Let's solve each pair of ratios to determine if they are
equivalent. Two ratios are equivalent if their simplified forms are the same or if their cross-products are equal.
We'll go through each pair one by one and answer with
"yes" or
"no".
---
1. 5 : 20 and 1 : 4
- Simplify 5:20 → divide both by 5 →
1:4
- Compare to 1:4 →
Same
✔ Yes
---
2. 30 : 10 and 10 : 30
- Simplify 30:10 → 3:1
- Simplify 10:30 → 1:3
- 3:1 ≠ 1:3
✘ No
---
3. 2 : 12 and 12 : 60
- Simplify 2:12 → 1:6
- Simplify 12:60 → divide by 12 → 1:5
- 1:6 ≠ 1:5
✘ No
---
4. 50 : 100 and 25 : 50
- 50:100 → 1:2
- 25:50 → 1:2
✔ Yes
---
5. 10 : 20 and 100 : 300
- 10:20 → 1:2
- 100:300 → 1:3
- 1:2 ≠ 1:3
✘ No
---
6. 4 : 16 and 15 : 60
- 4:16 → 1:4
- 15:60 → 1:4
✔ Yes
---
7. 5 : 25 and 4 : 18
- 5:25 → 1:5
- 4:18 → 2:9
- 1:5 ≠ 2:9
✘ No
---
8. 10 : 60 and 6 : 36
- 10:60 → 1:6
- 6:36 → 1:6
✔ Yes
---
9. 3 : 24 and 8 : 64
- 3:24 → 1:8
- 8:64 → 1:8
✔ Yes
---
10. 10 : 50 and 100 : 450
- 10:50 → 1:5
- 100:450 → divide by 50 → 2:9
- 1:5 ≠ 2:9
✘ No
---
11. 3 : 2 and 30 : 22
- 3:2 → already simplified
- 30:22 → divide by 2 → 15:11
- 3:2 ≠ 15:11
✘ No
---
12. 3 : 5 and 21 : 35
- 3:5 → stays same
- 21:35 → divide by 7 → 3:5
✔ Yes
---
13. 10 : 25 and 30 : 75
- 10:25 → divide by 5 → 2:5
- 30:75 → divide by 15 → 2:5
✔ Yes
---
14. 10 : 45 and 15 : 60
- 10:45 → divide by 5 → 2:9
- 15:60 → divide by 15 → 1:4
- 2:9 ≠ 1:4
✘ No
---
✔ Final Answers (in order):
1.
Yes
2.
No
3.
No
4.
Yes
5.
No
6.
Yes
7.
No
8.
Yes
9.
Yes
10.
No
11.
No
12.
Yes
13.
Yes
14.
No
---
Summary:
To check if two ratios are equivalent:
- Simplify both ratios.
- Or use cross-multiplication: $ a:b = c:d $ if $ a \times d = b \times c $
This method ensures accuracy.
Let me know if you'd like this formatted as a completed worksheet!
Parent Tip: Review the logic above to help your child master the concept of equivalent ratio worksheet.
