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
