Multiplication and Division Worksheets: Multiply by parts (Distributive property) - 20 practice problems for math learning.

Let's solve each of these multiplication problems using the distributive property (also known as "multiplying by parts"). The distributive property states:

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

We will break down the larger number into easier parts (like 100, 90, 10, etc.) and then multiply.

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1. $ 9 \times 97 $

Break 97 as $ 100 - 3 $
$$
9 \times 97 = 9 \times (100 - 3) = 9 \times 100 - 9 \times 3 = 900 - 27 = \boxed{873}
$$

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2. $ 8 \times 107 $

Break 107 as $ 100 + 7 $
$$
8 \times 107 = 8 \times (100 + 7) = 8 \times 100 + 8 \times 7 = 800 + 56 = \boxed{856}
$$

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3. $ 3 \times 108 $

Break 108 as $ 100 + 8 $
$$
3 \times 108 = 3 \times (100 + 8) = 3 \times 100 + 3 \times 8 = 300 + 24 = \boxed{324}
$$

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4. $ 4 \times 93 $

Break 93 as $ 90 + 3 $
$$
4 \times 93 = 4 \times (90 + 3) = 4 \times 90 + 4 \times 3 = 360 + 12 = \boxed{372}
$$

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5. $ 5 \times 102 $

Break 102 as $ 100 + 2 $
$$
5 \times 102 = 5 \times (100 + 2) = 5 \times 100 + 5 \times 2 = 500 + 10 = \boxed{510}
$$

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6. $ 5 \times 100 $

This is straightforward:
$$
5 \times 100 = \boxed{500}
$$

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7. $ 4 \times 94 $

Break 94 as $ 90 + 4 $
$$
4 \times 94 = 4 \times (90 + 4) = 4 \times 90 + 4 \times 4 = 360 + 16 = \boxed{376}
$$

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8. $ 4 \times 106 $

Break 106 as $ 100 + 6 $
$$
4 \times 106 = 4 \times (100 + 6) = 4 \times 100 + 4 \times 6 = 400 + 24 = \boxed{424}
$$

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9. $ 7 \times 91 $

Break 91 as $ 90 + 1 $
$$
7 \times 91 = 7 \times (90 + 1) = 7 \times 90 + 7 \times 1 = 630 + 7 = \boxed{637}
$$

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10. $ 8 \times 97 $

Break 97 as $ 100 - 3 $
$$
8 \times 97 = 8 \times (100 - 3) = 8 \times 100 - 8 \times 3 = 800 - 24 = \boxed{776}
$$

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11. $ 9 \times 105 $

Break 105 as $ 100 + 5 $
$$
9 \times 105 = 9 \times (100 + 5) = 9 \times 100 + 9 \times 5 = 900 + 45 = \boxed{945}
$$

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12. $ 4 \times 98 $

Break 98 as $ 100 - 2 $
$$
4 \times 98 = 4 \times (100 - 2) = 4 \times 100 - 4 \times 2 = 400 - 8 = \boxed{392}
$$

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13. $ 3 \times 96 $

Break 96 as $ 90 + 6 $
$$
3 \times 96 = 3 \times (90 + 6) = 3 \times 90 + 3 \times 6 = 270 + 18 = \boxed{288}
$$

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14. $ 2 \times 106 $

Break 106 as $ 100 + 6 $
$$
2 \times 106 = 2 \times (100 + 6) = 2 \times 100 + 2 \times 6 = 200 + 12 = \boxed{212}
$$

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15. $ 4 \times 96 $

Break 96 as $ 90 + 6 $
$$
4 \times 96 = 4 \times (90 + 6) = 4 \times 90 + 4 \times 6 = 360 + 24 = \boxed{384}
$$

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16. $ 4 \times 109 $

Break 109 as $ 100 + 9 $
$$
4 \times 109 = 4 \times (100 + 9) = 4 \times 100 + 4 \times 9 = 400 + 36 = \boxed{436}
$$

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17. $ 5 \times 103 $

Break 103 as $ 100 + 3 $
$$
5 \times 103 = 5 \times (100 + 3) = 5 \times 100 + 5 \times 3 = 500 + 15 = \boxed{515}
$$

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18. $ 8 \times 101 $

Break 101 as $ 100 + 1 $
$$
8 \times 101 = 8 \times (100 + 1) = 8 \times 100 + 8 \times 1 = 800 + 8 = \boxed{808}
$$

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19. $ 7 \times 90 $

Straightforward:
$$
7 \times 90 = \boxed{630}
$$

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20. $ 8 \times 102 $

Break 102 as $ 100 + 2 $
$$
8 \times 102 = 8 \times (100 + 2) = 8 \times 100 + 8 \times 2 = 800 + 16 = \boxed{816}
$$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1. $ 9 \times 97 $ | 873 |
| 2. $ 8 \times 107 $ | 856 |
| 3. $ 3 \times 108 $ | 324 |
| 4. $ 4 \times 93 $ | 372 |
| 5. $ 5 \times 102 $ | 510 |
| 6. $ 5 \times 100 $ | 500 |
| 7. $ 4 \times 94 $ | 376 |
| 8. $ 4 \times 106 $ | 424 |
| 9. $ 7 \times 91 $ | 637 |
| 10. $ 8 \times 97 $ | 776 |
| 11. $ 9 \times 105 $ | 945 |
| 12. $ 4 \times 98 $ | 392 |
| 13. $ 3 \times 96 $ | 288 |
| 14. $ 2 \times 106 $ | 212 |
| 15. $ 4 \times 96 $ | 384 |
| 16. $ 4 \times 109 $ | 436 |
| 17. $ 5 \times 103 $ | 515 |
| 18. $ 8 \times 101 $ | 808 |
| 19. $ 7 \times 90 $ | 630 |
| 20. $ 8 \times 102 $ | 816 |

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📌 Summary:

The key idea here is to use the distributive property to break numbers near 100 into parts like $ 100 + x $ or $ 100 - x $, making multiplication simpler. This method helps in mental math and builds number sense.

Let me know if you'd like this as a printable PDF or with step-by-step breakdowns for each!