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
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