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:
- Made larger
- In excess
- More than
- Added to
- Increased by
- In addition
- Raised by
- Thirty-five and eighty-six are what?
Translation: 35 + 86 = (?)
- Three hundred sixteen increased by eight is what amount?
Translation: 316 + 8 = (?)
- 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
- Less than
- Made smaller by
- Take away
- Eighty-nine is how much less than one hundred forty-seven?
Translation: 147 – 89 = (?)
- Seventy-six decreased by sixteen is what?
Translation: 76 – 16 = (?)
- Find the difference between 19 and 62.
Translation: 62 – 19 = (?)
- 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.)
- Multiplied by
- Doubled, tripled, etc.
- Times as much
- Percent of
- Interest on
- 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 = (?)
- Seventeen tripled equals what?
Translation: 17 x 3 = (?)
- What is the product of twenty, six and sixteen?
Translation: (?) = 20 x 6 x 16
- 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.)
- Go(es) into
- How many
- Divided by
- Contained in
- How many times does 11 go into to 121?
121 ÷ 11 = (?) or 121/11
- What is the quotient with a dividend of forty-four and the divisor of 4?
4 ÷ 44 = (?) or 4/44
- How many gallons of oil are contained in 400 quarts? (Note: 4 quarts = a gallon.)
400 ÷ 4 = (?) or 400/4
Words that signal equality:
- Will be
- How many of the 18 jobs will be left after reducing them by half?
18 – 18/2 = (?)
- 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 ≤
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 ( )
- 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)|