Go To:  http://www.101science.com  -  Your internet science directory and learning center.

What is Algebra?

Algebra is a branch of mathematics that uses mathematical statements to describe relationships between things that change over time. These variables include things like the relationship between supply of an object and its price. When we use a mathematical statement to describe a relationship, we often use letters to represent the quantity that varies, since it is not a fixed amount. These letters and symbols are referred to as variables. (See the Appendix One for a brief review of constants and variables.)


But first an example: An arithmetic problem might look like this: 7 + ? = 10 and we are to find a value for the ? that makes this equation true.  From inspection we see that the ? represents 3 since 3 is the only number that makes the equation true.  So, 7 + 3 = 10 is the answer and that means the ? = 3.

Another Example in algebraic form:  A + B = C and we are given the facts that A=7 and C=10 so what is the value of B?  We can re-write the equation substituting what is known and we have as our algebraic equation: 7 + B = 10 and this looks a lot like our arithmetic equation.  We can use a simple algebraic rule to find the value of B which right now is the unknown to us.  The rule says you can subtract the same amount from each side of the equation to help get the answer.  The idea is to eliminate everything on one side of the equation except the unknown, B in our example.  Our unknown is B so subtract 7 from each side of the equation to get B by itself on one side, like this.

(7 - 7) + B = 10 - 7, subtracting 7 from each side of the equation results in; 0 + B = 3 or simplified B = 3, the unknown we were looking for.


The Rules of Algebra:


The rule of "symmetry": This simply means each side of the equals sign = must be equal. For example 3 = 3, or A = B.  Since a = b (whatever value A is, B is the same value). So, if A = 7 then we also know B = 7 since A = B.  Since this is true then B = A is true as well.


The commutative rules: The order of terms does not matter.  As we saw above, A = B and B = A.  So, A + B = B + A.  Either way organize the terms it is still true. Since this is true it is also true that; A * B = B* A.  This is called the commutative rule of multiplication. A multiplied by B is equal to B multiplied by A.  


The inverse of adding:  The inverse of an operation like addition for example, undoes the operation.  For example if we add 5 to something then immediately subtract 5 we have inversely added 5.  So, 2 + 5 - 5 = 2 + 0 = 2. Right now that may make no sense to you and you might say what's the point.  The point is that in algebra with an unknown it is often helpful to do inverse adding to eliminate terms of an equation.


Two rules for equations: 

1.  You can add the same value to each side of the equation. For example, given: A = B then it is also true that A + C = B + C. C can be any number and the equation is still true. 

2. You can multiply each side of an equation with the same value and the equation will still be true.  For example if A = B then it is also true that A*C = B*C.

See more help here and here.


Hint: Select the above text and print it out for study later.



Algebra Links

What is Algebra? Explained.
Algebra - basic essentials
Algebra (Weisstein and Wolfram Research)
By Topic (Math.com)
Pre-Algebra By Topic (Math.com)
Algebra (AOL - Academic Assistance Center)
Algebra Resources (Fife and Husch)
Algebra Resources (ISLMC) 11-99
Linear and Matrix Algebra Resources (Fife and Husch)
Algebra Questions and Answers (Math Forum - Ask Dr. Math)


Learning Algebra

ALGEBRA Software to Assist in Learning Algebra
Purpose of learning algebra
Learning algebra in a computer algebra environment
Wiley::Dr. MathExplains Algebra: Learning Algebra Is Easy! Just
Algebra Online Learning Sites
Carnegie Learning :: Algebra I
Carnegie Learning :: Algebra II
Learning Algebra Through Chess?!


Algebra - General 

Algebra.help -- Calculators, lessons, and resources!
Algebra Homework Help at Algebra.Com!
Introduction to Algebra
SOS Math - Algebra
Algebra Story and Word Problems
Purplemath - Your Algebra Resource
Algebra Solutions


Advanced Algebra

Practical Algebra Lessons from Purplemath
Welcome to the Discovering Advanced Algebra TRC
Key Curriculum Press | Advanced Algebra Resource Center
S-Cool! - AS & A2 Level Maths Revision Guide
PH@School: Mathematics: Advanced Algebra: Student Table of 
Advanced Algebra Projects
Mathematics - GA: Advanced Algebra and Trigonometry
Basic Algebra Calculators
Mr. Jost - Advanced Algebra: Home
WI Math 400-level Algebra


Study the following three links and you will be far ahead of the rest of the class.






BACK TO MATH PAGE - 101science.com


Return to www.101science.com home page.