Distributive Property worksheet for practicing multiplication using the distributive property.

Let's solve each problem using the distributive property. The distributive property states:

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

We'll break down the second number into two parts that add up to it (usually tens and ones), then apply the distributive property.

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① $ 8 \times 15 = (8 \times 10) + (8 \times 5) = 80 + 40 = 120 $

✔ Already solved correctly.

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② $ 4 \times 18 $

Break 18 into 10 + 8:
$ 4 \times 18 = (4 \times 10) + (4 \times 8) = 40 + 32 = 72 $

✔ Answer:
$ (4 \times 10) + (4 \times 8) = 40 + 32 = 72 $

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③ $ 10 \times 15 $

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

✔ Answer:
$ (10 \times 10) + (10 \times 5) = 100 + 50 = 150 $

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④ $ 4 \times 12 $

Break 12 into 10 + 2:
$ 4 \times 12 = (4 \times 10) + (4 \times 2) = 40 + 8 = 48 $

✔ Answer:
$ (4 \times 10) + (4 \times 2) = 40 + 8 = 48 $

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⑤ $ 6 \times 28 $

Break 28 into 20 + 8:
$ 6 \times 28 = (6 \times 20) + (6 \times 8) = 120 + 48 = 168 $

✔ Answer:
$ (6 \times 20) + (6 \times 8) = 120 + 48 = 168 $

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⑥ $ 12 \times 8 $

Break 12 into 10 + 2:
$ 12 \times 8 = (10 \times 8) + (2 \times 8) = 80 + 16 = 96 $

✔ Answer:
$ (10 \times 8) + (2 \times 8) = 80 + 16 = 96 $

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⑦ $ 8 \times 24 $

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

✔ Answer:
$ (8 \times 20) + (8 \times 4) = 160 + 32 = 192 $

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⑧ $ 6 \times 8 $

This is a smaller multiplication. We can break 8 into 5 + 3 or 4 + 4, but let’s use 5 + 3 for variety.

$ 6 \times 8 = (6 \times 5) + (6 \times 3) = 30 + 18 = 48 $

Alternatively, $ (6 \times 4) + (6 \times 4) = 24 + 24 = 48 $

But since no specific breakdown is required, we’ll go with:
$ (6 \times 5) + (6 \times 3) = 30 + 18 = 48 $

✔ Answer:
$ (6 \times 5) + (6 \times 3) = 30 + 18 = 48 $

*(Note: Other valid breakdowns exist, but this is acceptable.)*

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⑨ $ 7 \times 22 $

Break 22 into 20 + 2:
$ 7 \times 22 = (7 \times 20) + (7 \times 2) = 140 + 14 = 154 $

✔ Answer:
$ (7 \times 20) + (7 \times 2) = 140 + 14 = 154 $

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⑩ $ 6 \times 2 $

This is small, but we can still use distributive property.

Break 2 into 1 + 1:
$ 6 \times 2 = (6 \times 1) + (6 \times 1) = 6 + 6 = 12 $

✔ Answer:
$ (6 \times 1) + (6 \times 1) = 6 + 6 = 12 $

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✔ Final Answers:

1. $ 8 \times 15 = (8 \times 10) + (8 \times 5) = 80 + 40 = 120 $
2. $ 4 \times 18 = (4 \times 10) + (4 \times 8) = 40 + 32 = 72 $
3. $ 10 \times 15 = (10 \times 10) + (10 \times 5) = 100 + 50 = 150 $
4. $ 4 \times 12 = (4 \times 10) + (4 \times 2) = 40 + 8 = 48 $
5. $ 6 \times 28 = (6 \times 20) + (6 \times 8) = 120 + 48 = 168 $
6. $ 12 \times 8 = (10 \times 8) + (2 \times 8) = 80 + 16 = 96 $
7. $ 8 \times 24 = (8 \times 20) + (8 \times 4) = 160 + 32 = 192 $
8. $ 6 \times 8 = (6 \times 5) + (6 \times 3) = 30 + 18 = 48 $
9. $ 7 \times 22 = (7 \times 20) + (7 \times 2) = 140 + 14 = 154 $
10. $ 6 \times 2 = (6 \times 1) + (6 \times 1) = 6 + 6 = 12 $

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🔍 Explanation of the Distributive Property:

The distributive property helps us break down harder multiplication problems into simpler ones. For example, instead of calculating $ 6 \times 28 $ directly, we split 28 into 20 and 8, multiply each by 6, and add the results. This method is especially helpful when learning multiplication or working with larger numbers.

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