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 solve each problem.
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✔ 1. 20 × 4
Break 20 into 10 + 10:
$$
20 \times 4 = (10 + 10) \times 4 = (10 \times 4) + (10 \times 4) = 40 + 40 = 80
$$
✔ Answer:
80
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✔ 2. 8 × 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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✔ 3. 7 × 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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✔ 4. 10 × 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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✔ 5. 8 × 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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✔ 6. 7 × 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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✔ 7. 6 × 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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✔ 8. 9 × 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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✔ 9. 5 × 26
Break 26 into 20 + 6:
$$
5 \times 26 = 5 \times (20 + 6) = (5 \times 20) + (5 \times 6) = 100 + 30 = 130
$$
✔ Answer:
130
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✔ 10. 4 × 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. 20 × 4 | (10 + 10) × 4 = (10×4) + (10×4) = 40 + 40 |
80 |
| 2. 8 × 14 | 8 × (10 + 4) = (8×10) + (8×4) = 80 + 32 |
112 |
| 3. 7 × 20 | 7 × (10 + 10) = (7×10) + (7×10) = 70 + 70 |
140 |
| 4. 10 × 15 | 10 × (10 + 5) = (10×10) + (10×5) = 100 + 50 |
150 |
| 5. 8 × 24 | 8 × (20 + 4) = (8×20) + (8×4) = 160 + 32 |
192 |
| 6. 7 × 16 | 7 × (10 + 6) = (7×10) + (7×6) = 70 + 42 |
112 |
| 7. 6 × 4 | 6 × (2 + 2) = (6×2) + (6×2) = 12 + 12 |
24 |
| 8. 9 × 8 | 9 × (5 + 3) = (9×5) + (9×3) = 45 + 27 |
72 |
| 9. 5 × 26 | 5 × (20 + 6) = (5×20) + (5×6) = 100 + 30 |
130 |
| 10. 4 × 8 | 4 × (5 + 3) = (4×5) + (4×3) = 20 + 12 |
32 |
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💡 Tip:
You can choose how to break the number — usually breaking it into tens and ones (like 14 → 10 + 4) works best, but any valid split is acceptable.
Let me know if you'd like this in printable format or with more examples! 😊
Parent Tip: Review the logic above to help your child master the concept of multiplying whole numbers and decimals worksheet.
