equations. PEMDAS stands for Parenthesis, Exponents, Multiplication/Division and Addition/Subtraction. An example of this is that if you had 4+12/2-8, according to pemdas you would have to do the division fist for this problem. So when you divide 12 by 2, you get 6 and you start adding 4 and 6 because from left to right addition would come next. You take the 10 and subtract by 8 to finish off the expression.

Classifying numbers is finding which categories a number falls into from rational numbers, irrational numbers, whole numbers and integers. Rational numbers are any numbers you can put into a fraction, such as 5.1. Irrational numbers are the oppisites of rational numbers, where it can't be put into fractions, such as pi. Whole numbers are numbers like 1, 2, 3, 4. Integers can be negative or positive numbers, such as -4 and 9.

What i have learned so far in algebra class is about variables/expressions/equations, orders of operation and classifying numbers.

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Aaron Riesel
10/03/2012 4:59pm

Aaron Riesel.
Math blog.

Algebra is like a language In order to speak it fluently you must learn the concepts, such as, Expressions / Variables, order of operations, and classifying numbers.

As a 9th grader in Sof I have learned about expressions and variables. Variables can be used as a substitution for anything. For example, X ( the variable of my choice. ) = 74 & P = 6.
That being said those variables are then used for a math problem just like this, PX + 4P - 7XP. This is also an example of order of operations.

Now, what are order of operations? Order of operations are the order you must fallow to operate, but there is more to that then it might sound.
Perenthasis
Exponents
MD multiplication & division.
AS addition & subtraction
Pemdas, but why are md / as next to each other ? It is written like this because it goes in order which ever one comes first from left to right is the one you must operate on first.

What we have also learned in the 9th grade is how to classify numbers ? But what does it mean? Just like humans are classified weather it's social power, wealth, job, etc numbers are classified too. In math they're are things called whole numbers, rational numbers, integers and irrational numbers.
Whole numbers are numbers that start from O and go up, that being said 1,2,3,4 etc.
integers on the other hand are kind of like whole numbers except it can also go backwards or negative so -1,-2,-3 and so forth.
Rational numbers are numbers that repeat them selves for example 100 divided by 3 is 33.333333333333333 and so on
But irrational numbers are numbers like the sqaure root of 7.
So furthermore As a 9th grade student at Sof we have learned about expressions / variables. Order of operations. And classifying numbers.

- Aaron Riesel

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Sarahi
10/03/2012 5:02pm

Algebra is a language and in order to speak it well you must follow the rules. Things we have learned so far are expressions, equations, order of operations and classifying numbers.
First i will start by introducing the definition of a variable. A variable is a symbol usually a letter used to represent a number. For example: 2x-12=15x+17(hte x's are representing a number) A expression is as mathematical phrase that can include variables, numbers, and operating symbols. For example: 3x6-4, this is an expression NOT and equation. The thing the distinguishes a equation from an expression is the equal sign, you will not find an equal sign in an expression. An equation is a mathematical sentence that uses the equal sign. For example: 2x-12=15x+17.
I use PEMDAS for when im doing order of operations. For me PEMDAS is really helpful because sometimes i forget how the order goes and i immediatly thing PEMDAS!. PEMDAS stands for parenthesis, exponents, multiplication, addicion, addition, and subtraction. For example(5+2)-12 i would go with the parenthesis first which equals to 7 then if i have exponents i will solve that and on with the order of PEMDAS.
Natural numbers are 1,2,3... A whole number would be from 0 and up. An irrational number isn't a rational number because an irrational numbers are never ending (3.14) and cant be written as a fraction while a rational number can be fraction and has an ending point (1.75) A whole number isn't and integer because integers can be negative while a whole numbers aren't.
Algebra is a language and algebraic expressions model real world quantities. Variables, Expressions, Equations, Order of operations are important to learn for our future.








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Summer Rowland
10/03/2012 5:11pm

Math is an important subject that is used in everyday life and can benefit you in the future. For me algebra is a language and for someone to understand it you must learn the rules. Parts of this language include variables/expressions/equations, order of operations and classifying numbers.

A variable is a symbol, usually a letter, that represents one or more numbers. An expression is a mathematical phrase that can include numbers, variables and symbols. An equation is a mathematical sentence that uses and equal sign. An example of a variable is "n". The "n" is a latter that is taking place of a number because we aren't given the number. An example of an algebraic expression is "the quotient of 4.2 and c" the expression would then be 4.2/c. An example of an equation is 4x-4=8.. The fact that an equal sign is present tells us that it is an equation. The difference between an expression and equation is the equal sign.

When doing the order of operations, an exponent, multiplication, division, addition and subtraction are present. When solving the order of operations, PEMDAS is always used to make sure that your work will be accurate. Sometimes we use BPEMDAS when a bracket in an expression in present.
B- Bracket
P- Parenthesis
E- Exponent
M- Multiplication-
D- Division
A- Addition
S- Subtraction
Multiplication and division: Solve whatever comes first
Addition and subtraction: Solve whatever comes first
To solve an expression:
6 / 2x5
Solve 6 divided by 2 and then 12 multiplied by 5

Classifying Numbers
Rational Numbers: A rational number is any number that you can write in the form a/b where there are integers "a" "b".
Irrational Numbers: Cannot be expressed in the form in which a/b, a and b are integers.
Natural Numbers: 1, 2, 3, 4, 5....
Integers: -3, -2, -1, 0, 1, 2, 3
Real Numbers: Rational and irrational numbers form the set of real numbers.

In the end math is an important subject where everything that you will learn will probably benefit you in the future. Knowing how to solve equations and expressions along with order of operations and classifying numbers can help you.


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Veronica Wright
10/03/2012 5:41pm

I say that Algebra is like a language in order to understand it u know to understand the rule to that language.
Variable is a symbol for a number we don't know yet. it usually a letter For example, x+2=6, x is the variable and if there not a variable is called a constant.
I say that order of operation is like a language but is like baking a cake, in order to bake the cake successfully u need to follow the recipe to put all the ingredient together just like order of operation u need to go in order to able to get your answer or else the outcome of the answer will be wrong.
To understand Algebra u to classify number. For example rational number and irrational number are different because rational numbers you can put into a fraction (a/b) and decimal. while irrational numbers is like the number pie that continues going on and can't be express into a fraction. Also whole numbers are positive number (0,1,2,3,4,5....) and negatives are number that aren't whole number (-1,-2,-3,-4,-5.....).Another is absolute value where negative number can be positive ( |-12| > 12) and real numbers are also rational and irrational number.

Algebra at first can be confusing but after learning all the concept that connect to algebra u will come to understand it little by little just like learning a different language.

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Brittany Rodriguez
10/03/2012 5:59pm

Algebra is a vast subject to learn. So far this year we have gon through 3 big topics in the path to achieving great knowledge of algebra. The first topic is variables, expressions and equations. The second topic is order of operations. The third topic is classifying numbers.

In variables, expressions and equations we learned about what a variable is as well as expressions and equations. A variable is a symbol that can represent one number or more. The difference between a expression and a equation is that expressions and mathematical sentence that contains variables, operations symbols and numbers. An equation is a mathematical sentence that contains numbers, operation symbols and equal signs.

In order of operations we learned about how PEMDAS works. PEMDAS is a culture in algebra. A way of functioning through equations and expressions. PEMDAS stands for:
P = parenthesis
E = exponents
M = multiplications / division
D = division / multiplication
A = addition / subtraction
S = subtraction / addiction
For example lets try an equation together. 4+8/2+6*2. The answer to that would be 20 because there were no parenthesis or exponents so we skipped to multiplication and division. 6* 2 is 12 and 8 divided into 2 is 4. Then we move onto addition and subtraction. 4+4 is 8 and 8+12 is 20... Get it?

The last but not least thing we have learned about this year was classifying numbers. In this unit we learned about ration and irrational numbers. We learned how to classify numbers. A rational number is a positive or negative number that can be put in a fraction. A irrational number can't be put in a fraction because it is a non terminating number such as pie which is a ongoing non terminating number. 3.14...etc

I hope to learn more this year.

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Matthew Chun
10/03/2012 6:00pm

Algebra is a language and is very significant for everyday life that requires math. Algebra is a very helpful tool in math. It is almost like learning another language. Some of the components of algebra are expressions/variables, order of operations, and classifying numbers. These are all very important in math, as variables can be used to find an unknown, order of operations tells what should be done first in a problem, and it is important to classify numbers to know which numbers are what.
A variable is a symbol that represents one or more numbers. An expression is a mathematical phrase that includes numbers, variables, and operation symbols. Variables and expressions are very important in real life, as they can be used to solve an “unknown”. An example of this is if one were to figure out how many $4 shirts were bought in orders to have a total of $16 (4X=16).
Order of operations is very important because it shows (using PEMDAS, parentheses, exponents, multiply, divide, add, then subtract) what order to do things in. There can only be one answer to math. For example, 2+10x5. There is only one answer to this problem, as PEMDAS shows to multiply first, then add, thus getting 52 as an answer, not 60.
Knowing where to classify numbers is a very important part of math. The reason for this is because it can be very hard to apply certain rules to certain numbers without knowing where to classify them. For example, “real numbers” are rational and irrational. Without knowing where to classify numbers, one could easily make a common misconception by stating that “all real numbers are rational”. This is wrong because a number such as the square root of negative ten is not rational, but rather irrational.
Learning algebra; expressions and variables, order of operations, and classifying numbers are all very important in everyday life. Without math, we probably could not do half of what we do today.

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Kelvin Ayala
10/03/2012 6:56pm

Algebra is a basic skill that must be learned by all to help make everyday life easier. It is like a language and in order to speak it fluently the person must know some of it’s basics. One thing everyone must know is the difference between and expression and equation and also everyone must know what a variable is. Another thing that everybody must know is the order of operations to know what to do first to get the correct answer. To solve more advance algebra problems the person must be able to classify numbers. Algebra is a language that can be taught to all.
There is one solid difference all people must know about expressions and equations. Equations have an equal symbol (=) and expressions don’t. Besides that everyone must also know that variables are symbols that represents a number and in order to make a algebraic expressions or equations must have a variable in them to make a algebraic problem. For example 9x+8x is an algebraic expression because it has no equal sign and it has variables. It is simple when you know what they are.
Another thing everyone must learn to do every algebraic problem is to know the order of operations. The order is Parenthesis, Exponents, Multiplication and Division, Addition and Subtraction, aka PEMDAS. This is important to know to get the correct answer because in math there is only one answer. For example, 9*7+2-3/1 is a problem that needs the solver to follow the order of operations. First we multiply 9 and 7 then ¾, and that gives us 63 and 3. Afterwards the problem can be done from left to right to get the final answer. This is a rule that must be followed all the time when solving algebraic equation or expressions.
To further advance someone’s knowledge on algebra they must also learn how to classify numbers. The main categories are rational, irrational, whole numbers, and integers. Rational numbers are numbers that have an end like 1.3 or just 1,and irrational numbers go on forever like pie and the square root of 7. Whole numbers are numbers that are numbers that have no portions like 1 or 18, and Integers are negative numbers like -100 or - 1000. There are many more categories but these are the simple ones and numbers can be in more than one category.
It is not difficult to learn to speak algebra because with these rules or commands anyone can do almost any problem. I have learned all this in this unit and it is simple if the person learning listens and review their mistakes. Also they must check their work to see if they have done something wrong. Just following the order of operations, what expressions, equations, and variables are algebra can be solved. Algebra is a language that all must learn to make everyday life easier.

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Nhajee Sanoh-Monroe
10/03/2012 7:20pm

Algebra is a language and in order to become well versed you must learn about different topics-classification. So, in order to understand it you would need to know the topics. Like, variables, equations, order of operations and etc. You would also need to know how to determine and classify numbers.

In order to understand the language you would need to know the first thing, which makes Algebra a language, variables. Variables are symbols, usually a letter that represents one or more numbers. So basically, someone would have to solve problems/equations to find the answer for what the variable is. A variable is like a box with a value. Here’s an example: 9-x=3. X would equal three because 9-(3) =3.

We need order of operations. We need order of operations because, if we don’t have it then how will we be able to solve any type of equation or problem. Order of Operations is to perform any operation(s) inside grouping symbols, simplify powers, multiply and divide in order from left to right, add and subtract in order from left to right. If you are not able to understand order of operations, then what’s the whole point of you doing math, or math in general? Example: 9/3x2 what would you do first? Even though, pemdas says parenthesis, exponents, multiplication, division, addition, and subtraction you would divide nine divided by three which equals 3 times that by two and, your answer is six. It’s just a very logically process that people have to know in order to succeed.

It’s necessary to classify numbers. It’s necessary to classify numbers because; in order to know how to do it you would need to know what is the natural, rational, irrational number, and etc. By evaluating and, solving, and doing research you will find out and know what type of number it is. A rational number is any number that you can write in the form a/b, where a and b are integers and b = 0. An irrational is a number that cannot be expressed in the form a/b, where a and b are integers. Ad, a real/natural number is rational numbers and irrational numbers form a set.

Overall, variables, order of operations, classifying numbers are all important/main topics that make Algebra, Algebra/ making it a language. So, without it Algebra would be nothing, nothing at all.

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Oliver Martin
10/03/2012 7:38pm

Like we learned algebra is a language and in order to speak it you must know how to use expressions, equations and variables, use and understand the order of operations and PEMDAS, and to be able to classify numbers. This unit I have tuned up my skills in all these subtopics and now I think that I can do these skills very well. Like a language algebra needs different skills to be spoken.

Variables, expressions, and equations are a very important subtopic because you must know the differences between a expression and a equation. Honestly I used to not really know the difference but now I know that a equation includes something called a variable while an expression does not have a variable. A variable is just a letter that represents a number for example the famous x or could even be the letter q, it just represents any number. A example of a expression is like y= 2 x 1 + 7 compared to a equation which would be something like y= 2n + 7.

Another one of my subtopics that is very important and is just something that you should learn is order of operations. This unit I learned about PEMDAS, what I learned was instead of following the order of PEMDAS you actually go left to right for the letters M/D (multiplication and division) and A/S (addition and subtraction) instead of following the order. For example if I had a problem 9 - 2 +3 even though in PEMDAS it says that addition is first you would do subtraction first instead because you are going in the order of left to right.

The last subtopic I am talking about is is classifying numbers. Classifying numbers is a very important thing that I learned because this unit I really learned what a irrational number is. I used to think that a irrational number was any number that had a decimal at the end but now I have learned that really most of numbers with decimals are rational numbers because they can still be put in fraction form. For example a number with a decimal that is rational is like 8.5 but a number that is irrational with a decimal is the number pi.

In conclusion algebra is a language an in order to speak it you must know about variables, expressions, and equations, know about your order of operations, and classifying numbers. This unit I really started to learn about how to "speak," algebra.

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Ryan Andujar
10/03/2012 7:42pm

Expressions and variables, order of operations, and classifying numbers are all parts of Algebra that you NEED to know.

One very important things to know in algebra is expresions (number sentences without the equal sign) and variables(symbol or letter that represents one or more numbers). Before we get into this you will have to know some very important words. One term which that you need to know is an equation. An equation is a mathematical sentence that uses an equal sign, unlike an expression which doesnt use an equal sign. For example 3x-9=12 is an equation that has variables in it because it has an equal sign. The x would be the variable.

The second topic is order of operations. We need order of operations so it could help us simplify(replace a numerical expression with its simplest form) harder equations that include many operations, such as (9-8)+1. To answer this question you need to use PEMDAS (Parenthesis, Exponents, Multiplication/Division and Addition/Subtraction). You would have to do the parenthesis first according to this problem. So what you do is 9-8 which equals 1, then after your done with the parenthesis you have to finish the problem. So 1+1= 2. The answer to this question is 2.

The third topic is classifying numbers. Classifying numbers is finding what categrie a number falls into. The categories are rational numbers, irrational numbers, whole numbers and integers. Rational numbers are any numbers you can put into a fraction, such as 5.1. Irrational numbers is the opposite of rational numbers, it can't be put into fractions, such as pi(π) . Whole numbers are numbers like 1, 2, 3, 4. Integers can be negative or positive numbers, such as -4 and 9.

The only way to fully understand the language of algebra you have to understand the rules and deffinitions of algebra which have to do with expressions and variables, order of operations, and classifying numbers.

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Kashfina Chowdhury
10/03/2012 7:46pm

Algebra is a language, and to be able to understand algebra you need to know all the subtopics that make up algebra. The subtopics that are involved with algebra is Variables and expression ( which also includes solving equations), Order of operations, and classifying the number system.

The first topic that you need to understand algebra is Variables/Expressions/ Equations. Variable are a symbol that represents one or more numbers. An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. Lastly, an equation is a mathematical sentence that uses an equal sign. An example of an equation is C=10.99n, and an algebraic expression would be 4x+12.

The second topic to understanding algebra is order of operations. In order to solve an equation with order of operations you'll need to use PEMDAS, P standing for Parenthesis, E being Exponents, M/D for Multiplication and Division, and A/D which are Addition and subtraction.For example, ( 2+3) x (3*5). First you would start with the P which is parenthesis. By starting off with parenthesis you would get " 5^15". Then you would do multiplication and your answer would be 75.

The last topic that is needed to understand algebra is classifying the number system. To classify a number you must determine whether it is a rational number or an irrational numbers. A rational number is any number than you can write in the form of a/b ( fraction form ) and an irrational number cannot be expressed in the fraction form, where a and b are integers. Extra information you should know is fractions are never integers, integers are rational numbers, and whole numbers are integers.

Note:
Natural Numbers: 1,2,3
Whole Numbers: 0,1, 2, 3
Integers: -2, -1,0, 1, 2,3

Algebra is a language, and to fully understand it you must learn the subtopics which are Variables/Expressions/Equations, Order of Operations, and classifying real numbers.

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Tabatha Romam
10/03/2012 7:47pm

 In algebra 1 so far I have learned three major things and they have been rather easy. Algebra is a language in its own so if you follow the rules and steps you will catch on quickly. The three things that i have learned about are variables, order of operations and classifying numbers. Each topic has specific vocabulary words and examples that you can use to help you understand.
  
When using variables (a symbol usually a letter that represents one or more number) you must have an algebraic expression. An algebraic expressions is a mathematical phrase that can include numbers, variables and operation symbols. For example 6x + 2 = 14. When using variables you can also have open sentences. An open sentence is an equation that contains one or more variable. For example 6c+b =24.

The second thing that we learned about was order of operations. To efficiently get the answer in an expression you must follow the order of operations which is P.E.M.D.A.S (parentheses, exponent, multipulcation, division, addition, subtraction). Order of operations is basically the rule to winning in algebra. For example, you have the expression 12÷2×3. You first would do multipulcation because there are no parentheses or exponents so you go straight to that. 2×3 would be 6. You would then proceed to divide, 12÷6=2. By following order of operations you will always get the correct answer.

The last topic we discussed in algebra class was classifying numbers. It is imperative that everyone know the difference between the number sets. There a 6 different types of number classifications (natural, whole, integers, rational, irrational, real numbers). Natural numbers are all the numbers on the positive number line (1,2,3,45...). Whole numbers are natural numbers but include zero. Integers are include the same numbers but with negatives (-2,-1,0,1,2...). Rational numbers are any numbers in decimal or fraction form that you can quote. Irrational numbers are the numbers you can not quote. Real numbers are both irrational and rational numbers. Its important to know this so you know what type of number you are working with.

So far the three major important and interesting things that I have learned in algebra so far are variables, order of operations and classifying numbers. These things are the foundation or starting point in my career as a math magician. So far all of these topics have been easy to learn.

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Ellen Sekhniashvili
10/03/2012 7:52pm



In learning about variables, expressions and equations, I learned to define each term and what they represent. A variable is a symbol that is usually a letter that represents one of more numbers. An algebraic expression is a mathematical phrase that can include numbers, variables and operation symbols. An equation is a mathematical sentence that uses an equal sign. The difference between an expression and an equation is that an equation needs to have an equal sign unlike an expression which doesn't. An example of a variable is 'x'. An example of an expression is x-4 and an example of an equation is x-4=8.

The order of operations talks about the order in which you solve the problem to the right answer. PEMDAS is the method of correct order. Parenthesis, exponents, multiplication, division, addition and subtraction. If you follow the method you'll be able to solve the problem correctly. Algebra is a language and in order to speak it, you must be able to follow the rules. To solve a problem such as 6/2 x 5, you would first divide 6/2 to get 3 and then multiply by 5 to get 15. For 4-2+3, you would first subtract 4-2 to get 2 and then add 3 to get 5. We learned to define exponents, base, power and the act to simplify and evaluate. An exponent is a number that shows repeated multiplication such as 2 squared which means 2 x 2. A base is a number that is multiplied repeatedly. A power is a base and the exponent of an expression. Simplification is also very important. To simplify it means to replace an expression with its most simplest name or form. To evaluate it means to substitute a given number for each variable and then simplify.

To classify numbers includes natural numbers, whole numbers, integers, irrational numbers, rational numbers, counter qualities, absolute value and opposites. The difference between a whole number, an integer, a rational number and a irrational number is that a whole number is a non negative integer such as you. An integer is a whole and its opposites which means is can be a whole number that is positive or negative, it could be 4 or -4. A rational number is a real number that can be written as a ratio of two integers. An irrational number is a number that cannot be written as a ratio of two integers and it is also non terminating. An example of a rational number is the square root of nine of a fraction such as one half. An example of an irrational number would be the square root of seven and pie. The number system is just a way to classify numbers just like we classify things in everyday life.

In math class so far we have learned a lot about algebra and how it also connects to our daily lives. This essay summarizes everything that we have learned in math class.

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Kayla Malcolm
10/03/2012 7:57pm


Algebra is like a language, it is universal and spoken the same all over the world. Algebra is a language, spoken by mathematicians. In algebra, I have learned many things, such as variables and expressions, why we need order of operations, and why it is necessary to classify numbers.
Some people wonder, “What is a variable ?” A variable is a symbol, usually a letter, which represents one or more numbers. Variables can be used in both expressions and equations. For example, if a variable is being used in an expression it would look like this: x-9. The variable in the expression was x. The expression means “Nine less than a number, x.” Sometimes, equations and expressions will have more than one variable representing a number. For example, you might see an equation such as “4+9c-2x” The variables in the equations are “c” and “x.” To solve that equation, we would use a method called “order of operations.” Which leads us to…
Order of operations is a method used to solve equations in which more than one thing is needed to be done. A way to remember order of operations is by remembering PEMDAS, which stands for Parenthesis, Exponent, Multiplication, Division, Addition and Subtraction. You must follow PEMDAS in order to get the correct answer, however, sometimes there will be exceptions. Order of operations is important because it helps us solve equations requiring multiple steps correctly.
When classifying numbers, you are basically describing the characteristics of a number. There are many categories for classifying numbers, two popular ones being rational and irrational numbers. Rational numbers are numbers that can be represented as a fraction and a decimal. They are also square numbers. Irrational numbers are the extreme opposite.
In conclusion, this is what I have learned about algebra so far this year. Hopefully after reading this, you've learned something too !

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Jarrett Grosbard
10/03/2012 7:57pm

In math we learn many things, some like these.

In variables/ expressions/ equations we learned how variables ( variable- a symbol usually a letter, that represents one or more numbers . ) work as symbol in equations that take the place of numbers. Equation ( equation- is a mathmathic sentence that uses a equal sign ) is something that represents a expression ( expression- is a math term that can include variables, and operation symbols. ) All of these thing intertwine together to help you understand each other much better. An example of variable is 10x + 5 and x= 7 which means 7 times 10 would be 70 and plus five would be 75. An example of an equation would be 9 + 6 - 7.

Order of operations is quite simple if you study it in a certain type of method. the order has a simple way to help solve it called pemdas which stands for
P- ( parenthesis )
E- exponent
M- multiplication
D- division
A- addition
S- subtraction. simplify- is a numerical expression that is simplified to its simple form. exponent- tells how may times itself. base- is what is used as a factor. power- is what an exponent and a base make combined. evaluate- is an algebraic expression that changes based on a given number for each variable. An example of order of operations is ( 6* - 20 )4 + 10 divided by ( 7 times 5 + 2 )

Classifying numbers is very important for many different reasons. It can help you tell the difference between a ratio and a proportion. It can also help you understand different numbers in different equations. A percent could be put against a real number in a equation on why there different and know why is very important when it comes to money and groups of people.

Math can teach us many things such as things that may help us in our life.

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Jacky Lau
10/03/2012 7:59pm

Algebra is a mathematical language and in order to understand it, all of these concepts must be applied. Variables, expressions and equations are used in algebra as a way to express numbers and represent quantities. Order of operations is used to be precise when solving equations and it tells you the order to solve the equation. Classifying numbers is used to understand the number system and the concept classifying objects based on its kind. All of these forms of algebra are used to in order to have a better understanding of the language as a whole.
Each variable and expression has to do with algebraic expressions. Algebraic Expressions is a mathematical phrase that usually include numbers, variables, and symbols. So an example of variables and expressions is 8 less than N. Then it would be translated as n-8. There are 4 different words that is used for variables. Quotient is division, Difference/Less is subtraction, More than is addition , and Product is multiplication. Expressions uses numbers and variables, but Equations uses the equal sign and expressions don't.
Order of operations usually involves PEMDAS. PEMDAS stands for Parenthesis, Equation, Division, Multiplication, Addition, and Subtraction. Algebra Problems mostly has to do with PEMDAS and is used in that order. Although there is a order that is used, it may not always have to be in that order. For a question like 6/2x5 even though in PEMDAS it clearly multiplication comes first, division comes first in this situation because both multiplication and division are both in the same level. Same goes for addition and subtraction. An Example would be 4-2+3 both addition and subtraction are on the same level so you have to go from left to right.
Classifying numbers are usually " Real Numbers". Real Numbers are another form of rational and irrational numbers combined. Rational numbers can be used in a a/b form but irrational numbers can't. Whole numbers, integers, rational, and irrational numbers aren't the same. Whole numbers are numbers that are 0 and up(0,1.2.3 Etc.). Integers can be used in negatives(-1,-2,-3,-4). And as I've mentioned before Rational numbers can be used in a/b (8/10) form and irrationals can't.
Algebra is a language and in order to understand the full concept each of the Rules that is required to understand it. Variables, expressions, equations, order of operations and the classification of numbers all forms the language of algebra. In order to fully understand the concept of this language each of topics above must be the first things you will remember.

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Jacky Lau
10/03/2012 8:05pm

Algebra is a mathematical language and in order to understand it, all of these concepts must be applied. Variables, expressions and equations are used in algebra as a way to express numbers and represent quantities. Order of operations is used to be precise when solving equations and it tells you the order to solve the equation. Classifying numbers is used to understand the number system and the concept classifying objects based on its kind. All of these forms of algebra are used to in order to have a better understanding of the language as a whole.
Each variable and expression has to do with algebraic expressions. Algebraic Expressions is a mathematical phrase that usually include numbers, variables, and symbols. So an example of variables and expressions is 8 less than N. Then it would be translated as n-8. There are 4 different words that is used for variables. Quotient is division, Difference/Less is subtraction, More than is addition , and Product is multiplication. Expressions uses numbers and variables, but Equations uses the equal sign and expressions don't.
Order of operations usually involves PEMDAS. PEMDAS stands for Parenthesis, Equation, Division, Multiplication, Addition, and Subtraction. Algebra Problems mostly has to do with PEMDAS and is used in that order. Although there is a order that is used, it may not always have to be in that order. For a question like 6/2x5 even though in PEMDAS it clearly multiplication comes first, division comes first in this situation because both multiplication and division are both in the same level. Same goes for addition and subtraction. An Example would be 4-2+3 both addition and subtraction are on the same level so you have to go from left to right.
Classifying numbers are usually " Real Numbers". Real Numbers are another form of rational and irrational numbers combined. Rational numbers can be used in a a/b form but irrational numbers can't. Whole numbers, integers, rational, and irrational numbers aren't the same. Whole numbers are numbers that are 0 and up(0,1.2.3 Etc.). Integers can be used in negatives(-1,-2,-3,-4). And as I've mentioned before Rational numbers can be used in a/b (8/10) form and irrationals can't.
Algebra is a language and in order to understand the full concept each of the Rules that is required to understand it. Variables, expressions, equations, order of operations and the classification of numbers all forms the language of algebra. In order to fully understand the concept of this language each of topics above must be the first things you will remember.

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10/03/2012 8:13pm

Algebra is a language that you have to learn before you are able to understand it. You must learn about the expressions, equations, variables, PEMDAS, and classifying numbers.

Expressions is a mathematical phrase that contains numbers, variables, and an operation to solve the problem. For example & less than x would be x - 7. A variable is a symbol that represents one number or more. For example, n could mean 5. However, equations are different from expressions. Equations are mathematical sentences that uses an equal sign. For example, 5+x = 6+5.

PEMDAS is the order of the operations. Each letter represents one operation, it goes in order. First, P means parentheses, it means to do everything in the parentheses first. For example, 2(6+5) = 2(11). Second, is E, meaning exponents. This means after the parentheses, we solve the exponents. For example, 2^2+5 = 4+5. Next, M & D means multiplication and division. They both are on the same level, meaning from left to right must be solved in that order. For example, 6/12 *2 = 2*2. Same goes for A & S, addition and subtraction has the same procedure. One example would be 5+2-3+9 = 10-3+9 = 13+9 = 22.

Classifying numbers is very important to learn how to do. Irrational numbers are numbers that never have an ending decimal. For example pie, never has an ending decimal it goes on. Rational numbers are decimal numbers that has an ending. For example, 4.3 is a rational number because, it ends on 3. It is not on going. Whole numbers are numbers that are not decimal, but also not negative numbers. For example, 1, 2, 3, ... Integers are similar to whole numbers but are negative numbers. For example, -1, -2, -3, -.... are integers.

As shown in the text above, algebra is a language worth learning. Its good to know in the future, where it actually comes in handy in the future. It'll be a good prior knowledge to know and learn about.

-Samantha Mei
-Freedom.

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Carmen Yan
10/03/2012 8:31pm

Algebra is a language and in order to speak it well you must follow the rules. In this unit, I learned about variables/expressions/equations, order of operations and classifying numbers.

A variable is a symbol, usually letters, that represents one or more numbers. For example, in the equation, 2x=10, the variable is "x". It represents a number. An equation is mathematical sentence that uses an equal sign. An expression would be a mathematical phrase that can include numbers, variables and symbols. For example, this would be an expression, 2x. To turn it into an equation, it would be 2x=10.

P.E.M.D.A..S is a very useful way to solve equations with many terms and different signs. The order of operations uses P.E.M.D.A.S. It's an acronym and it stands for Parenthesis, Exponent, Multiplication, Division, Addition and Subtraction. For example, in an equation that says 6+5(10-2)x2. The parenthesis comes first so it becomes 6+5(8)x2. Then multiplication, but since there is two signs of multiplication here, you go left to right. So it's 6+40x2, then 6+80. Lastly, the sum is 86.

Number can be categorized into groups. That is called classifying numbers. There are groups such as natural numbers, whole numbers, integers, rational numbers, irrational numbers and real numbers. Natural numbers are all positive numbers starting from 1, like 1, 2, 3, etc. Whole numbers are like natural numbers except it has the number 0, like 0, 1, 2, etc. Rational numbers are numbers you can put in the form of a/b, whereas a or b does not equal to 0, like 1/2. Irrational numbers cannot be expressed as a/b, basically the opposite of rational numbers, for example, pi. Integers are all negative and positive numbers like -2, -1, 0, 1, 2 etc. Real numbers are where rational and irrational numbers form.

During this unit so far, I've learned a variety of topics for algebra. It is a big part of everyday life and it's very useful in the future. Knowing the difference between variables, expressions and equations is vital for algebra. Learning the order of operations and classifying numbers can go a long way in life.

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Taylor Southerland (Rockefeller)
10/03/2012 8:59pm

Math is indeed a language. In order to "speak" it, you must learn the rules of it's "grammar", and comprehend mathematical "sentences". In learning the basics of algebra, you'll notice yourself beginning to understand the basics of the language. Things we've focused on in algebra can be easily correlated to the adaptation to a new language.

We began exploring math as a language with the difference between two types of mathematical sentences: expressions and equations. Expressions are mathematical sentences that contain numbers, and operations without an equal sign while equations feature an equal sign. This is the only difference between the two. Within equations and expressions are variables, or symbols that represent a numerical value. This helped us learn the basics of putting a mathematical sentence or phrase together.

We moved on to reading these mathematical sentences that we learned the construction of. As you would read from left to right, in algebra, you would simplify or solve from P to S. In math, we use an acronym to remind us how to simplify, labeled P.E.M.D.A.S.| P is for Parenthesis ; E is for exponents; M is for Multiplication; D is for Division; A is for addition; and S is for subtraction. We refer to this simplification method as the Order of Operations. As all grammar in languages has irregular quirks, so does math. With the acronym PEMDAS, parenthesis is always first, and exponents are always second, but multiplication OR division can be third. When solving using the Order of Operatons, multiplication and divison, and well as addition and subtraction are done in what ever order they are written in from left to right.

Just as we classify items, we are also able to classify numbers. Types of numbers include: Natural Numbers (1,2,3) , Whole Numbers (0,1,2,3), Integers (-2,-1,0,1,2), and Real Numbers (rational/irrational numbers). Rational Numbers are any number that can be written as a simple fraction(1.5 = 3/2), while Irrational Numbers cannot (π =3.14159...). Classifying numbers is important in understanding the basic linguistics of math.

Math is indeed a language. We must learn how to "read" equations and expressions properly, and understand the operations and numbers that make them up. We do this through classification of numbers, and eventually solve through the order of operations which was all featured in our Unit 1 study.

Math is a complex language, but with the proper study, you could speak it just as fluently as you speak English, and always get your universal answer.

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Zaki Messaoud
10/03/2012 10:34pm

Within ninth grade we have learned three major things. These following subtopics are them. Expressions and Variables, Order of Operations, and classifying numbers.
First off are expressions and variables. A few definitions must be mentioned. A variable is a symbol, usually a letter, that represents one or more numbers. Here's an example (6+n=12) n acts as the variable. Next is an open sentence. An open sentence is an equation that contains one or more variables. Example: (6n +3y=30) Last but not least is knowing the difference between and expression and an equation. An equation is a mathematical sentence that uses an equal sign (x+1=4), while an expression is a mathematical phrase that may contain numbers, variables,operation symbols, and no equals sign. (6n+4)
Order of Operations is something which I like to think of as an instruction. It's telling you how to order an operation. Something used for order of operations is P.E.M.D.A.S it stands for Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction. This is the order at which you go upon solving expressions or equations.
Classifying numbers is important to have knowledge on. It involves the different groups of numbers. The four different groups of numbers which I have learned about are Whole numbers, Integers, Rational numbers, Irrational numbers, and Natural numbers. Whole numbers are Positive, non-negative numbers, including zero. Examples are 0, 1,2, and three. Integers are whole numbers that can also be negative numbers. Rational numbers are Numbers which can be put into fraction form example:( 3=3/1) irrational numbers are numbers which cannot be put in fraction form. An example of a irrational number is Pi. Last on the list is the Natural number. A Natural number is the number one and one added to it again repeatedly as much as wanted.
In conclusion, Algebra is a language which includes three major parts. (Expressions and Variables, Order of Operations, and classifying numbers.) Once you are able to understand the three topics you are able to know the language somewhat well.

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Andrew Yutsis
10/03/2012 11:10pm

There are many elements in mathematics. This due to many subcategories within math. With these many categories, math is organised in a manner aimed towards success with different calculations and real world problems.

One of the most commonlly taught and used math skills is algebra. Algebra consists of a number of basic elements. It includes your basic operations (addition, subtraction, multiplication, division) and variables to establish your algebraic equation.

The concept of a variable is used to manipulate an unknown number. The definition of a variable is classified as a symbol (typically a letter) that represents one or more numbers. With your various operations, numbers, and variables, you can now create a equation. A equation can be defined as a mathematical sentence that uses a equal sign. An expression is similar to an equation, however it does not include an equal sign.

For many students and people alike, the first math skills you learn in math, is PEMDAS or order of operations. The common acronym PEMDAS, actually does have mathematical value, besides being a completely ridiculous word. PEMDAS stands for parenthesis, exponents, multiplication/, division, addition, and lastly subtraction. This is the order in which a mathematical expression is solved, however in problems where there is both multiplication and division, the solution should be established by working from the left of the problem to the right, during the multiplication/division phase of PEMDAS.

Another important skill, is learning the different classifications of numbers. Numerical values can all fall into many different categories, approximately 6 being the most commonlly used. The 6 consist of, natural numbers, whole numbers, rational numbers, irrational numbers, real numbers and finally integers. With knowledge of each of the 6 main classifications, one can easily organize his numbers sets or groups.

With a solid foundation, and a good understanding of the concepts of these 3 subtopics, one can create a solid base in his or her algebraic skills. I like to explain subtopics through a simile I created. Think of math as a camera and the subtopics as the tripod. If your only skilled in 2 of the subtopics, your camera will fall as 1 leg of the tripod is missing. However if you have all around solid knowledge on all 3 subtopics, you tripod will safely hold and support your math.

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Jackie Shi
10/04/2012 11:49am

A variable is one or more number that is represented by a symbol. The symbol is usually represent by a letter. The variable is usually used in a expression.

In order of operation the first step is Parenthesis.Parenthesis is the two () things that show that it is suppose to be done first. The parenthesis is just the first step of Pemdas

Secondly you have to do exponents. In the exponents the people have to know about the base and the power. This determines hoe big the exponent will be.

Lastly the people have to know about the last two steps. First you have to Multipliy or Divide the number that shows up first. And the final step is to add or subtract from the rest of the numbers.

To adress the last question I believe that classfiying numbers are important because it shows what numbers are in what catgories. With this people can stop getting mixed up by what to call the numbers.

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Dave Sanchez
10/04/2012 2:27pm

The first thing you have taught us is that, "Algebra is a language" that statement is important because if you have two professional mathematicians from two different countries and you give them the same problem they should get the same solution.

A variable is a symbol usually a letter that represents one or more numbers.
In some equations you have to find out what the equation is. But other times you know what the number is but you have to figure out the equation

We need order or operations because its the order in which we solve problems.
P- Parenthesis
E- Exponents
M/D- Multiplication and Divison
A/S- Addition and Subtraction

Its important we classify numbers because it apply's to tons of categories. Another reason is because we need to identify numbers. To see if their rational,positive,irrational etc.

In conclusion I think we should all know this because Algebra is a language

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Jackey Liu
10/04/2012 2:48pm

Algebra is just like speaking a language. In order to be good at Algebra you must know the different rules just like in speaking a language. The rules to Variables, Equation/Expression, the order of operation (PEMDAS), and last but not least, the reason to why we need to classify a number. A algebraic expression is a mathematical phrase that can include numbers, varaible, and operation sym

Variable is a symbol,usually a letter that represent one or more numbers. A equation is a mathematical sentence that uses an equal sign. A algebraic expression is a mathematical phrase that can include numbers, variable, and operation symbol. An example of a variable is "n" or "x", basically almost any letter. Although a expression and equation is kind of similar, a expression does not contain an equal sign. A example of a expression and equation is "n+7" and "6n=15".

Order of operation is the rule on solving equation or expression. Order of operation are sometimes refer as "Pemdas". Pemdas stands for parenthesis, exponent, multiplication, division, addition, and subtraction. Although multiplication comes before division and addition comes before subtraction, they are on the same level. For example "(5 + 8) -2+3 x 2", you would first start with solving the parenthesis. Then you would subtract and not add because subtraction and addition are on the same level. Then you would multiply to get your answer. Remember this, always solve from left to right which means if you have a division and multiplication next to each other, you would do the one that comes first.

Classifying a number is important because if you don't classify a number, you will all the numbers mixed up and confuse yourself. In math it's best to keep organize so classifying a number is a way to do it. Classifying is like putting numbers into the groups they belong in. The groups are natural numbers, whole numbers, real numbers, rational numbers, integer, and irrational numbers. Whole numbers are positive numbers like 0,1,2,3,4, and so on. Natural numbers are just like whole numbers, but it does not contain the "0". Integers are positive and negative numbers. Rational numbers are fractions and numbers with negative like 2.51. Irrational numbers are numbers with never ending such as pie. Real number consist of both rational and irrational numbers.

In conclusion, Algebra is very similar to language speaking. In order to master it, you must learn the basics and rules. Variables are symbols and letters that represent a number such as "x". Order of operation is the rule to solving a expression or equation. Classifying numbers is organizing numbers into group and it is important because it keeps you organized.

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Alena Berry
10/04/2012 2:51pm

Algebra is like a language. You have to learn to read, write, and decipher what it means. You have basic grammar rules, in algebra it’s PEMDAS. You need sentences (expressions and equations), and the letters (exponents). Last but not least, you need definitions for your words (classifying numbers).
Expression is a mathematical phrase containing numbers, operations, variables, and no equal sign. An example of an expression is 2x+3. Equation is a mathematical sentence that uses an equal sign. An example of an equation 10x+5=6. Expressions and equations might sound the same, but there is one distinct difference that sets the two apart, equations always include an equal sign, while expressions always don’t. Variables are symbols (that usually appear in expressions and equations) that are often expressed as letters, but they represent numbers.
An important part of Algebra is Order of operations, better known and expressed as PEMDAS. P stands for parenthesis, e stands for exponent, m for multiplication, d for division, a for addition, and s for subtraction. One misconception about PEMDAS is that because the multiplication goes before division in the acronym, so people do multiplication even when division is on the left. That’s wrong! You do multiplication and division left to right, and complete whatever comes first, same with addition and subtraction. An example of PEMDAS in use is as follows.
(2+3)+2^2×4/2
First parenthesis:
5+2^2×4/2
Next Exponents:
5+4×4/2
Then multiplication:
5+16/2
Then division:
5+8
And last but not least, subtraction:
13 is the answer.
Classifying numbers include integers, whole numbers, irrational and rational numbers. Whole numbers are natural numbers from 0 and up. Integers are Integers are positive and negative whole numbers. Whole numbers are positive, natural numbers starting from one, excluding fractions and decimals. Rational numbers include positive, negative, decimals, and fractions, as long as they have an end to them (example is .45). Irrational are numbers with no end (example is pi or the square root of 7).
While algebra is difficult, like a language, it is worth it in the end. It becomes easier once you learn the significant, basic things, everything sprouts from those, and the basics are the roots. These basics include expressions, equations, variables, order of operations, and classifying numbers.

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Layla Diaz
10/04/2012 4:49pm

Layla Diaz
Freedom - Oct.4th.2012
Understanding Algebra.

Algebra is a language and to speak it well you must follow the rules. In this paper I will explain the difference between expressions and equations. I will explain order of operations and classifying variables.
Often people confuse a mathematical expression from a mathematical equation. A expression is a mathematical phrase that can include numbers, variables, and operation symbols. For example:
x+8
An equation is a mathematical sentence that uses an equal sign. For example:
x+8=
The difference is the equation sign. A tip for remembering this; EQUAtion. The first four letters are capitalized because when I see those for letters they remind me of the word equal. This lets me know that I need to use the equal sign.

In algebra there is a system to solving a problem. This is called order of operations. Or P/E/M-D/A-S.
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction.
You use pemdas to solve problems. When solving with pemdas you solve left to right (as if you are reading).

A major part of any math is classifying numbers. There are six ways to classify numbers.
1) Real number- any rational or irrational number
2) Rational number- an integer or a fraction
3) Integer- negative numbers
4) Whole number- a number without fractions
5) Natural Number- the number 1 and any other ordinary number (5,6,10)
6) Irrational- a number that goes on forever and ever. For example Pi!

Algebra is a language and in order to speak it well you need to follow the rules. You need to understand the difference between and expression and an equation. You need to understand and follow the rules of PEMDAS. You need to be able to categorize numbers properly. If you follow this you will speak algebra well.

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Allyson D'Antonio
10/04/2012 5:08pm

Math is a subject that we’ve been taught for years. Something’s have gotten repeated, and some have only recently been introduced to us. The thing is, that the concept of Math as a language is a new idea to me, but something that I’ve come to realize is that Math, as a language, is one of the easiest to learn. You have sentences, words, and letters/numbers, such as expressions, equations, and variables. Then you have the rules of the rode, which in math is order of operations, and lastly you have the way that we classify words, similar to verbs, which we call classifying numbers.
Math as a language needs words of some kinds, as well as numbers and sentences. That’s variables, equations, and expressions. Variables are similar to letters, helping form the language. Its actual definition says that a variable is a symbol, usually a letter than can mean one or more numbers. After that you have equations, which can be used much like words, and expressions that are similar to sentences. An example of something like this is 2n+14=26.
The order of operations spells out clear and simple rules for how the mathematic language is supposed to go. It explains what should go before something else as well as showing us how to solve things. PEMDAS (Parenthesis, Exponents, Multiplication/Division, Addition/Subtraction) is like a guideline to math problems. The order of operations spells out plainly; you do the problems in the parenthesis first, and then the exponents after that. Then, you do multiplication or division, depending on which comes first left to right, and then does the same with addition and subtraction. That’s it plainly. A problem like that would be 5(x+6)-10= 40, where you do (x+6) first, then multiply that by five, and then subtract 10 from that, equaling 40. It’s really quite simple.
Classifying numbers was a really new concept to me. In the math language, we needed a way to describe things. We do this to help our minds make sense of things. We classify numbers for the same reason. We need to find categories so that we can make things simpler, more organized. I mea, if you were filing something, would you put the number 2 with the number 3.3333333333… no! You would put them into different categories, so you wouldn’t get confused! This way we can figure out where things go and make sense of them when we need to.
Math is a language that is taught in hundreds of places around the world. It is the one language that always stays the same, always has one correct answer. It is a universal language that every student I have ever known is being taught to speak.

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John Sanchez
10/04/2012 5:24pm

Math, specifically algebra, is important to understand. Algebra is a language and algebraic expressions model real-world quantities. Algebra is a language and in order to speak it well one must follow the rules. The number system is just another way to classify numbers, just as how we classify things such as birds, food, and music.

An algebraic expression is an expression built up from constants, variables, and a good number of algebraic operations. Variables are letters used to express an unknown number, such as n and x. Equations are different from algebraic expressions, as they can be solved, rather than just simplifying it, as how you do with expressions. A good example for an equation would be 2+3=5, rather than 2x+3, which is an expression.

The Order of Operations is one of the most important things to remember in math, being the difference from getting an answer in the thousands and receiving two-digit answers. P.E.M.D.A.S. is the highlight of this subtopic, since it is the most important thing to remember when completing algebraic expressions. The P is for parenthesis (), E is for exponents (2 to the 4th power), M is for multiplication (2x3), D is for division (2/3), A is for addition (2+3), and S is for subtraction (2-3). Parenthesis comes first when completing an expression, then exponents, then either multiplication or division (whichever comes first), then finally addition or subtraction (again, whichever comes first). To solve an equation using P.E.M.D.A.S., one must use an expression, like 7 + (6 × 5^2 + 3). Since there is a sub-expression in the parenthesis, you must complete that first: 5^2=25 = 6+25+3 = 34. Now that you completed what is in the parenthesis, you add the two variables together: 7+34=41.

Classifying numbers are just the same as classifying food, people, and music. There are multiple types of classifications for numbers, such as real, rational, and irrational numbers, along with integers. A rational number is a number that you can write in the form a/b, where a and b are integers and b cannot equal 0, such as 26/1. An irrational number is a number that cannot be expressed in the form a/b, such as 3.456434 or 7.12905336436. Real numbers are a set of rational and irrational numbers, such as 1, 2.3, -4.0343, and 4. Whole numbers are any number from 0 and forward, like 1, 2, 3, 4, 5, etc. Integers are literally whole numbers that also include the negative value, such as -2, -1, 0, 1, 2, 3, etc.

Math, especially algebra, is a topic that is dealt with regularly in the real world; it is the most important thing to remember besides being able to read, write, and speak. Algebra is broken up into multiple categories, such as order of operations, expressions and equations, and classifying numbers. Algebra is a language in today's world that is forever changing.

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Sarah Mouddene
10/04/2012 5:31pm

To fully master Algebra you must follow by the rules just like a game has a set of rules, but many people believe that Algebra consists of just numbers and a few addition and subtraction signs thrown in. But it’s not, Algebra is a language and to be capable of understanding it you must know Order of Operations (The rules of Algebra), Variables (The product of an equation or expression), and the ability to categorize numbers.

The Order of Operations are like the set of rules in a cardboard game or the vowels in english ! Without them, you would get many confusing answers and many of you think oh it’s just a lousy problem. But a lot of times math can affect people’s lives and one wrong mistake and they could lose it all. Order of Operations are mainly known as PEMDAS which stand for P=Parentheses, E=Equations, M=Multiplication, D=Division, A=Addition, and S=Subtraction. Lets say you have the equation 9-3+(5-4) you must always start with the parentheses because in the Order of Operations parentheses must always be solved first .

Variables are the products of an expression or equation and they’re like the shoelace in a shoe ! They’re really important in Algebra, but you have to be able to use them right. For example in an equation there is the Dependent Variable and the Independent Variable. Usually x is the Independent and y is the Dependent. So in an equation it usually looks like this y = 3x+4, and so x and y are the variables !

Categorizing numbers if very important in math because you must always know what type of numbers they are and what sort of effect they have. The categories of numbers are Real, Integer, Irregular, Regular, and Whole Numbers. If we didn’t classify numbers then lets say you have -3+2= and if we didn’t classify -3 as a integer we would have the answer being 5 or -5.

Algebra relates to many things in life, everywhere there are numbers they surround our world. But numbers can also affect our lives, lets say you put the wrong number in a SATs test and end up having to go to a lousy college where with that degree you might not be able to find a job. Everything has an effect , it will always be cause and effect and that implies for Algebra too !

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Jeremy Gurvitz
10/04/2012 5:39pm

What I have learned about in Algebra so far would be expressions and equations, order of operations and classifying numbers.

First expressions are "a mathematical phrase that can include numbers, variables and operations symbols" an equation "is a mathematical sentence that uses an equal sign" and variables are "a symbol usually a letter that represents one or more numbers" last there is an open sentence the are"equations that contain one or more variables"

In the order of operations(p.e.m/d.a/s)and goes Parenthesis Exponent Multiplication/ Division Addition/Subtraction those slashes mean that it won't be in that order depending on witch is first right to left.

classifying numbers includes things like whole numbers that are any numbers that don't have a fraction or decimal and be above zero(to the right) then there are rational numbers that can be written as fractions example 13 would be 13/1. Irrational numbers cannot be written in fractions for example pi.

this is a vary vague explanation of what I have learned so far. It is good to know what you are doing and not to just know how to solve it.

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Patryk Borkowski
10/04/2012 5:44pm

Algebra is a language, and in order to speak it well you must follow the rules. Algebra has a lot of things in it, the main things being: Variables/Expressions/Exponents, the order of operations,and classifying numbers. Without these main components, Algebra would impossible. I will explain each of these main components, what they are, and give examples in this paper.

Algebra is all about variables, expressions, and equations. A variable is a symbol that represents one or more numbers. An expression is a mathematical sentence containing numbers, variables, and operating symbols. An equation is a mathematical sentence that uses an equal sign. The difference between an expression and an equation is that an equation has an equal sign. For example, 4n+3 is an expression, and 4n+3=b is an equation. Four plus the quantity of 2 and 3 in an algebraic form would be 2/3+4.

Without the order of operations, there would be millions of ways to solve complicated problems. The order of operations is a set of rules you must follow when solving problems such as expressions and equations. PEMDAS stands for parenthesis, exponents, multiplication, division, addition, and subtraction. For example, in order to solve 6 divided by 2 times 5, you would start with 6 divided by 2, and that times 5, which would be 15. Another example would be 4-2+3. You would start with 4-2 first, and then add 3, so it would be 5.

In order to understand algebra, you must know how to classify numbers, There are many types of numbers: Natural, Whole, Integers, Rational, Irrational, and real. Natural numbers are positive numbers such as 1,2,3,etc. Whole numbers are natural numbers, but the include 0. Integers have negative numbers, zero, and positives. Rational numbers are numbers that can be fractions, and Irrational numbers cant be fractions. Real numbers are rational and irrational numbers. Some examples of these types: Irrational=Pi, Integer=2, Rational=3/6.

Consequently, Algebra is a language and in order to speak it well you must follow the rules. Algebra consists of three main components: Variables/Expressions/Equations, the order of operations, and classifying numbers. Without these three rules Algebra would not be possible.

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Grace Yip
10/04/2012 5:58pm

Algebra is a language and if you wish to understand it you must follow the rules. Some of the things I had to learn before I started understanding algebra were variables, equations, expressions, order of operations, and classifying numbers. For me you would need to learn all of the things stated before you can fully understand algebra.
Variables are a letter you use to represent one or more numbers. An expression is a mathematical phrase that can include variables, symbols and numbers. An equation is an expression but with an equal sign. You need to be sure you don’t get them mixed them up. An example of a variable could be “x” or any letter that you want. An example of an expression is 4x-5. An equation is 45x+53=143.
Another thing you need to know when learning algebra is Order of Operations. For order of operations you need to follow PEMDAS. PEMDAS stands for:
P-parenthesis
E-exponents
M-multiplication
D-division
A-addition
S-subtraction
If there is both multiplication and division you do there problem from left to right, you do the same thing addition and subtraction. An example on PEMDAS is 5(45x2+10). To solve you first multiply 45 by 2 which gives you 90. Then you add 10 which gives you 100. Then you need to multiply by 5 which would give us our answer of 500.
One last thing you need to know is how to classify numbers. There is real numbers, whole numbers, integers, rational and irrational numbers. Real numbers are numbers that can be rational and irrational. Rational numbers are that can be written as a ratio of 2 integers for example 1 ½ is a rational number. Irrational numbers are numbers that can’t be written as a ratio of two integers for example pi and the square foot of the seven are both irrational numbers. Whole numbers are nonnegative integers like 1,2,3,4 etc. Integers are whole numbers and there opposites like 1, 2, 3,-3,-10 etc.
Those were the things I had to learn to understand algebra. Algebra is a language and you don’t just learn languages easily. You need to earn all the little part that makes it a whole. That is exactly what I did to learn about algebra.

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Anderson Alleyne
10/04/2012 6:21pm

Their is alot to know about algebra.Algebra is a language but they are a few things to understand.
An expression is a mathematical phrase that can include numbers,variables,and opperation symbols.Such as n-5 which is 5 less than a number.The difference between an expression and a equation is a equation has an equal sign.Such as n-5=2.Variables is a symbol usually a letter,that represents one or more numbers.Such as n-5, n is the number.
The order of operations is PEMDAS.It stands for parentheses,exponents,multiplication,division,addition,and subtraction.Division and multiplication and addition and subtraction rank equally.You go from left to right. For example 2+5*3,you multiply before you add.Another example is 9*3/9,you just go from left to right.Which the answer would be 3.
Whole numbers are positive numbers such as 0,1,2,3,4.Integers are whole numbers including negative numbers such as -3,-2,-1,0,1,2,3. A rational number has an end such as the square root of 9 which is 3.It is also a number that can be expressed as a quotient or fraction. Irrational numbers do not have and end such as pie and the square root of 5. It can also not be expressed as a simple fraction. Also natural numbers is a whole number without 0.
Their is alot to know about algebra.Expressions,equations,variables,order of operations,etc.For example PEMDAS,it stands for parentheses,exponents,muliplication,division,addition,and subtraction.Also classifying numbers such as rational or irrational.

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Eldin Pjetrovic
10/04/2012 6:23pm

Math is something you use almost everyday and is needed if you want to get anywhere in life. Algebra is a language, and to understand it you need to know the rules. Some of the thing you need to know are Variables,Expressions, and Equations, Order of Operations, and Classifying Numbers.

One thing you need to know about math is Variables, Expressions, and Equations. A variable is a symbol, usually a letter, that represents one or more numbers. Ex: x+3=? unless someone tells you what x is, there is no way of solving this equation. An expression is a mathematical sentence that has no equals sign. Ex: 7x4 or 15-7. An equation is a mathematical sentence with an equals sign. Ex: 7x4=28 or 15-7=8.

Another thing you need to know about math is Order of Operations. An easy way to remember the order of operations is PEMDAS.
P- Parenthesis
E- Exponents
M/D- Multiplication and Division (what comes first from left to right)
A/S- Addition and Subtraction (what comes first from left to right)
Ex: (1+2)+3. This would be solved by first solving whats in the parenthesis then adding the two numbers together.
Ex: 1+2x3. This would be solved by multiplying first even though addition is first from left to right.

Another thing you need to know about math is Classifying Numbers.
Natural Numbers: 1, 2, 3, 4, 5, etc.
Rational Numbers: Any number that can be written as a ratio of two integers.
Irrational Numbers: Any number that cant be written as a ratio of two integers.
Real Numbers: A number that is either rational or irrational.

In conclusion math is very important and without it, you wont be able to have a good life. So if you want to go somewhere in life, learn the language of algebra. Variables, Expressions, and Equations, Order of Operations, and Classifying Numbers are a few of the many of the things to know about math to understand math.

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Jamice Thompson
10/04/2012 6:27pm

So far, I have learned about new vocabulary, and the differences between equations and expressions. Variables and expressions was about interpreting expressions that represents a quantity in terms of its context. Exponents and order of operations was about using order of operations for algebra to communicate algebraically. Real numbers was about classifying numbers.
In the first topic we learned that variables , expressions, and equations are all a part of an algebraic problem. A variable is a symbol, usually a letter, that represents more than one number. that means if there is an equation like 2+n, n would be the variable because it represents a number. An algebraic expression is a mathematical phrase that includes numbers. An equation is a mathematical sentence that uses an equal sign. These two vocabulary words are different because one is a phrase (expression) and another is a mathematical (sentence). The equation must have a solution with an equal sign or it it is just a phrase.

The next topic is about using order of operations, (PEMDAS) in your algebraic operations. We learned that there are rules in algebra and they require order of operations. We learned about different ways to solve equations using PEMDAS and simplifying the equations to find the solution.

The last thing we learned so far was real numbers. In this topic we talked about classifying numbers. We talked about rational, irrational, real numbers, inequality, opposites and absolute values. All of these vocabulary words lead up to classifying numbers. Classifying numbers is basically separating numbers based on their factors and what they add up to.

We have been learning about variables and expressions, exponents and order of operations, and real numbers. All of these topics make up algebra. We use all of these methods to find solutions for algebraic sentences.

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Justin Holch
10/04/2012 6:36pm

Math has a lot of topics and subtopics to learn about in the little over a decade your in school. These many things can help you in every day life your in the job you end up having. For me algebra is the most important one. There are expressions, equations and variables. There is order of operations (PEMDAS) and then there is classifying numbers.
Expressions are a mathematical phrase that can include numbers, variable and operation symbols. Then there are equations which are similar to expressions but they have to have an equal sign to be called an equation. A variable is a symbol usually a letter that represents one or more numbers. Here are some examples of expressions and equations.

Expression: 7 – x or in written from (seven less then a number)

Equation: 5 + 5= 10


When doing order of operations you have to follow same very simple steps to figure what looks to be a very complicated equation. PEMDAS that’s it you remember that you will be fine.

P= Parentheses
E= Exponents
M= Multiplication
D= Division
A= Addition
S= Subtraction

Now if you don’t know what exponents are they are the little number about a regular number and they tell you how many times or multiply something by. Now you must go from left to right with the equation no matter if its M/D or A/S but all the M/D must be done first. Then A/S.

Classifying numbers consist of the following categories…
• Rational Numbers: A rational number is any number that you can write in the form a/b where A and B are integers. For example (a/b a

• Irrational Numbers: Cannot be expressed in the form in which a/b, a and b are integers. (Fractions)

• Real Numbers: 5, 6, 7, 8, 9, 10…

• Integers: -3, -2, -1, 0, 1, 2, 3

• Real Numbers: Are numbers that can be put on a number line. They can include fractions.

In the end math is an important subject where everything that you will learn will probably benefit you in any thing you end up doing in life or in school. Learning how to solve equations and expressions, order of operations and classifying numbers will help you in math all the way around.


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Kyra Hagerman
10/04/2012 6:39pm

"What I've learned in Algebra So Far"

Expressions, Equations, and Variables have been an easy topic for. This is mainly because I understand it. Most of the time in math, if you understand the concept, the rest is easy. This topic for me, like other topics, is like the song "Happy Birthday" to a piano student; if you know how to play the piano it's a simple song and you can play it well, but for someone with no experience with a piano, it can be very difficult.

Like Expressions, Equations and Variables, Order of Operations was an easy topic. Again, it's all about understanding the concept. However, Order of Operations was a bit more difficult because the smallest mistake can have a big impact. If you mess up one little thing, you get the problem wrong and that will delay you progress with the topic. While this has happened to me many times, overall I'm good wit Order of Operations.

Classifying Numbers is the hardest of the three topics for me. Like with the second topic, little mistakes would throw me off, preventing me from progressing and getting better. I made little mistakes more often when learning this topic than with the other two topics, so that's why I found this one the hardest.

In conclusion, like many people, I have had my high points and low points in algebra. Overall, though, as long as I practice and have people to help me, I can do anything I set my mind to.

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Tynasia Scott
10/04/2012 6:39pm


Everywhere you go, math can be used. Algebra is just like a language.To learn the rules of algebra, you must understand it. Some things algebra includes are variables/expressions/equations, order of operations, and classifying numbers.


A variable is a symbol, usually a letter that represents one or more numbers. An example of an variable is x=1. An expression is a mathematical phrase that can include numbers, variables, and an operation symbol. For example 6x+1 is an expression. An equation is a mathematical sentence that uses an equal sign. An example of an equation would be 6x+1=20. The difference between an expression and an equation is the equal sign. An expression doesn't have an equal sign, but an equation does.


While using order of operations, PEMDAS is always used. To get the answer right, you have to follow the order. P is for parenthesis, E is for exponents, M is for multiplication, D is for division, A is for addition, and S is for subraction. For multiplication and division you solve whichever comes first ( left to right. ) For additon and subtraction, you also solve whichever comes first ( left to right. ) An example using order of operations/ pemdas:
8/ (9-7) + ( 13/2)
8/ 2+ 6.5
4 + 6.5
Answer: 10.5.

Simplify is a numerical expression, you replace it with it with its simplest name. For example if you have a fraction that is 5/10 it simplifed to it's lowest terms would be 2/5. An exponent tells you how many times a number, the base is used. Example: 5 to the 2nd power would mean 5 times 5. Power has 2 parts, a base and an exponent.


Classiflying numbers is figuring out what number goes in what category. Some of the categories are natural numbers, whole numbers, rational numbers, irrational numbers,and real numbers. Natural numbers are 1, 2, 3, 4, 5, etc. Whole numbers are 0, 1, 2, 3, 4, 5, etc. Rational numbers are any numbers that you can write in the form a over b where a and b are integers and b does not equal 0. Irrational numbers cannot be expressed in the form a over b, where a and b are integers. Rational numbers, and irrational numbers form the set of real numbers.

Math will be everywhere you go. You will need to know math in order to get through life. Math will help you in the future. Algebra is just like a language.

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Athena Villard
10/04/2012 8:07pm

I have learned a lot of different math strategies in the years. A few of those strategies are using variables, expressions, and equations, order of operations, and classifying of numbers. We are constantly using these strategies fluently, as if they are a language that comes naturally to human kind.

Expressions and equations are the ways you will usually see a number problem. An expression has no equal sign, but an equation does. Variables are number substitues, in the form of a letter. For example 4n is an expression with a variable; but 4n=12 is an equation since the equal sign is used here. The difference between an expression and an equation is that an equation shows that two expressions are equal and the expression is the one on either side of the equal sign in an equations.

Order of operations is a strategy you use when an equation has more than one kind of an operation in it. The easy way to remember how to use this strategy is to use the acronym called PEMDAS.
PEMDAS stands for:
P:erenthesis
E:xponent
M:ultiplication
D:ivision
A:ddition
S:ubtraction
Also, with multiplication and division you go in order from right to left and the same applies with addition and subtraction. For example, if you need to solve the equation 6/2•5=x you need to use division first because its first on the left. The answer to this equation is x=15. Order of operations is one of the most used strategies in math, and most useful.

Classifying numbers is a good strategy to know. The categories are whole numbers, integers, rational, and irrational. A whole number is any number that is 0 or more, unincluding decimals or fractions. An integer is any non-decimal number. A rational number is any number that you can write in the form a/b, are integers, and are not zero, and they have to be terminating decimals if they have decimals. Irrational numbers cannot be expressed in the form of a/b, where a and b are integers, pi is an irrational number that is non-terminating, for example.

All in all, I learned a lot of different algebraic strategies, they provide much help.

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Janey Singh
10/04/2012 8:08pm

Algebra is a language that we need to learn because it is something that we will need to know for everyday life. Algebra has many parts to it like variables, expressions, equations, order of operations, and classifying numbers. These are things that people need to know to be able to do any algebra work.

Variables expressions and equations are all used in algebra. They are very important to understand because they will help you solve problems. Variables are letters that are in the place of a number when the number is unknown like 5n. An expression is a mathematical phrase that includes variables, numbers, and operation signs like 5n+7. An equation is a mathematical phrase that uses numbers and operation signs like 7+9. These are very important things to know because they is the language of algebra and that is a good language to know.

Order of operations is when you have an equation with more than one operation and you have to solve it using PEMDAS and that stands for parenthesis, exponents, multiplication, division, addition, and subtraction. You have to follow the order of operations to be able to get the correct answer.Order of operations is very important even though they don't look that important. Depending if you use PEMDAS your answer will be very different like (3+3)^2=36 that is the answer if you use PEMDAS you get 36 if you don't you might get answers like 11.

Classifying numbers is when certain numbers fit in a certain category. A whole number is when the numbers are from 0 to positive infinity like 546. A negative number is any number from 0 to negative infinity like -758. A rational number is a number that has a fraction like 2.5. A irrational is when the number keeps going on and on like pie 3.1415926... All of these categories are very different even though they are all numbers that we use all the time.

I have learned a lot in algebra so far, I have learned about variables, expressions, and equations that are the language of algebra. I have also learned about the order of operations and classifying numbers. This is very important in algebra because it can help you figure things out even outside of school and that is why it is important to learn the language of algebra.

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Raisa Talal
10/04/2012 8:13pm

There is a question that everyone must know,"Why is algebra considered a language?" Algebra is considered a language because mathematics contain numbers and letters,and everyone in the world should understand numbers and letters.Also algebra can model real world quantities,it is also important that mathematicians be precise and organized because you can risk some ones life and it will effect them and the world surrounding us.
I will apply the rules of algebra by using the subtopic of variable/expressions/equations.Here are the definitions for this subtopic. A variable; is a symbol,usually a letter that represents one or more numbers. An Algebraic Expression is a mathematical Phrase that can include numbers variables and operation symbols. An Equation is a mathematical sentence that uses an equal sign.An open sentence is an equation that contains one or more variables. An example of this would be t minus 15 which is t-15. The difference between an expression is that it's a problem that only includes numbers,variables, and operation symbols,and with an equation its known as a mathematical sentence that includes an equal sign.
I will apply the rules of algebra by using the subtopic Order Of Operations.Here are the definitions for this subtopic. simplify means to replace an expression with its simplest name. An exponent is a number that shows repeated multiplication. A base is a number that is multiplied repeatedly. A power is the base and the exponent of an expression of the form a to the power of n. evaluate is a substitute that is given a number for each variable, and then simplify. An example of this would be 5 to the power of 3 +90/3. P.E.M.D.A.S stands for parenthesis( ),exponent x to the power of 2,multiplication *, division /,addition +, Subtraction - .The way you would solve for 6/2*5 is by using P.E.M.D.A.S,multiply first then divide. another example is that,you can solve for 4-2+3 by also using P.E.M.D.A.S. Add then subtract, and thats how you use P.E.M.D.A.S
I will apply the rules of algebra by using the subtopic of classifying numbers.Here are the definitions for this subtopic.they are complexed numbers real numbers,rational numbers,integrate numbers and natural numbers. the example; natural numbers
N={0,1,2,3,4,…}
variables,expressions,order of operations and classifying numbers involve simplifying equations also it requires to understand the language of algebra.

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Kaylah Tucker
10/04/2012 8:20pm

Kaylah Tucker
Empire

Math is a very important subject because you use it every day in your life. If you don’t know Math, it is easy for someone to take advantage of you. For example, if you go to the store and by something, you have to know how much to give and how much change you should get back. Some people find Math easy, and some people find it difficult. But, there are many terms in Math that can help you to understand what you need to do to get it right.
There are many terms that are used in Math. Two algebraic terms that are used a lot are equation and expression. An equation is a mathematical sentence that uses an equal sign. An expression is a mathematical phrase that can include numbers, variables, and operation symbols. Very often, people get mistaken by these two phrases because of how similar the meaning is. The differences between the two words are that an equation is a mathematical sentence, and an expression is a mathematical phrase. There are also other mathematical phrases used in math like variable. A variable is a symbol, usually a letter that represents one or more numbers. For example, 6 less than a number is n-6. The n represents the variable.
PEMDAS is a formula that is used in Math. PEMDAS stands for (P) Parenthesis, (E) exponents, (M) multiplication, and (D) division, (A) addition, and (S) subtraction. The PEMDAS is very important because that is the order of operation in a math problem. It is basically a tool we need to answer an expression. For example: 63/2 X 5. You follow the order of PEMDAS when you are solving the expression. If an expression doesn’t have any of the elements in PEMDAS, for example, parenthesis or exponents, you skip those steps and move right along.
When you classify numbers, you want to make sure they are under the right category. In Math, those categories are rational numbers (1/2), irrational numbers (for example, pi), and real numbers. The difference between a whole number, an integer, a rational number and irrational numbers is that since integers and whole numbers are listed under rational numbers, then the real question is: what is the difference between a rational number and an irrational number. The answer is that rational numbers can be shown as a ratio of two integers, and an irrational number cannot be expressed in that way.

What I have learned in Algebra so far has been helpful and it has made me a better Math student. I always go back to the terms that I have learned and it helps me to figure out a problem because it tells me what I need to do. Overall, Algebra is going well for me so far, and I am hoping that I will continue to learn and do well.

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Dorian Hoxha
10/04/2012 8:56pm

What is algebra? Algebra is a part of math that makes symbol like letters of the alphabet, stand for numbers.Instead of calling something a number, it is used as a variable.Algebra is like a language because you have to translate it and solve it.
A variable is a symbol for a number we don't know yet.It is usually a letter like x or y.This method of solving problems is called Algebra.An expression is a mathematical statement that can use numbers, variables, or a combination of the two.sometimes, there are operations but there is never an equal sign.An equation says that two things are the same, using a equal sign.An example of an expression is a + b – c. An example of an Equation is 5+5=10.A verbal expression is a math expression written in words.so if your homework says 5+x then the verbal expression would be "five more than a number x". These are easy to translate, you have to work your way backwards.So if your homework says "n less than 5" you have to do 5 - n,
The order of operations is the rules of which calculation comes first in an expression.A tool used to help understand the order of operations is "PEMDAS". "PEMDAS"stands for parenthesis, exponents,multiplications,division,addition,subtraction When you are doing a order of operations problem, you need to do it based on that order.For example"4+8/2" You divide 8 and 2 first because division comes before addition. then you get 4, you add both and get 8.Sometimes you need to follow the "PEMDAS" rule differently. When its multiplication and division you have to do it from left to right, so now the tool is "P,E,MD,AS".If multiplication comes first you have to do it before division.
Classifying topics is when you can differentiate each real number.
An irrational number is a number that can be written as a decimal, but not as a fraction.An rational number is a number that can be written as a fraction where the numerator and denominator are both whole numbers.Wholes Numbers are numbers without fractions ; integers.Integers are numbers that are not fractions;whole numbers, that can also be negative.Irrational numbers include: π, √3. Rational numbers include:3/4,0.125. Rational numbers end and can also be fractions but irrational numbers dont end and cant be fractions. Integers include:-1,-2,1,2.Whole numbers include:1,2,3,4. Whole numbers cant be negative and integers can but both can have 0 as classified.
There are many types of algebra but the order of operations,expressions and variables and equations, and the real number system are key things for mathematicians to learn and understand. The basic rules and operations of algebra are one of the main branches of mathematics.

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Damary Guzman
10/04/2012 8:58pm

Speaking a different language is pretty much the same as learning about Algebra. There are rules that have to be followed in order to speak the language well. In Algebra, you have to make sure you follow the correct rules for solving order of operations problems (PEMDAS).

Expressions, equations, and variables are the main concepts to a problem in algebra. Although, there is a slight difference between an expression and equation. An expression is pretty much just an equation except the difference is that expression DOES NOT include an equal sign. For example, 2x-4=4 is an equation. If you were to remove the equal sign (transforms to 2x-4), then you would end up with an expression. There is another part to algebra that includes variables, the main function in algebra. A variable is any number that is substituted by a letter. For example, when you have an equation: 2x-4=4, you would have to end up solving for x and finding (using math, of course) the number, which x=4.

In order to to solve an algebra problem, you would have to use a simple system called Order of Operations. In order to follow the system, you have to follow its main rule function: PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction). There is a slight confusion while doing this rule, though. When solving an algebraic expression, you have to do it from left to right, meaning if the problem has a multiplication sign first and then a division, you would solve the multiplication first then continue on to solving it with division. This rule also applies to the subtraction/addition part of PEMDAS. Following rules in algebra are essential to getting the correct answer.

Although it doesn't seem like it, but there are different types of numbers. Wholes numbers are basic, simple numbers like 1,2,3,4. Integers are numbers that include negative numbers ( -1, -2, -3). Rational numbers are numbers that include decimals and fractions. Irrational numbers are the opposite of rational numbers; they are numbers that never end (rational numbers have an end to them decimal wise). And lastly, real numbers are just numbers that get to have the best of both worlds; they have rational and irrational numbers.

Overall, knowing everything about algebra is key to understanding it and solving it well. Following its rules is highly important. Order of Operations is a very useful and important system to use when solving equations or expressions, which are two different things. Algebra can be a challenging language, but following the rules will help you understand it and proceed to excel in it.

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