Key Words for Solving Word Problems
The hardest part of solving word problems is actually understanding
the problem and determining the operation (or operations) that need to
be performed. Listed below are a few of the most commonly used
key words in word problems and the operations that they signal.
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 |
|
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 |
|
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 |
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) |
|
|
is, are, was, were, will be, gives, yields |
|
