Key words in word problems

One of the most important things in solving word problems is to identify the key words that tell you what operation is needed to find a solution. Here is a short list of words to determine the clues of whether to use addition, subtraction, multiplication or division.

ADDITION

Key Words/Phrases	Selected Examples
increased by	the class was increased by 15 students
more than	his collection had 10 cars more than before
combined	they combined their allowances to buy the present
together	together the had 12 eggs
“total” or “total of”	There were 8 roses, 12 carnations, and 2 daisies. How many flowers did they have total?
sum	the sum of their earnings was $28
added to
altogether	How much money do they have altogether?
both
in all
additional
all
another

SUBTRACTION

Key Words/Phrases	Selected Examples
decreased by	The population decreased by 400
“minus” or “less”
difference between/of
more than/less than	Jacob has 6 more than Carlos
fewer than	Jenny has six fewer cookies than Marla
How many more	How many more marbles does Kate have than Jacob?
How much more	How much more money does Susan Have than Charlie?
left	How many eggs were left?
“remain” or “remains”	How many students remain?
Words ending with “er” Examples: higher, longer, faster, heavier, larger, shorter, slower, farther, etc.	How much heavier is Jack’s bag than Mark’s?
take away
only

MULTIPLICATION

Key Words/Phrases	Selected Examples
of	Granpa gave half of his share to Johnny. (multiplication by ¹/2)
times	John is 4 times as old as Jake.
multiplied by	the population multiplied by 12
product of	the product of 4 and 7
increased/decreased by a	The population increased by 10 percent. (multiplication by 0.10)
factor of
every
at this rate
in all	There are 12 rows with 6 plants in each row. How many plants in all?
total	How many plants total?
each	Each pair of socks cost $1.50. How much will 6 pair cost?
doubled, tripled, quadrupled, etc.	the population of rabbits tripled

DIVISION

Key Words/Phrases	Selected Examples
each	Pens cost $1 each. How many pens can you buy with $6?
equal/equally	The items were packed equally into 3 bags. How many items were in each bag?
per	The car gets 23 miles per gallon.
separate
a	The steak cost $3.69 a pound.
ratio of
quotient of
percent (division by 100)

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