Math Signal Words

Often, working on word problems is a difficult task because a student doesn’t know how to translate words into mathematical symbols.

The following examples may help.

Words that signal addition:

  • And
  • Sum
  • Add
  • Made larger
  • In excess
  • Greater
  • More than
  • Added to
  • Increased by
  • In addition
  • Plus
  • Raised by

Examples:

  1. Thirty-five and eighty-six are what?
    Translation:  35 + 86 = (?)
  2. Three hundred sixteen increased by eight is what amount?
    Translation:  316 + 8 = (?)
  3. Ellen has sixteen candy bars to sell.  If this amount is raised by twenty, how many will she have?
    Translation: 16 + 20 = (?)

Words that signal subtraction:

  • Decreased by
  • Diminished by
  • Subtract
  • Reduce
  • Difference
  • Less than
  • From
  • Minus
  • Made smaller by
  • Take away

Examples:

  1. Eighty-nine is how much less than one hundred forty-seven?
    Translation:  147 – 89 = (?)
  2. Seventy-six decreased by sixteen is what?
    Translation:  76 – 16 = (?)
  3. Find the difference between 19 and 62.
    Translation:  62 – 19 = (?)
  4. Tommy has two hundred fifty-three baseball cards.  If his collection is made smaller by thirty cards, how many will he have?
    Translation:  253 – 30 = (?)

Words that signal multiplication:

(The answer to a multiplication problem is called a product.)

  • Product
  • Times
  • Multiplied by
  • Doubled, tripled, etc.
  • Times as much
  • Percent of
  • Of
  • Interest on

Examples:

  1. Susan runs around her block six times every day.  If the distance around the block is ½ (.5) of a mile, how many miles a day does she run?
    Translation:  ½ x 6 = (?)
  2. Seventeen tripled equals what?
    Translation: 17 x 3 = (?)
  3. What is the product of twenty, six and sixteen?
    Translation:  (?) = 20 x 6 x 16
  4. What is 37% of 500?
    Translation:  (?) = .37 x 500

Words that signal division:

(The answer to a division problem is called a quotient.  The number being divided is called a dividend and the number doing the dividing is called the divisor.)

  • Per
  • Quotient
  • Go(es) into
  • How many
  • Divided by
  • Contained in

Examples:

  1. How many times does 11 go into to 121?
    121 ÷ 11 = (?)  or   121/11
  2. What is the quotient with a dividend of forty-four and the divisor of 4?
    4 ÷  44 = (?)   or  4/44
  3. How many gallons of oil are contained in 400 quarts?  (Note: 4 quarts = a gallon.)
    400 ÷ 4 = (?)   or   400/4

Words that signal equality:

  • Is
  • Will be
  • Equal
  • Was
  • Results

Examples:

  1. How many of the 18 jobs will be left after reducing them by half?
    18 – 18/2 = (?)
  2. Seven percent of forty is what?
    .07 (40) = (?)

Words that signal inequality:

Greater than >
Greater than or equal to ≥
Less than <
Less than or equal to ≤

Examples:

1. Four plus a number is greater than seven.
4 + X > 7

2. Fourteen divided by a number is less than or equal to two.
14/X <  2

Quantity is signaled by ( )

Example:

  1. Four times the quantity seven plus X is equal to 40.
    4 ( 7 + X ) = 40

English words Algebraic Expression
Ten more than X X + 10
A number added to 5 5 + X
A number increased by 13 X + 13
5 less than 10 10 – 5
A number decreased by 7 X – 7
Difference between X and 3 X – 3
Twice a number 2X
Ten percent of X .10X
Ten times X 10X
Quotient of X and 3 3X
The product of 2 times a number is 10 2X = 10
5 times the sum of X and 2 5( X + 2 )
7 is greater than X 7 > X
The sum of two consecutive integers (X) + (X + 1)
The sum of two consecutive odd integers (X) + (X + 2)
The sum of two consecutive even integers (X) + (X + 2)

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