Let's solve each of these ratio simplification problems step by step. To
simplify a ratio, we divide both numbers by their
greatest common divisor (GCD).
---
1) 6 : 3
- GCD of 6 and 3 is
3
- $ 6 ÷ 3 = 2 $, $ 3 ÷ 3 = 1 $
-
Answer: 2 : 1
---
2) 4 : 8
- GCD of 4 and 8 is
4
- $ 4 ÷ 4 = 1 $, $ 8 ÷ 4 = 2 $
-
Answer: 1 : 2
---
3) 5 : 10
- GCD of 5 and 10 is
5
- $ 5 ÷ 5 = 1 $, $ 10 ÷ 5 = 2 $
-
Answer: 1 : 2
---
4) 8 : 16
- GCD of 8 and 16 is
8
- $ 8 ÷ 8 = 1 $, $ 16 ÷ 8 = 2 $
-
Answer: 1 : 2
---
5) 5 : 20
- GCD of 5 and 20 is
5
- $ 5 ÷ 5 = 1 $, $ 20 ÷ 5 = 4 $
-
Answer: 1 : 4
---
6) 9 : 15
- GCD of 9 and 15 is
3
- $ 9 ÷ 3 = 3 $, $ 15 ÷ 3 = 5 $
-
Answer: 3 : 5
---
7) 15 : 3
- GCD of 15 and 3 is
3
- $ 15 ÷ 3 = 5 $, $ 3 ÷ 3 = 1 $
-
Answer: 5 : 1
---
8) 9 : 27
- GCD of 9 and 27 is
9
- $ 9 ÷ 9 = 1 $, $ 27 ÷ 9 = 3 $
-
Answer: 1 : 3
---
9) 25 : 10
- GCD of 25 and 10 is
5
- $ 25 ÷ 5 = 5 $, $ 10 ÷ 5 = 2 $
-
Answer: 5 : 2
---
10) 18 : 3
- GCD of 18 and 3 is
3
- $ 18 ÷ 3 = 6 $, $ 3 ÷ 3 = 1 $
-
Answer: 6 : 1
---
11) 6 : 14
- GCD of 6 and 14 is
2
- $ 6 ÷ 2 = 3 $, $ 14 ÷ 2 = 7 $
-
Answer: 3 : 7
---
12) 12 : 14
- GCD of 12 and 14 is
2
- $ 12 ÷ 2 = 6 $, $ 14 ÷ 2 = 7 $
-
Answer: 6 : 7
---
13) 30 : 20
- GCD of 30 and 20 is
10
- $ 30 ÷ 10 = 3 $, $ 20 ÷ 10 = 2 $
-
Answer: 3 : 2
---
14) 21 : 6
- GCD of 21 and 6 is
3
- $ 21 ÷ 3 = 7 $, $ 6 ÷ 3 = 2 $
-
Answer: 7 : 2
---
15) 10 : 35
- GCD of 10 and 35 is
5
- $ 10 ÷ 5 = 2 $, $ 35 ÷ 5 = 7 $
-
Answer: 2 : 7
---
16) 40 : 48
- GCD of 40 and 48 is
8
- $ 40 ÷ 8 = 5 $, $ 48 ÷ 8 = 6 $
-
Answer: 5 : 6
---
17) 49 : 56
- GCD of 49 and 56 is
7
- $ 49 ÷ 7 = 7 $, $ 56 ÷ 7 = 8 $
-
Answer: 7 : 8
---
18) 24 : 64
- GCD of 24 and 64 is
8
- $ 24 ÷ 8 = 3 $, $ 64 ÷ 8 = 8 $
-
Answer: 3 : 8
---
19) 24 : 54
- GCD of 24 and 54 is
6
- $ 24 ÷ 6 = 4 $, $ 54 ÷ 6 = 9 $
-
Answer: 4 : 9
---
20) 72 : 16
- GCD of 72 and 16 is
8
- $ 72 ÷ 8 = 9 $, $ 16 ÷ 8 = 2 $
-
Answer: 9 : 2
---
✔ Final Answers:
| Problem | Simplified Ratio |
|--------|------------------|
| 1) | 2 : 1 |
| 2) | 1 : 2 |
| 3) | 1 : 2 |
| 4) | 1 : 2 |
| 5) | 1 : 4 |
| 6) | 3 : 5 |
| 7) | 5 : 1 |
| 8) | 1 : 3 |
| 9) | 5 : 2 |
| 10) | 6 : 1 |
| 11) | 3 : 7 |
| 12) | 6 : 7 |
| 13) | 3 : 2 |
| 14) | 7 : 2 |
| 15) | 2 : 7 |
| 16) | 5 : 6 |
| 17) | 7 : 8 |
| 18) | 3 : 8 |
| 19) | 4 : 9 |
| 20) | 9 : 2 |
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💡
Tip: Always look for the largest number that divides both parts of the ratio evenly. That’s the GCD. You can use prime factorization or trial division to find it.
Let me know if you'd like a printable version or help with any other math topic!
Parent Tip: Review the logic above to help your child master the concept of simplifying ratios worksheet.
