Let's solve each ratio by
simplifying it to its
lowest terms. To simplify a ratio, we divide both numbers by their
greatest common divisor (GCD).
---
1) 65 : 15
- GCD of 65 and 15 is
5
- $ 65 ÷ 5 = 13 $
- $ 15 ÷ 5 = 3 $
-
Answer: 13 : 3
---
2) 56 : 45
- GCD of 56 and 45 is
1 (they are coprime)
- So, the ratio is already simplified.
-
Answer: 56 : 45
---
3) 98 : 24
- GCD of 98 and 24 is
2
- $ 98 ÷ 2 = 49 $
- $ 24 ÷ 2 = 12 $
-
Answer: 49 : 12
---
4) 380 : 56
- GCD of 380 and 56:
- Factors: 380 = 2×2×5×19, 56 = 2×2×2×7
- Common: 2×2 =
4
- $ 380 ÷ 4 = 95 $
- $ 56 ÷ 4 = 14 $
-
Answer: 95 : 14
---
5) 246 : 39
- GCD of 246 and 39:
- 246 ÷ 3 = 82, 39 ÷ 3 = 13 → GCD is
3
- $ 246 ÷ 3 = 82 $
- $ 39 ÷ 3 = 13 $
-
Answer: 82 : 13
---
6) 98 : 112
- GCD of 98 and 112:
- 98 = 2×7×7, 112 = 2×2×2×2×7 → GCD = 2×7 =
14
- $ 98 ÷ 14 = 7 $
- $ 112 ÷ 14 = 8 $
-
Answer: 7 : 8
---
7) 54 : 12
- GCD of 54 and 12 is
6
- $ 54 ÷ 6 = 9 $
- $ 12 ÷ 6 = 2 $
-
Answer: 9 : 2
---
8) 87 : 15
- GCD of 87 and 15:
- 87 = 3×29, 15 = 3×5 → GCD =
3
- $ 87 ÷ 3 = 29 $
- $ 15 ÷ 3 = 5 $
-
Answer: 29 : 5
---
9) 47 : 17
- 47 and 17 are both prime numbers
- GCD =
1
- Already simplified
-
Answer: 47 : 17
---
10) 90 : 117
- GCD of 90 and 117:
- 90 = 2×3×3×5
- 117 = 3×3×13 → GCD = 3×3 =
9
- $ 90 ÷ 9 = 10 $
- $ 117 ÷ 9 = 13 $
-
Answer: 10 : 13
---
✔ Final Answers:
1) 65 : 15 =
13 : 3
2) 56 : 45 =
56 : 45
3) 98 : 24 =
49 : 12
4) 380 : 56 =
95 : 14
5) 246 : 39 =
82 : 13
6) 98 : 112 =
7 : 8
7) 54 : 12 =
9 : 2
8) 87 : 15 =
29 : 5
9) 47 : 17 =
47 : 17
10) 90 : 117 =
10 : 13
---
Let me know if you'd like this in a printable format or with steps shown for each!
Parent Tip: Review the logic above to help your child master the concept of simplifying ratio worksheet for grade 7.
