Simplifying Ratios worksheet with a fun dragon theme, designed to help students practice reducing ratios to their simplest form.

Let's solve each ratio by simplifying it to its simplest form. To simplify a ratio, we divide both numbers by their greatest common divisor (GCD). For decimals, we can convert them to fractions or multiply to eliminate decimals first.

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1. 25 : 150

- GCD of 25 and 150 is 25
- $ \frac{25}{25} : \frac{150}{25} = 1 : 6 $

✔ Answer: 1 : 6

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2. 30 : 75

- GCD of 30 and 75 is 15
- $ \frac{30}{15} : \frac{75}{15} = 2 : 5 $

✔ Answer: 2 : 5

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3. 34 : 102

- GCD of 34 and 102 is 34
- $ \frac{34}{34} : \frac{102}{34} = 1 : 3 $

✔ Answer: 1 : 3

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4. 148 : 111

- GCD of 148 and 111:
- 148 ÷ 111 = 1 R37
- 111 ÷ 37 = 3 R0 → GCD = 37
- $ \frac{148}{37} : \frac{111}{37} = 4 : 3 $

✔ Answer: 4 : 3

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5. 97 : 194

- 97 is prime; 194 ÷ 97 = 2 → GCD = 97
- $ \frac{97}{97} : \frac{194}{97} = 1 : 2 $

✔ Answer: 1 : 2

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6. 52 : 130

- GCD of 52 and 130:
- 52 = 2×2×13
- 130 = 2×5×13 → GCD = 26
- $ \frac{52}{26} : \frac{130}{26} = 2 : 5 $

✔ Answer: 2 : 5

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7. 112 : 320

- GCD of 112 and 320:
- 112 = 2⁴ × 7
- 320 = 2⁶ × 5 → GCD = 16
- $ \frac{112}{16} : \frac{320}{16} = 7 : 20 $

✔ Answer: 7 : 20

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8. 2.4 : 5.6

- Eliminate decimals: Multiply both by 10 → 24 : 56
- GCD of 24 and 56 is 8
- $ \frac{24}{8} : \frac{56}{8} = 3 : 7 $

✔ Answer: 3 : 7

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9. 32 : 480

- GCD of 32 and 480:
- 32 = 2⁵
- 480 = 2⁵ × 3 × 5 → GCD = 32
- $ \frac{32}{32} : \frac{480}{32} = 1 : 15 $

✔ Answer: 1 : 15

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10. 7.8 : 9.1

- Multiply both by 10 → 78 : 91
- GCD of 78 and 91:
- 78 = 2×3×13
- 91 = 7×13 → GCD = 13
- $ \frac{78}{13} : \frac{91}{13} = 6 : 7 $

✔ Answer: 6 : 7

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11. 128 : 160

- GCD of 128 and 160:
- 128 = 2⁷
- 160 = 2⁵ × 5 → GCD = 32
- $ \frac{128}{32} : \frac{160}{32} = 4 : 5 $

✔ Answer: 4 : 5

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12. 2.5 : 3.5

- Multiply by 10 → 25 : 35
- GCD of 25 and 35 is 5
- $ \frac{25}{5} : \frac{35}{5} = 5 : 7 $

✔ Answer: 5 : 7

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13. 42 : 280

- GCD of 42 and 280:
- 42 = 2×3×7
- 280 = 2³×5×7 → GCD = 14
- $ \frac{42}{14} : \frac{280}{14} = 3 : 20 $

✔ Answer: 3 : 20

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14. 66 : 30

- GCD of 66 and 30 is 6
- $ \frac{66}{6} : \frac{30}{6} = 11 : 5 $

✔ Answer: 11 : 5

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15. 84 : 156

- GCD of 84 and 156:
- 84 = 2²×3×7
- 156 = 2²×3×13 → GCD = 12
- $ \frac{84}{12} : \frac{156}{12} = 7 : 13 $

✔ Answer: 7 : 13

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16. 378 : 105

- GCD of 378 and 105:
- 105 = 3×5×7
- 378 ÷ 3 = 126, 105 ÷ 3 = 35
- 126 ÷ 7 = 18, 35 ÷ 7 = 5 → GCD = 21
- $ \frac{378}{21} : \frac{105}{21} = 18 : 5 $

✔ Answer: 18 : 5

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17. 250 : 750

- GCD of 250 and 750 is 250
- $ \frac{250}{250} : \frac{750}{250} = 1 : 3 $

✔ Answer: 1 : 3

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18. 32 : 28.8

- Multiply by 10 → 320 : 288
- GCD of 320 and 288:
- 320 = 2⁶ × 5
- 288 = 2⁵ × 3² → GCD = 32
- $ \frac{320}{32} : \frac{288}{32} = 10 : 9 $

✔ Answer: 10 : 9

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19. 2.4 : 1.8

- Multiply by 10 → 24 : 18
- GCD of 24 and 18 is 6
- $ \frac{24}{6} : \frac{18}{6} = 4 : 3 $

✔ Answer: 4 : 3

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20. 25 : 45

- GCD of 25 and 45 is 5
- $ \frac{25}{5} : \frac{45}{5} = 5 : 9 $

✔ Answer: 5 : 9

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✔ Final Answers:

| Ratio | Simplified Form |
|--------------|------------------|
| 25 : 150 | 1 : 6 |
| 30 : 75 | 2 : 5 |
| 34 : 102 | 1 : 3 |
| 148 : 111 | 4 : 3 |
| 97 : 194 | 1 : 2 |
| 52 : 130 | 2 : 5 |
| 112 : 320 | 7 : 20 |
| 2.4 : 5.6 | 3 : 7 |
| 32 : 480 | 1 : 15 |
| 7.8 : 9.1 | 6 : 7 |
| 128 : 160 | 4 : 5 |
| 2.5 : 3.5 | 5 : 7 |
| 42 : 280 | 3 : 20 |
| 66 : 30 | 11 : 5 |
| 84 : 156 | 7 : 13 |
| 378 : 105 | 18 : 5 |
| 250 : 750 | 1 : 3 |
| 32 : 28.8 | 10 : 9 |
| 2.4 : 1.8 | 4 : 3 |
| 25 : 45 | 5 : 9 |

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💡 Tips for Simplifying Ratios:
- Always find the GCD of the two numbers.
- If decimals are present, multiply both sides to make them whole numbers.
- Reduce the ratio just like a fraction.

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