Algebra Review Help

Updated on Oct 27, 2011


Let's get reacquainted with the players in the game.

Whole Numbers

First, you have whole numbers. Whole numbers are also called "counting numbers" and include 0, 1, 2, 3, 4, 5, 6, . . . You see the pattern here.


Next on the roster are integers. Integers are all positive and negative whole numbers including zero: –3, –2, –1, 0, 1, 2, 3, . . .

Rational Numbers

Rational numbers, good old rational numbers. Rational numbers are all numbers that can be written as fractions , terminating decimals (0.75), and repeating decimals (0.666. . .).

Irrational Numbers

And rounding out the team are irrational numbers. Irrational numbers cannot be expressed as terminating or repeating decimals. Some examples: π or √2

Order of Operations

Most people remember the order of operations by using a mnemonic device such as PEMDAS, or Please Excuse My Dear Aunt Sally. These stand for the order in which operations are done:


Multiplication and division are done in the order that they appear from left to right. Addition and subtraction work the same way—left to right.

Parentheses also include any grouping symbol such as brackets [ ] and braces {}.


Example 1:

–5 + 2 × 8 =

–5 + 16 =


Example 2:

9 + (6 + 2 × 4) – 32 =

9 + (6 + 8) – 32 =

9 + 14 – 9 =

23 – 9 =


Absolute Value

The absolute value is the distance of a number from zero and is expressed by placing vertical bars on either side of the number. For example, |–5| is 5 because –5 is 5 spaces from zero. Most people simply remember that the absolute value of a number is its positive form.


|–39| = 39

|92| = 92

|–11| = 11

|987| = 987

Variables - Numbers and Letters Meet

Variables are letters that are used to represent numbers. Once you realize that these variables are just numbers in disguise, you'll understand that they must obey all the rules of mathematics, just like the numbers that aren't disguised. This can help you figure out what number the variable at hand stands for.'


When a number is placed next to a variable, indicating multiplication, the number is said to be the coefficient of the variable. For example,

8c      8 is the coefficient to the variable c.

6ab    6 is the coefficient to both variables a and b.

Like Terms

If two or more terms have exactly the same variable(s), they are said to be like terms.

    7x + 3x = 10x

The process of grouping like terms together performing mathematical operations is called combining like terms. It is important to combine like terms carefully, making sure that the variables are exactly the same.

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