Let's solve each ratio by reducing it to its
lowest form. To reduce a ratio, we find the
greatest common divisor (GCD) of the two numbers and divide both numbers by that GCD.
---
Example: 50 : 35
- GCD of 50 and 35 is
5
- $ 50 ÷ 5 = 10 $, $ 35 ÷ 5 = 7 $
- Reduced form:
10 : 7
Now let’s go through each problem:
---
1) 49 : 21
- GCD of 49 and 21 is
7
- $ 49 ÷ 7 = 7 $, $ 21 ÷ 7 = 3 $
-
7 : 3
---
2) 42 : 54
- GCD of 42 and 54 is
6
- $ 42 ÷ 6 = 7 $, $ 54 ÷ 6 = 9 $
-
7 : 9
---
3) 12 : 32
- GCD of 12 and 32 is
4
- $ 12 ÷ 4 = 3 $, $ 32 ÷ 4 = 8 $
-
3 : 8
---
4) 45 : 20
- GCD of 45 and 20 is
5
- $ 45 ÷ 5 = 9 $, $ 20 ÷ 5 = 4 $
-
9 : 4
---
5) 15 : 24
- GCD of 15 and 24 is
3
- $ 15 ÷ 3 = 5 $, $ 24 ÷ 3 = 8 $
-
5 : 8
---
6) 12 : 8
- GCD of 12 and 8 is
4
- $ 12 ÷ 4 = 3 $, $ 8 ÷ 4 = 2 $
-
3 : 2
---
7) 2 : 16
- GCD of 2 and 16 is
2
- $ 2 ÷ 2 = 1 $, $ 16 ÷ 2 = 8 $
-
1 : 8
---
8) 35 : 28
- GCD of 35 and 28 is
7
- $ 35 ÷ 7 = 5 $, $ 28 ÷ 7 = 4 $
-
5 : 4
---
9) 20 : 36
- GCD of 20 and 36 is
4
- $ 20 ÷ 4 = 5 $, $ 36 ÷ 4 = 9 $
-
5 : 9
---
10) 14 : 63
- GCD of 14 and 63 is
7
- $ 14 ÷ 7 = 2 $, $ 63 ÷ 7 = 9 $
-
2 : 9
---
11) 27 : 36
- GCD of 27 and 36 is
9
- $ 27 ÷ 9 = 3 $, $ 36 ÷ 9 = 4 $
-
3 : 4
---
12) 70 : 10
- GCD of 70 and 10 is
10
- $ 70 ÷ 10 = 7 $, $ 10 ÷ 10 = 1 $
-
7 : 1
---
13) 10 : 60
- GCD of 10 and 60 is
10
- $ 10 ÷ 10 = 1 $, $ 60 ÷ 10 = 6 $
-
1 : 6
---
14) 42 : 30
- GCD of 42 and 30 is
6
- $ 42 ÷ 6 = 7 $, $ 30 ÷ 6 = 5 $
-
7 : 5
---
15) 48 : 42
- GCD of 48 and 42 is
6
- $ 48 ÷ 6 = 8 $, $ 42 ÷ 6 = 7 $
-
8 : 7
---
16) 90 : 10
- GCD of 90 and 10 is
10
- $ 90 ÷ 10 = 9 $, $ 10 ÷ 10 = 1 $
-
9 : 1
---
17) 9 : 18
- GCD of 9 and 18 is
9
- $ 9 ÷ 9 = 1 $, $ 18 ÷ 9 = 2 $
-
1 : 2
---
18) 5 : 20
- GCD of 5 and 20 is
5
- $ 5 ÷ 5 = 1 $, $ 20 ÷ 5 = 4 $
-
1 : 4
---
19) 64 : 72
- GCD of 64 and 72 is
8
- $ 64 ÷ 8 = 8 $, $ 72 ÷ 8 = 9 $
-
8 : 9
---
20) 42 : 12
- GCD of 42 and 12 is
6
- $ 42 ÷ 6 = 7 $, $ 12 ÷ 6 = 2 $
-
7 : 2
---
✔ Final Answers:
| Problem | Reduced Ratio |
|--------|----------------|
| 1) | 7 : 3 |
| 2) | 7 : 9 |
| 3) | 3 : 8 |
| 4) | 9 : 4 |
| 5) | 5 : 8 |
| 6) | 3 : 2 |
| 7) | 1 : 8 |
| 8) | 5 : 4 |
| 9) | 5 : 9 |
| 10) | 2 : 9 |
| 11) | 3 : 4 |
| 12) | 7 : 1 |
| 13) | 1 : 6 |
| 14) | 7 : 5 |
| 15) | 8 : 7 |
| 16) | 9 : 1 |
| 17) | 1 : 2 |
| 18) | 1 : 4 |
| 19) | 8 : 9 |
| 20) | 7 : 2 |
---
You can now fill in the
Answers column on the worksheet accordingly. Let me know if you'd like this formatted for printing or as a downloadable file!
Parent Tip: Review the logic above to help your child master the concept of math ratio worksheet.
