Multiplicative Comparison Word Problems Worksheets - Set 1 | Made ... - Free Printable

The image you've uploaded is a Multiplicative Comparison Word Problems – Set 1 Answer Key from a math worksheet designed for students, likely in the 4th grade (aligned with Common Core standard 4.OA.A.2). It includes six word problems involving multiplicative comparisons, with visual models (tape diagrams), equations, and solutions.

Let me solve and explain each problem step-by-step based on the answer key provided:

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Problem 1:

Peter picked 7 apples. Mary picked 4 times as many apples as Peter. How many apples did they pick altogether?

- Step 1: Peter = 7 apples
- Mary = 4 × 7 = 28 apples
- Total = 7 + 28 = 35 apples

✔ Answer: 35 apples

> ✔ The diagram shows:
> - Peter: [7]
> - Mary: [7][7][7][7] → 4 groups of 7
> - Equation: 5 × 7 = n → n = 35 (Note: This is a shortcut — it’s actually 7 + (4×7) = 5×7)

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Problem 2:

Nora has 8 yards of rope. Nina has 3 times as many yards of rope as Nora. How many yards of rope do they have altogether?

- Nora = 8 yards
- Nina = 3 × 8 = 24 yards
- Total = 8 + 24 = 32 yards

✔ Answer: 32 yards

> ✔ Diagram:
> - Nora: [8]
> - Nina: [8][8][8]
> - Equation: 4 × 8 = 32

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Problem 3:

Steve has 6 times as many toy cars as Brian. If Brian has 3 toy cars, how many toy cars do they have altogether?

- Brian = 3 cars
- Steve = 6 × 3 = 18 cars
- Total = 3 + 18 = 21 cars

✔ Answer: 21 toy cars

> ✔ Diagram:
> - Brian: [3]
> - Steve: [3][3][3][3][3][3] → 6 groups of 3
> - Equation: 7 × 3 = 21 (since 1 group for Brian + 6 for Steve = 7 total groups)

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Problem 4:

Last month, Pamela read 4 times as many books as Sharon. If they read 35 books altogether, how many books did Sharon read?

Let:
- Sharon = n books
- Pamela = 4n books
- Total: n + 4n = 5n = 35

Solve:
- 5n = 35 → n = 35 ÷ 5 = 7

✔ Answer: 7 books

> ✔ Diagram:
> - Sharon: [n]
> - Pamela: [n][n][n][n]
> - Total: 5n = 35 → n = 7

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Problem 5:

Elizabeth has 12 pets altogether. If Elizabeth has 3 times as many cats as dogs, how many dogs does she have?

Let:
- Dogs = n
- Cats = 3n
- Total: n + 3n = 4n = 12

Solve:
- 4n = 12 → n = 12 ÷ 4 = 3

✔ Answer: 3 dogs

> ✔ Diagram:
> - Dogs: [n]
> - Cats: [n][n][n]
> - Total: 4n = 12 → n = 3

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Problem 6:

There are 5 times as many monkeys as lions at the zoo. If there are 30 monkeys and lions altogether, how many monkeys are there?

Let:
- Lions = n
- Monkeys = 5n
- Total: n + 5n = 6n = 30

Solve:
- 6n = 30 → n = 30 ÷ 6 = 5 → Lions = 5
- Monkeys = 5 × 5 = 25

✔ Answer: 25 monkeys

> ✔ Diagram:
> - Lions: [n]
> - Monkeys: [n][n][n][n][n]
> - Total: 6n = 30 → n = 5 → 5 × 5 = 25 monkeys

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✔ Summary of Answers:

| Problem | Answer |
|--------|--------|
| 1 | 35 apples |
| 2 | 32 yards |
| 3 | 21 toy cars |
| 4 | 7 books |
| 5 | 3 dogs |
| 6 | 25 monkeys |

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🔍 Teaching Notes:

This worksheet emphasizes multiplicative comparison, where one quantity is a multiple of another. Students use:
- Tape diagrams (bar models)
- Equations (like 5n = 35)
- Logical reasoning to find unknowns

These problems build foundational algebraic thinking by introducing variables (n) and solving simple equations.

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