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

equation

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

equation

  • 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