Math Help: Basic Pre-Algebra

Pre-Algebra Terms Defined

Expression

A mathematical phrase that does not include an equal sign. Examples: 3 X 5, 6+8, 5x + 7

Equation

A mathematical sentence with an equal sign. Examples: 3 X 5 = 15, 6 + 8 = 14, 5x + 7 = 27

Variable

An unknown number in an algebraic expression or equation. It's usually represented by an x, but it can be any letter.

Coefficient

A number that's multiplied by a variable in an algebraic equation or expression. The coefficient will almost always come just before the variable. For example, in the expression 5x + 7, the number 5 is the coefficient because it's next to the variable, x.

Constant

A number in an equation or expression that doesn't change. In the expression 5x +7, the number 7 is the constant because it isn't attached to any variable.

Integer

Positive and negative whole numbers, including zero. These numbers can be written without a decimal or fraction. Examples: -1, 500, -1987

Negative numbers

Any number that's less than zero. A negative number will always be expressed with a - sign in front of it. You can express any negative number as 0 -x. For example: -7 is really just 0 - 7.

Order of operations

Also known as the precedence rule, the order of operations determines which actions will be performed in which order in an algebraic expression or equation. It's important to have an established order of operations for complex expressions and equations, otherwise you may not always get the same answer. For example: 6 X 3 + 2 could equal either 20 or 30 depending on whether you start with the multiplication of 6 X 3 or the addition of 3 + 2.

The order of operations states that first you solve anything that's inside parentheses. It also states that multiplication and division will always be performed before addition and subtraction, so the correct answer to 6 X 3 + 2 would be 20. Because parentheses come first, 6 X (3+2) would equal 30, but (6 X 3) +2 would still equal 20.

Sample Problems

Using your knowledge of basic pre-algebra terms, try solving the following example problems:

1. Write 'six times x plus four' as an algebraic expression.
2. Write 'twelve times x minus 3 equals nine' as an algebraic equation.
3. Identify the variable, coefficient and constant in the following equation: 3x + 1 = 13
4. Solve this expression with the order of operations: 14/2 + 3 X 5 - 8
5. Use the order of operations to solve this expression: 6 + 4 X 9 -8/2
6. Write 'nine times x equals 5 times x plus 8' as an algebraic equation.
7. What's another way to express the integer -18?