Multiplying Decimals (B) Worksheet | Fun and Engaging 5th Grade ... - Free Printable

Let's solve each section of the worksheet step by step and explain the reasoning.

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Section A: Quick Decimal Multiplication & Division

These problems involve multiplying or dividing decimals by powers of 10 (100, 1000), which is done by moving the decimal point.

#### 1) $ 0.09 \times 100 $
- Multiply by 100 → move decimal point 2 places to the right.
- $ 0.09 \rightarrow 9 $
- ✔ Answer: 9

#### 2) $ 597 \div 100 $
- Divide by 100 → move decimal point 2 places to the left.
- $ 597 \rightarrow 5.97 $
- ✔ Answer: 5.97

#### 3) $ 302.19 \times 100 $
- Multiply by 100 → move decimal point 2 places to the right.
- $ 302.19 \rightarrow 30219 $
- ✔ Answer: 30219

#### 4) $ 28074 \div 1000 $
- Divide by 1000 → move decimal point 3 places to the left.
- $ 28074 \rightarrow 28.074 $
- ✔ Answer: 28.074

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Section B: Whole Number Multiplication

We'll use standard multiplication algorithm.

#### 1) $ 108 \times 7 $
```
108
× 7
-----
756
```
- $ 8 × 7 = 56 $ → write 6, carry 5
- $ 0 × 7 = 0 + 5 = 5 $
- $ 1 × 7 = 7 $
- ✔ Answer: 756

#### 2) $ 693 \times 8 $
```
693
× 8
-----
5544
```
- $ 3 × 8 = 24 $ → write 4, carry 2
- $ 9 × 8 = 72 + 2 = 74 $ → write 4, carry 7
- $ 6 × 8 = 48 + 7 = 55 $
- ✔ Answer: 5544

#### 3) $ 32 \times 15 $
```
32
× 15
-----
160 ← 32 × 5
32 ← 32 × 10 (shifted)
-----
480
```
- $ 32 × 5 = 160 $
- $ 32 × 10 = 320 $
- $ 160 + 320 = 480 $
- ✔ Answer: 480

#### 4) $ 97 \times 46 $
```
97
× 46
-----
582 ← 97 × 6
388 ← 97 × 40 (shifted)
-----
4412
```
- $ 97 × 6 = 582 $
- $ 97 × 40 = 3880 $
- $ 582 + 3880 = 4462 $
- ✔ Answer: 4462

#### 5) $ 826 \times 58 $
```
826
× 58
-----
6608 ← 826 × 8
4130 ← 826 × 50 (shifted)
-----
47908
```
- $ 826 × 8 = 6608 $
- $ 826 × 50 = 41300 $
- $ 6608 + 41300 = 47908 $
- ✔ Answer: 47908

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Section C: Decimal Multiplication

Multiply as if whole numbers, then count total decimal places.

#### 1) $ 6 × 0.04 $
- $ 6 × 4 = 24 $
- 0.04 has 2 decimal places, so answer has 2 decimal places.
- $ 0.24 $
- ✔ Answer: 0.24

#### 2) $ 0.9 × 0.7 $
- $ 9 × 7 = 63 $
- Total decimal places: 1 + 1 = 2
- $ 0.63 $
- ✔ Answer: 0.63

#### 3) $ 0.8 × 0.03 $
- $ 8 × 3 = 24 $
- Decimal places: 1 + 2 = 3
- $ 0.024 $
- ✔ Answer: 0.024

#### 4) $ 0.09 × 0.2 $
- $ 9 × 2 = 18 $
- Decimal places: 2 + 1 = 3
- $ 0.018 $
- ✔ Answer: 0.018

#### 5) $ 3 × 8.42 $
- $ 3 × 842 = 2526 $
- 8.42 has 2 decimal places → answer has 2
- $ 25.26 $
- ✔ Answer: 25.26

#### 6) $ 1.904 × 6 $
- $ 1904 × 6 = 11424 $
- 1.904 has 3 decimal places → answer has 3
- $ 11.424 $
- ✔ Answer: 11.424

#### 7) $ 1.4 × 9.6 $
- $ 14 × 96 = 1344 $
- Decimal places: 1 + 1 = 2
- $ 13.44 $
- ✔ Answer: 13.44

#### 8) $ 7.7 × 0.15 $
- $ 77 × 15 = 1155 $
- Decimal places: 1 + 2 = 3
- $ 1.155 $
- ✔ Answer: 1.155

#### 9) $ 9.53 × 7.4 $
- $ 953 × 74 $
- $ 953 × 4 = 3812 $
- $ 953 × 70 = 66710 $
- $ 3812 + 66710 = 70522 $
- Decimal places: 2 + 1 = 3
- $ 70.522 $
- ✔ Answer: 70.522

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✔ Final Answers:

#### Section A
1. $ 0.09 × 100 = 9 $
2. $ 597 ÷ 100 = 5.97 $
3. $ 302.19 × 100 = 30219 $
4. $ 28074 ÷ 1000 = 28.074 $

#### Section B
1. $ 108 × 7 = 756 $
2. $ 693 × 8 = 5544 $
3. $ 32 × 15 = 480 $
4. $ 97 × 46 = 4462 $
5. $ 826 × 58 = 47908 $

#### Section C
1. $ 6 × 0.04 = 0.24 $
2. $ 0.9 × 0.7 = 0.63 $
3. $ 0.8 × 0.03 = 0.024 $
4. $ 0.09 × 0.2 = 0.018 $
5. $ 3 × 8.42 = 25.26 $
6. $ 1.904 × 6 = 11.424 $
7. $ 1.4 × 9.6 = 13.44 $
8. $ 7.7 × 0.15 = 1.155 $
9. $ 9.53 × 7.4 = 70.522 $

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✔ All answers are now complete and explained! Let me know if you'd like a printable version or step-by-step visual for any problem.