# 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

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?

• 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

Q11:

Select the problem that can be solved by the equation .

• 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.

 Name Score David Ethan James Anthony Matthew William 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 Amount Saved Matthew David Daniel Jacob William \$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
• 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