Multiplication and Division Worksheets: Multiply by Parts (Distributive Property) with Answers

You're looking at a Multiplication and Division Worksheet titled “Multiply by parts (Distributive property)”. The goal is to solve each multiplication problem using the distributive property, which means breaking down one of the numbers into easier parts (like hundreds, tens, and ones), multiplying each part separately, and then adding the results.

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✔ All 20 problems are already solved correctly in red ink.

But since you asked to “solve the problem and explain the solution,” I’ll walk you through how to solve them using the distributive property, as intended by the worksheet.

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## 🔍 What is the Distributive Property?

The distributive property says:

> a × (b + c) = (a × b) + (a × c)

So for multiplication like `5 × 105`, we can break 105 into `100 + 5`, then multiply:

> `5 × 105 = 5 × (100 + 5) = (5 × 100) + (5 × 5) = 500 + 25 = 525`

Let’s apply this to a few examples from the sheet.

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## 🧮 Step-by-Step Examples

✔ Problem 1: `5 × 105`

Break 105 → 100 + 5
→ `5 × 100 = 500`
→ `5 × 5 = 25`
→ `500 + 25 = 525` ✔️

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✔ Problem 3: `8 × 99`

Break 99 → 100 - 1 (you can also use subtraction!)
→ `8 × 100 = 800`
→ `8 × 1 = 8`
→ `800 - 8 = 792` ✔️

*(Note: Distributive property works with subtraction too: `a × (b - c) = (a × b) - (a × c)`)*

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✔ Problem 6: `8 × 103`

Break 103 → 100 + 3
→ `8 × 100 = 800`
→ `8 × 3 = 24`
→ `800 + 24 = 824` ✔️

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✔ Problem 10: `4 × 102`

Break 102 → 100 + 2
→ `4 × 100 = 400`
→ `4 × 2 = 8`
→ `400 + 8 = 408` ✔️

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✔ Problem 16: `9 × 95`

Break 95 → 100 - 5
→ `9 × 100 = 900`
→ `9 × 5 = 45`
→ `900 - 45 = 855` ✔️

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✔ Problem 20: `8 × 109`

Break 109 → 100 + 9
→ `8 × 100 = 800`
→ `8 × 9 = 72`
→ `800 + 72 = 872` ✔️

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## 📝 Summary

All 20 problems on the worksheet were solved using the distributive property, breaking the larger number (usually a 3-digit or near-100 number) into simpler components (like 100 + x or 100 - x), multiplying each part by the single-digit number, and summing (or subtracting) the results.

This method helps students understand place value and makes mental math easier.

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## ✔ Final Answer:

All 20 multiplication problems have been correctly solved using the distributive property.
Each answer shown in red is accurate. Here they are listed for reference:

1. 525
2. 728
3. 792
4. 270
5. 321
6. 824
7. 588
8. 190
9. 372
10. 408
11. 744
12. 294
13. 742
14. 546
15. 736
16. 855
17. 816
18. 455
19. 630
20. 872

✔ Worksheet is complete and correct!

If you’d like, I can generate similar practice problems or show how to write out the full distributive steps for any specific problem.