Algebraic Expressions Study Guide: GED Math
Practice problems for these concepts can be found at:
What Are Algebraic Expressions?
An algebraic expression is a group of numbers, variables (letters), and operation signs (+, –, ×, ÷). Variables are usually written in italics. For example, the x in the following algebraic expressions is the variable:
Any letter can be used to represent a number in an algebraic expression. The letters x, y, and z are commonly used.
Algebraic expressions translate the relationship between numbers into math symbols.
When multiplying a number and a variable, you just have to write them side by side. You don't need to use a multiplication symbol.
Translate the following math relationship into an algebraic expression: the quotient of 3 divided by a number plus the difference between 3 and 2.
You know that the word quotient indicates division, so write "3 ÷."
The word number represents your variable, so write "3 ÷ x."
The word plus means to add, so write "3 ÷ x +."
The word difference means to subtract, so write: "3 ÷ x + (3 – 2)."
(Remember that parentheses are used to indicate an operation that should be performed first.)
So, the answer is 3 ÷ x + (3 – 2).
When translating a math relationship into an algebraic expression, keep these key words in mind.
Translating Math Relationships into Algebraic Expressions
Remember that the order of the numbers and the exact wording are very important when dividing and subtracting. For example:
- The difference between 3 and 2 means 3 – 2 (which equals 1).
- Three less 2 means 3 – 2 (which equals 1).
- Three less than 2 means 2 – 3 (which equals –1).
- Four divided by 2 means 4 ÷ 2 (which equals 2).
- Two divided by 4 means 2 ÷ 4 (which equals ).
- Two divided into 4 means 4 ÷ 2 (which equals 2).
It's the same when variables are used:
- The difference between 3 and a number means 3 – x.
- Three less than a number means x – 3.
- Four divided by a number means 4 ÷ x.
- A number divided by 4 means x ÷ 4.
Translate the following math relationship into an algebraic expression: one-fourth of a number is decreased by nine.
You know that the word one-fourth is a fraction, so write "."
The word number represents your variable, and when you are talking about fractions, the word of indicates that you should multiply, so write "x."
The words decreased by mean to subtract, so write "x – 9."
The answer is x – 9.
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