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