Let's solve each problem on the worksheet using the
distributive property. The distributive property states:
> $ a \times (b + c) = a \times b + a \times c $
This means we break apart one of the numbers into smaller parts, multiply each part by the other number, and then add the results.
---
Problem 1: 8 × 9
We can break 9 into 6 + 3:
$$
8 \times 9 = 8 \times (6 + 3) = (8 \times 6) + (8 \times 3)
$$
$$
= 48 + 24 = 72
$$
✔ So:
- $ (8 \times \boxed{6}) + (8 \times \boxed{3}) $
- $ 8 \times 9 = \boxed{72} $
---
Problem 2: 12 × 3
Break 12 into 10 + 2:
$$
12 \times 3 = (10 + 2) \times 3 = (10 \times 3) + (2 \times 3)
$$
$$
= 30 + 6 = 36
$$
✔ So:
- $ (\boxed{10} + \boxed{2}) \times 3 $
- $ (\boxed{10} \times 3) + (\boxed{2} \times 3) $
- $ 12 \times 3 = \boxed{36} $
---
Problem 3: 4 × 13
Break 13 into 10 + 3:
$$
4 \times 13 = 4 \times (10 + 3) = (4 \times 10) + (4 \times 3)
$$
$$
= 40 + 12 = 52
$$
✔ So:
- $ 4 \times (\boxed{10} + \boxed{3}) $
- $ (4 \times \boxed{10}) + (4 \times \boxed{3}) $
- $ 4 \times 13 = \boxed{52} $
---
Problem 4: 14 × 6
Break 14 into 10 + 4:
$$
14 \times 6 = (10 + 4) \times 6 = (10 \times 6) + (4 \times 6)
$$
$$
= 60 + 24 = 84
$$
✔ So:
- $ (\boxed{10} + \boxed{4}) \times 6 $
- $ (\boxed{10} \times 6) + (\boxed{4} \times 6) $
- $ 14 \times 6 = \boxed{84} $
---
Problem 5: 3 × 16
Break 16 into 10 + 6:
$$
3 \times 16 = 3 \times (10 + 6) = (3 \times 10) + (3 \times 6)
$$
$$
= 30 + 18 = 48
$$
✔ So:
- $ 3 \times (\boxed{10} + \boxed{6}) $
- $ (3 \times \boxed{10}) + (3 \times \boxed{6}) $
- $ 3 \times 16 = \boxed{48} $
---
Problem 6: 17 × 5
Break 17 into 10 + 7:
$$
17 \times 5 = (10 + 7) \times 5 = (10 \times 5) + (7 \times 5)
$$
$$
= 50 + 35 = 85
$$
✔ So:
- $ (\boxed{10} + \boxed{7}) \times 5 $
- $ (\boxed{10} \times 5) + (\boxed{7} \times 5) $
- $ 17 \times 5 = \boxed{85} $
---
✔ Final Answers:
| Problem | Expression Breakdown | Answer |
|--------|------------------------|--------|
| 1. | $ (8 \times 6) + (8 \times 3) $ | 72 |
| 2. | $ (10 + 2) \times 3 $ → $ (10 \times 3) + (2 \times 3) $ | 36 |
| 3. | $ 4 \times (10 + 3) $ → $ (4 \times 10) + (4 \times 3) $ | 52 |
| 4. | $ (10 + 4) \times 6 $ → $ (10 \times 6) + (4 \times 6) $ | 84 |
| 5. | $ 3 \times (10 + 6) $ → $ (3 \times 10) + (3 \times 6) $ | 48 |
| 6. | $ (10 + 7) \times 5 $ → $ (10 \times 5) + (7 \times 5) $ | 85 |
---
🎯 Summary:
The distributive property helps us simplify multiplication by breaking one number into easier-to-multiply parts. Always:
1. Break the larger number.
2. Multiply each part by the other number.
3. Add the products.
Let me know if you'd like this as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of distributive property worksheet 3rd grade.
