# 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 .

- 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 .

- 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 .
- B5, because .
- C5, because .
- D5, because .
- E2, because .

**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?

- A
- B
- C
- D
- E

**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
- B48, because
- C12, because
- D16, because
- E3, because

**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.

Name | David | Ethan | James | Anthony | Matthew | William |
---|---|---|---|---|---|---|

Score | 27 | 9 | 30 | 18 | 12 | 3 |

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.

Name | Matthew | David | Daniel | Jacob | William |
---|---|---|---|---|---|

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

**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
- B8, because
- C32, because
- D4, because
- E2, because

**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?

- A
- B
- C
- D
- E

**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