## Variables and Algebraic Expressions

A variable is a symbol used to denote any element of a given set—often a letter used to stand for a number. Variables are used to change verbal expressions into algebraic expressions.

Example 1

Give the algebraic expression.

Verbal Expression
Algebraic Expression
| The sum of a number n and 7  | n + 7 or 7 + n
| The number n diminished by 10  | n – 10
| Seven times the number n | 7 n
| x divided by 4  | | Five more than the product of 2 and n | 2 n + 5 or 5 + 2 n
| Seven less than the quotient of y and 4  | • Key words denoting addition:
•  | sum | larger than | enlarge
| plus | gain | rise
| more than | increase | grow
| greater than |  |
• Key words denoting subtraction:
•  | difference | smaller than | lower
| minus | fewer than | diminish
| lose | decrease | reduced
| less than | drop |
• Key words denoting multiplication:
•  | product | times | of
| multiplied by | twice |
• Key words denoting division:
•  | quotient | ratio
| divided by | half