Are the Ratios Equivalent? Math worksheet for students to determine if pairs of ratios are equivalent.

To determine if two ratios are equivalent, we can simplify each ratio to its lowest terms and check if they are the same. Alternatively, we can cross-multiply: if the products are equal, the ratios are equivalent.

Let's solve each pair:

1. 5:10 and 3:6
- 5:10 = 5/10 = 1/2
- 3:6 = 3/6 = 1/2
- 1/2 = 1/2
- Answer: yes

2. 10:20 and 50:150
- 10:20 = 10/20 = 1/2
- 50:150 = 50/150 = 1/3
- 1/2 ≠ 1/3
- Answer: no

3. 6:42 and 10:60
- 6:42 = 6/42 = 1/7
- 10:60 = 10/60 = 1/6
- 1/7 ≠ 1/6
- Answer: no

4. 100:200 and 30:60
- 100:200 = 100/200 = 1/2
- 30:60 = 30/60 = 1/2
- 1/2 = 1/2
- Answer: yes

5. 15:30 and 100:300
- 15:30 = 15/30 = 1/2
- 100:300 = 100/300 = 1/3
- 1/2 ≠ 1/3
- Answer: no

6. 5:15 and 40:120
- 5:15 = 5/15 = 1/3
- 40:120 = 40/120 = 1/3
- 1/3 = 1/3
- Answer: yes

7. 8:24 and 3:12
- 8:24 = 8/24 = 1/3
- 3:12 = 3/12 = 1/4
- 1/3 ≠ 1/4
- Answer: no

8. 30:60 and 45:90
- 30:60 = 30/60 = 1/2
- 45:90 = 45/90 = 1/2
- 1/2 = 1/2
- Answer: yes

9. 12:48 and 8:32
- 12:48 = 12/48 = 1/4
- 8:32 = 8/32 = 1/4
- 1/4 = 1/4
- Answer: yes

10. 40:80 and 125:200
- 40:80 = 40/80 = 1/2
- 125:200 = 125/200 = 5/8
- 1/2 ≠ 5/8
- Answer: no

11. 3:2 and 24:18
- 3:2 = 3/2 = 1.5
- 24:18 = 24/18 = 4/3 ≈ 1.333
- 3/2 ≠ 4/3
- Answer: no

12. 5:4 and 20:16
- 5:4 = 5/4 = 1.25
- 20:16 = 20/16 = 5/4 = 1.25
- 5/4 = 5/4
- Answer: yes

13. 11:22 and 44:88
- 11:22 = 11/22 = 1/2
- 44:88 = 44/88 = 1/2
- 1/2 = 1/2
- Answer: yes

14. 13:26 and 15:45
- 13:26 = 13/26 = 1/2
- 15:45 = 15/45 = 1/3
- 1/2 ≠ 1/3
- Answer: no

Final Answers:
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