Distributive property of multiplication worksheet for Grade 5 students, with examples and exercises.

Let's solve the Distributive Property of Multiplication worksheet step by step.

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🔷 What is the Distributive Property?

The distributive property of multiplication states:

> $ a \times (b + c) = (a \times b) + (a \times c) $

This means you can break down one of the numbers into smaller parts, multiply each part separately, and then add the results.

For example:
$ 3 \times 23 = 3 \times (20 + 3) = (3 \times 20) + (3 \times 3) = 60 + 9 = 69 $

We’ll use this method for all problems.

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Now, let’s go through each problem and rewrite it using the distributive property, then find the answer.

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✔ Problem 1: $ 20 \times 4 $

Break 20 into $ 10 + 10 $ or $ 20 = 10 + 10 $, but better to think of it as $ 2 \times 10 $, so:
$$
20 \times 4 = (10 + 10) \times 4 = (10 \times 4) + (10 \times 4) = 40 + 40 = 80
$$

✔ Answer: 80

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✔ Problem 2: $ 8 \times 14 $

Break 14 into $ 10 + 4 $:
$$
8 \times 14 = 8 \times (10 + 4) = (8 \times 10) + (8 \times 4) = 80 + 32 = 112
$$

✔ Answer: 112

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✔ Problem 3: $ 7 \times 20 $

Break 20 into $ 10 + 10 $:
$$
7 \times 20 = 7 \times (10 + 10) = (7 \times 10) + (7 \times 10) = 70 + 70 = 140
$$

✔ Answer: 140

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✔ Problem 4: $ 10 \times 15 $

Break 15 into $ 10 + 5 $:
$$
10 \times 15 = 10 \times (10 + 5) = (10 \times 10) + (10 \times 5) = 100 + 50 = 150
$$

✔ Answer: 150

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✔ Problem 5: $ 8 \times 24 $

Break 24 into $ 20 + 4 $:
$$
8 \times 24 = 8 \times (20 + 4) = (8 \times 20) + (8 \times 4) = 160 + 32 = 192
$$

✔ Answer: 192

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✔ Problem 6: $ 7 \times 16 $

Break 16 into $ 10 + 6 $:
$$
7 \times 16 = 7 \times (10 + 6) = (7 \times 10) + (7 \times 6) = 70 + 42 = 112
$$

✔ Answer: 112

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✔ Problem 7: $ 6 \times 4 $

Break 4 into $ 2 + 2 $:
$$
6 \times 4 = 6 \times (2 + 2) = (6 \times 2) + (6 \times 2) = 12 + 12 = 24
$$

✔ Answer: 24

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✔ Problem 8: $ 9 \times 8 $

Break 8 into $ 5 + 3 $:
$$
9 \times 8 = 9 \times (5 + 3) = (9 \times 5) + (9 \times 3) = 45 + 27 = 72
$$

✔ Answer: 72

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✔ Problem 9: $ 5 \times 28 $

Break 28 into $ 20 + 8 $:
$$
5 \times 28 = 5 \times (20 + 8) = (5 \times 20) + (5 \times 8) = 100 + 40 = 140
$$

✔ Answer: 140

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✔ Problem 10: $ 4 \times 8 $

Break 8 into $ 5 + 3 $:
$$
4 \times 8 = 4 \times (5 + 3) = (4 \times 5) + (4 \times 3) = 20 + 12 = 32
$$

✔ Answer: 32

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✔ Final Answers:

| Problem | Rewritten Using Distributive Property | Answer |
|--------|----------------------------------------|--------|
| 1 | $ (10 \times 4) + (10 \times 4) = 40 + 40 $ | 80 |
| 2 | $ (8 \times 10) + (8 \times 4) = 80 + 32 $ | 112 |
| 3 | $ (7 \times 10) + (7 \times 10) = 70 + 70 $ | 140 |
| 4 | $ (10 \times 10) + (10 \times 5) = 100 + 50 $ | 150 |
| 5 | $ (8 \times 20) + (8 \times 4) = 160 + 32 $ | 192 |
| 6 | $ (7 \times 10) + (7 \times 6) = 70 + 42 $ | 112 |
| 7 | $ (6 \times 2) + (6 \times 2) = 12 + 12 $ | 24 |
| 8 | $ (9 \times 5) + (9 \times 3) = 45 + 27 $ | 72 |
| 9 | $ (5 \times 20) + (5 \times 8) = 100 + 40 $ | 140 |
| 10 | $ (4 \times 5) + (4 \times 3) = 20 + 12 $ | 32 |

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💡 Tip:

Always choose a number to break apart that makes multiplication easier — usually into tens and ones (like 14 → 10 + 4), or other easy combinations.

Let me know if you'd like a printable version or visual help!