Worksheet: Word Problems: Comparison Problems

In this worksheet, we will practice solving additive and multiplicative comparison problems by drawing a bar model to help us choose the correct operation.

Q1:

Select the problem that can be solved by the addition equation 26+12=38.

  • AIn the morning, 26 boats set sail from a harbor. In the afternoon, 12 times as many boats set sail than in the morning. How many boats set sail in the afternoon?
  • BIn the morning, 26 boats set sail from a harbor. In the afternoon, 12 more boats set sail. How many boats are out sailing by the afternoon?

Q2:

Questions which tell you how much more (or less) one amount is compared to another are additive comparison problems.

Which of the following is an additive comparison problem?

  • AEmma has 3 brothers. Her friend has 2 times as many brothers as she does. How many brothers does her friend have?
  • BEmma has 3 brothers. Her friend has 2 more brothers than she does. How many brothers does her friend have?

Q3:

Jacob started training to join the basketball team. In the first week, he scored a total of 23 baskets. In the second week, he scored 12 more baskets than in the first week.

Should I add or multiply to find the number of baskets he scored in the second week?

  • Amultiply
  • Badd

Why?

  • Abecause “12 more” tells us to use addition
  • Bbecause “a total of” tells us to use addition
  • Cbecause “a total of” tells us to use multiplication
  • Dbecause “12 more” tells us to use subtraction
  • Ebecause “12 more” tells us to use multiplication

Q4:

Find the problem that can be solved by the multiplication equation 12×8=96.

  • AVictoria put 12 beads on a string to make a bracelet. Then, she made a necklace which had 8 times as many beads as the bracelet. How many beads did she use to make the necklace?
  • BVictoria put 12 beads on a string to make a bracelet. Then, she made a necklace, which had 8 more beads than the bracelet. How many beads did she use to make the necklace?

Q5:

Elizabeth and Michael were collecting leaves for a project. Michael collected 10 leaves. Michael collected 5 times more leaves than Elizabeth. How many leaves did Elizabeth collect?

  • A15, because 10+5=15.
  • B5, because 5×5=25.
  • C5, because 5×5=10.
  • D5, because 105=5.
  • E2, because 5×2=10.

Q6:

A cookbook costs 16 times more than a magazine. The cookbook costs $64.

If you want to know the price of the magazine, which equation will you use?

  • A64+16=?
  • B16×64=?
  • C16×?=64
  • D64×?=16
  • E6416=?

Q7:

Elizabeth is 42 years old. Her age is 7 times more than David’s age.

How old is David?

  • A49 years old
  • B6 years old
  • C4 years old
  • D35 years old
  • E5 years old

How many years older than David is Elizabeth?

Q8:

Jennifer has 14 coloring pencils. James has 4 times as many coloring pencils as Jennifer.

Which of the following models represents this situation?

  • A
  • B
  • C
  • D
  • E

Q9:

There are 9 trolls living under a bridge. There are some ogres living in a nearby cave.

There are 3 times as many trolls as ogres.

What calculation should we do to find the number of ogres?

  • Aadd 3 and 9
  • Bsubtract 3 from 9
  • Cdivide 9 by 3
  • Dmultiply 3 and 9

Q10:

Isabella painted 4 models for an art project. Her friend Jennifer painted 12 models. How many times as many models did Jennifer paint as Isabella? State the reason.

  • A8, because 124=8
  • B48, because 12×4=48
  • C12, because 3×4=12
  • D16, because 12+4=16
  • E3, because 3×4=12

Q11:

Select the problem that can be solved by the equation 5×18=90.

  • ANoah is 18 years old. Sophia is 5 years older than Noah. How old is Sophia?
  • BNoah is 18 years old. Sophia is 5 times as old as Noah. How old is Sophia?
  • CNoah is 90 years old. Sophia is 5 times as old as Noah. How old is Sophia?

Q12:

Questions which tell you how many times more (or less) one amount is compared to another are multiplicative comparison problems.

Which of the following is a multiplicative comparison problem?

  • ADavid is 8 years old. Emma is 4 years older than him. How old is Emma?
  • BDavid is 8 years old. Emma is 4 times older than him. How old is Emma?

Q13:

The table shows the scores of 6 ice skaters after a competition.

NameDavidEthanJamesAnthonyMatthewWilliam
Score2793018123

Who scored 3 times as many points as Ethan?

  • AJames
  • BWilliam
  • CDavid
  • DAnthony
  • EMatthew

Complete the sentence: Anthony scored more points than Matthew.

Complete the sentence: Anthony scored 6 times as many points as .

  • AMatthew
  • BEthan
  • CWilliam
  • DJames
  • EDavid

Q14:

The table shows the amount of money saved by different people in a month.

NameMatthewDavidDanielJacobWilliam
Amount Saved$32$8$4$12$2

Who saved 4 times more dollars than David?

  • AJacob
  • BWilliam
  • CMatthew
  • DDaniel

Who saved 4 more dollars than David?

  • AJacob
  • BDaniel
  • CWilliam
  • DMatthew

Q15:

Elizabeth has 48 badges. She has 3 times as many badges as Anthony.

Which of the following models represents this situation?

  • A
  • B
  • C
  • D
  • E

Q16:

Benjamin sold 8 cakes during a bake sale. William sold four times more cakes. How many cakes did William sell? State the reason.

  • A12, because 8+4=12
  • B8, because 4×2=8
  • C32, because 8×4=32
  • D4, because 84=4
  • E2, because 4×2=8

Q17:

The cost of a video game is $60. The cost of a book is $4. If you need to find out how many times more expensive the video game is compared to the book, which equation do you need to solve to find the answer?

  • A60×4=?
  • B60×?=4
  • C60+4=?
  • D?×4=60
  • E604=?

Q18:

Hannah started training to run a 5 km race. In the first week, she ran a total of 8 km. In the second week, she ran three times as many kilometres as in the first week.

Should I add or multiply to efficiently find out how far she ran in the second week?

  • Amultiply
  • Badd

Why?

  • Abecause “how many times” tells us to use division
  • Bbecause “a total of” tells us to use addition
  • Cbecause “a total of” tells us to use multiplication
  • Dbecause “how many times” tells us to use multiplication
  • Ebecause “how many times” tells us to use addition

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