Multiplicative comparison (problem solving) - Studyladder ... - Free Printable

Here’s the step-by-step solution to each of the 10 multiplicative comparison problems. These problems involve finding equal shares or balancing quantities — essentially, multiplication followed by division (or vice versa), which is the core of multiplicative comparison.

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Question 1

> Thomas has 3 boxes, each with 8 balls. He wants to place the balls evenly into 4 boxes. How many balls will be in each of the 4 boxes?

Step 1: Find total balls = 3 boxes × 8 balls = 24 balls
Step 2: Divide evenly into 4 boxes = 24 ÷ 4 = 6 balls per box

✔ Answer: 6 balls

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Question 2

> 4 teams of 9 children are asked to reorganise themselves into 6 equal teams. How many children will be in each new team?

Step 1: Total children = 4 teams × 9 = 36 children
Step 2: Divide into 6 teams = 36 ÷ 6 = 6 children per team

✔ Answer: 6 children

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Question 3

> Amelia placed four 10 kg weights on one side of an equal arm balance. How many 8 kg weights are needed on the other side to balance the scale?

Step 1: Total weight on one side = 4 × 10 kg = 40 kg
Step 2: Number of 8 kg weights needed = 40 ÷ 8 = 5 weights

✔ Answer: 5 weights

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Question 4

> Mrs Jones bought 5 packets of sweets, with 12 sweets in each packet. If she is to share the sweets equally between 6 children, how many sweets will each child get?

Step 1: Total sweets = 5 × 12 = 60 sweets
Step 2: Share among 6 children = 60 ÷ 6 = 10 sweets per child

✔ Answer: 10 sweets

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Question 5

> There are an equal number of students in Class 'A' and Class 'B'. Class 'A' has 5 table groups of 8 children. Class 'B' has 4 table groups. How many children in each table group in Class 'B'?

Step 1: Students in Class A = 5 × 8 = 40 students
→ So Class B also has 40 students
Step 2: Divide into 4 groups = 40 ÷ 4 = 10 children per group

✔ Answer: 10 children

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Question 6

> 8 lines of people each containing 10 people are divided into 5 equal groups. How many people in each new group?

Step 1: Total people = 8 × 10 = 80 people
Step 2: Divide into 5 groups = 80 ÷ 5 = 16 people per group

✔ Answer: 16 people

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Question 7

> James and Ian bought an equal number of stamps. Ian bought 5 packets with 12 stamps in each packet. James bought 3 packets. How many in each of James’ packets?

Step 1: Ian’s total stamps = 5 × 12 = 60 stamps
→ James also bought 60 stamps
Step 2: James has 3 packets → 60 ÷ 3 = 20 stamps per packet

✔ Answer: 20 stamps

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Question 8

> 12 teams each containing 4 students are reorganized into 2 equal teams. How many students in each new team?

Step 1: Total students = 12 × 4 = 48 students
Step 2: Divide into 2 teams = 48 ÷ 2 = 24 students per team

✔ Answer: 24 students

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Question 9

> Three 25 L drums of oil are used to fill 5 bottles. How much oil in each bottle?

Step 1: Total oil = 3 × 25 L = 75 L
Step 2: Divide into 5 bottles = 75 ÷ 5 = 15 L per bottle

✔ Answer: 15 L

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Question 10

> Five 8 cm sticks have the same length as how many 20 cm sticks?

Step 1: Total length of 5 sticks = 5 × 8 cm = 40 cm
Step 2: How many 20 cm sticks = 40 ÷ 20 = 2 sticks

✔ Answer: 2 sticks

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## ✔ Final Answers Summary:

| Question | Answer |
|----------|---------------|
| 1 | 6 balls |
| 2 | 6 children |
| 3 | 5 weights |
| 4 | 10 sweets |
| 5 | 10 children |
| 6 | 16 people |
| 7 | 20 stamps |
| 8 | 24 students |
| 9 | 15 L |
| 10 | 2 sticks |

These problems all follow the pattern:
Total = number of groups × items per group, then items per new group = total ÷ new number of groups.

This is the essence of multiplicative comparison: comparing quantities through multiplication and division to find equal shares or equivalents.

Let me know if you’d like a visual diagram for any problem!