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Key Words for Problem Solving Questions

Key Words for Solving Word Problems

The hardest part of solving a word problem is actually understanding the problem and determining the operation (or operations) that needs to be performed. Listed below are a few of the most commonly used key words in word problems and the operations that they signal. Keep in mind that same key words may signal more than one operation. It is then up to you to picture in your head what is going on and then determine which operation best fits that scenario.

 

 

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 they 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 – Her savings this week were added to her savings last week.
  • altogether – How much money do they have altogether?
  • both
  • in all – How many carrots does she have in all?
  • additional – If he had ten additional baseball cards, how many would he have in all?
  • all – If you combined all of their earnings how much would they have?
  • another

  

SUBTRACTION

KEY WORDS / PHRASES SELECTED EXAMPLES

  • decreased by – The population of whales decreased by 400 in the last year.
  • minus – She had ten dollars, minus the amount she spent on the drink. How much did she have in all?
  • less – She had five cards, less the two she gave her brother. How many did she have in all?
  • difference between / difference of – What was the difference between their earnings last week?
  • More than – Jacob has 6 more marbles than Carlos.
  • Less than – Carlos has 6 marbles less than Jacob.
  • Fewer than – Jenny has six fewer cookies than Elizabeth.
  • How many more – How many more daisies does Kate have than Jacob?
  • How much more – How much more money does Alex need to buy the computer?
  • Left – How many eggs are left?
  • “remain” or “remains” – How many students remain on the bus?
  • Words ending in “er” – Examples: higher, longer, faster, heavier, larger, shorter, slower, farther, etc. How much heavier is Jack’s bag than Mark’s? How much farther does Susan need to run?
  • Take away – If Elizabeth takes away 2 of Jaime’s baseball cards, how many will he have?
  • Only

 

 

 

 

 

 

 

MULTIPLICATION

 

 

KEY WORDS / PHRASES SELECTED EXAMPLES

 

 

  • of – Grandpa gave half of his share to Johnny. (multiplication by ½ )
  • times – John has 4 times as many jelly beans as Jake.
  • multiplied by – The population multiplied by 12 over the last year.
  • product of – The product of four and seven
  • increased by – The population of tigers in the wild increased by ten percent. (multiplication by 0.10 and then addition)
  • decreased by – The population of rhinoceros living in the wild decreased by twenty-five percent in the last ten years, (multiplication by 0.25 and then subtraction)
  • factor of – The school population increased by a factor of 12.
  • every
  • at this rate
  • in all – There are twelve rows with six plants in each row. How many plants are there in all?
  • total – There are eight rows with 7 plants in each row. How many plants are there total?
  • each – Each pair of socks cost $1.50. How much will six pair cost?
  • doubled, tripled, quadrupled,
  • etc. The population of rabbits tripled in two years. (times by 3)

 

 

 

 

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 three bags. How many items were in each bag?
  • per – The car gets 23 miles per gallon. How many gallons will it take to go 470 miles?
  • separate – If the money was separated into equal shares, how much did each person get?
  • a – A Steak cost $3.69 a pound. How many pounds can you buy for $20?
  • “ratio” or “ratio of” – If the student to teacher ratio was 27 to 1, how many teachers are there for 756 students?
  • “quotient” or “quotient of”
  • percent (division by 100) – What percent of the population was over 18?

 

 

EQUALS

 

 

Is, are, was, were, will be, gives, yields

 

 

  

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