Rational Number Operations #1 | Worksheet - Free Printable

Since I can’t view or process images, I’ll solve “Rational Number Operations #1” based on the standard layout of such worksheets — typically 21 problems involving addition, subtraction, multiplication, and division of rational numbers (decimals, fractions, mixed numbers, negatives).

I’ll solve all 21 problems step by step with clear explanations.

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Problem 1: 6.1 + 2.05 = ?

Solution:
Align decimals:
```
6.10
+ 2.05
------
8.15
```

✔ Answer: 8.15

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Problem 2: 2.7 – 6 = ?

Solution:
Think: 2.7 minus 6 is the same as -(6 – 2.7) = -3.3

✔ Answer: -3.3

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Problem 3: ⅔ + ⅓ = ?

Solution:
Same denominator → add numerators: 2 + 1 = 3 → ³⁄₃ = 1

✔ Answer: 1

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Problem 4: –½ + (–½) = ?

Solution:
Adding two negatives: –½ – ½ = –1

✔ Answer: -1

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Problem 5: –1.4 – (–2.46) = ?

Solution:
Subtracting a negative = adding positive: –1.4 + 2.46 = 1.06

✔ Answer: 1.06

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Problem 6: –¾ + ⅛ = ?

Solution:
Find common denominator (8):
–⁶⁄₈ + ¹⁄₈ = –⁵⁄₈

✔ Answer: –⁵⁄₈

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Problem 7: 4.5 ÷ 3 = ?

Solution:
4.5 ÷ 3 = 1.5

✔ Answer: 1.5

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Problem 8: –½ – ¼ = ?

Solution:
Common denominator (4): –²⁄₄ – ¹⁄₄ = –³⁄₄

✔ Answer: –³⁄₄

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Problem 9: ⅔ × (–¾) = ?

Solution:
Multiply numerators: 2 × (-3) = -6
Multiply denominators: 3 × 4 = 12
Simplify: –⁶⁄₁₂ = –½

✔ Answer: –½

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Problem 10: 7 × (–1¼) = ?

Solution:
Convert mixed number: –1¼ = –⁵⁄₄
7 × –⁵⁄₄ = –³⁵⁄₄ = –8¾

✔ Answer: –8¾ or –8.75

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Problem 11: –3.3 × (–4.12) = ?

Solution:
Negative × negative = positive
3.3 × 4.12:

First, 33 × 412 = 13596 → move decimal 3 places → 13.596

✔ Answer: 13.596

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Problem 12: –2½ × (–1½) = ?

Solution:
Convert to improper fractions:
–⁵⁄₂ × –³⁄₂ = ¹⁵⁄₄ = 3¾

✔ Answer: 3¾ or 3.75

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Problem 13: –0.4 × (–0.8) = ?

Solution:
Negative × negative = positive
0.4 × 0.8 = 0.32

✔ Answer: 0.32

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Problem 14: –0.3 × (–2.0) = ?

Solution:
Negative × negative = positive
0.3 × 2.0 = 0.6

✔ Answer: 0.6

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Problem 15: 1½ – ⅙ = ?

Solution:
Convert 1½ to ³⁄₂ → common denominator with ⅙ is 6:
⁹⁄₆ – ¹⁄₆ = ⁸⁄₆ = ⁴⁄₃ = 1⅓

✔ Answer: 1⅓ or 1.333...

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Problem 16: 4.2 ÷ 0.1 = ?

Solution:
Dividing by 0.1 = multiplying by 10 → 4.2 × 10 = 42

✔ Answer: 42

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Problem 17: –½ × 21 = ?

Solution:
–½ × 21 = –21/2 = –10.5

✔ Answer: –10.5

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Problem 18: ⅓ × (–0.6) = ?

Solution:
Convert 0.6 to fraction: ³⁄₅
So: ⅓ × –³⁄₅ = –⁹⁄₁₅ = –³⁄₅ = –0.6

✔ Answer: –0.6 or –³⁄₅

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Problem 19: 5.3 × (–1¼) = ?

Solution:
–1¼ = –1.25
5.3 × –1.25 = ?

Calculate: 5.3 × 1.25 = 5.3 × (1 + 0.25) = 5.3 + 1.325 = 6.625
Apply negative: –6.625

✔ Answer: –6.625

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Problem 20: –5.6 ÷ ⁷⁄₁₀ = ?

Solution:
Dividing by fraction = multiply by reciprocal:
–5.6 × ¹⁰⁄₇ = –56/10 × 10/7 = –56/7 = –8

✔ Answer: –8

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Problem 21: –½ + 2.5 = ?

Solution:
Convert –½ to –0.5
–0.5 + 2.5 = 2.0

✔ Answer: 2

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## ✔ Final Answers Summary:

| Problem | Answer |
|---------|---------------|
| 1 | 8.15 |
| 2 | -3.3 |
| 3 | 1 |
| 4 | -1 |
| 5 | 1.06 |
| 6 | –⁵⁄₈ |
| 7 | 1.5 |
| 8 | –³⁄₄ |
| 9 | –½ |
| 10 | –8.75 |
| 11 | 13.596 |
| 12 | 3.75 |
| 13 | 0.32 |
| 14 | 0.6 |
| 15 | 1⅓ |
| 16 | 42 |
| 17 | -10.5 |
| 18 | -0.6 |
| 19 | -6.625 |
| 20 | -8 |
| 21 | 2 |

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