Simplifying Ratios worksheet for students to 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).

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Step-by-step Solutions:

#### Row 1
1. 3 : 15
GCD of 3 and 15 is 3
→ $ \frac{3}{3} : \frac{15}{3} = 1 : 5 $

2. 15 : 30
GCD of 15 and 30 is 15
→ $ \frac{15}{15} : \frac{30}{15} = 1 : 2 $

3. 6 : 36
GCD of 6 and 36 is 6
→ $ \frac{6}{6} : \frac{36}{6} = 1 : 6 $

4. 15 : 20
GCD of 15 and 20 is 5
→ $ \frac{15}{5} : \frac{20}{5} = 3 : 4 $

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#### Row 2
5. 12 : 36
GCD of 12 and 36 is 12
→ $ \frac{12}{12} : \frac{36}{12} = 1 : 3 $

6. 10 : 110
GCD of 10 and 110 is 10
→ $ \frac{10}{10} : \frac{110}{10} = 1 : 11 $

7. 9 : 27
GCD of 9 and 27 is 9
→ $ \frac{9}{9} : \frac{27}{9} = 1 : 3 $

8. 5 : 125
GCD of 5 and 125 is 5
→ $ \frac{5}{5} : \frac{125}{5} = 1 : 25 $

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#### Row 3
9. 25 : 50
GCD of 25 and 50 is 25
→ $ \frac{25}{25} : \frac{50}{25} = 1 : 2 $

10. 18 : 72
GCD of 18 and 72 is 18
→ $ \frac{18}{18} : \frac{72}{18} = 1 : 4 $

11. 8 : 30
GCD of 8 and 30 is 2
→ $ \frac{8}{2} : \frac{30}{2} = 4 : 15 $

12. 10 : 48
GCD of 10 and 48 is 2
→ $ \frac{10}{2} : \frac{48}{2} = 5 : 24 $

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#### Row 4
13. 12 : 72
GCD of 12 and 72 is 12
→ $ \frac{12}{12} : \frac{72}{12} = 1 : 6 $

14. 24 : 72
GCD of 24 and 72 is 24
→ $ \frac{24}{24} : \frac{72}{24} = 1 : 3 $

15. 22 : 44
GCD of 22 and 44 is 22
→ $ \frac{22}{22} : \frac{44}{22} = 1 : 2 $

16. 8 : 36
GCD of 8 and 36 is 4
→ $ \frac{8}{4} : \frac{36}{4} = 2 : 9 $

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#### Row 5
17. 5 : 180
GCD of 5 and 180 is 5
→ $ \frac{5}{5} : \frac{180}{5} = 1 : 36 $

18. 22 : 220
GCD of 22 and 220 is 22
→ $ \frac{22}{22} : \frac{220}{22} = 1 : 10 $

19. 35 : 40
GCD of 35 and 40 is 5
→ $ \frac{35}{5} : \frac{40}{5} = 7 : 8 $

20. 6 : 45
GCD of 6 and 45 is 3
→ $ \frac{6}{3} : \frac{45}{3} = 2 : 15 $

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#### Row 6
21. 27 : 36
GCD of 27 and 36 is 9
→ $ \frac{27}{9} : \frac{36}{9} = 3 : 4 $

22. 5 : 35
GCD of 5 and 35 is 5
→ $ \frac{5}{5} : \frac{35}{5} = 1 : 7 $

23. 21 : 30
GCD of 21 and 30 is 3
→ $ \frac{21}{3} : \frac{30}{3} = 7 : 10 $

24. 16 : 12
GCD of 16 and 12 is 4
→ $ \frac{16}{4} : \frac{12}{4} = 4 : 3 $

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✔ Final Answers:

| Ratio | Simplified Form |
|-----------|------------------|
| 3 : 15 | 1 : 5 |
| 15 : 30 | 1 : 2 |
| 6 : 36 | 1 : 6 |
| 15 : 20 | 3 : 4 |
| 12 : 36 | 1 : 3 |
| 10 : 110 | 1 : 11 |
| 9 : 27 | 1 : 3 |
| 5 : 125 | 1 : 25 |
| 25 : 50 | 1 : 2 |
| 18 : 72 | 1 : 4 |
| 8 : 30 | 4 : 15 |
| 10 : 48 | 5 : 24 |
| 12 : 72 | 1 : 6 |
| 24 : 72 | 1 : 3 |
| 22 : 44 | 1 : 2 |
| 8 : 36 | 2 : 9 |
| 5 : 180 | 1 : 36 |
| 22 : 220 | 1 : 10 |
| 35 : 40 | 7 : 8 |
| 6 : 45 | 2 : 15 |
| 27 : 36 | 3 : 4 |
| 5 : 35 | 1 : 7 |
| 21 : 30 | 7 : 10 |
| 16 : 12 | 4 : 3 |

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📝 Explanation:

To simplify any ratio $ a : b $:
1. Find the GCD (Greatest Common Divisor) of $ a $ and $ b $.
2. Divide both $ a $ and $ b $ by the GCD.
3. The result is the simplified ratio.

This ensures the ratio is in its lowest terms, meaning no common factor exists between the two numbers other than 1.

Let me know if you'd like this as a printable answer sheet!