Answer :
The equivalent ratios to 36:42 are- A. 108:126, B. 6:7, and H.72:84. These ratios maintain the same proportional relationship as the original ratio.
To find ratios equivalent to the given ratio of 36:42, we first simplify the original ratio. Both 36 and 42 can be divided by their greatest common divisor (GCD), which is 6. This gives us the simplified ratio of 6:7.
Next, we multiply this simplified ratio by different integers to find equivalent ratios:
- Multiplying by 2: 6×2 : 7×2 = 12:14
- Multiplying by 3: 6×3 : 7×3 = 18:21
- Multiplying by 4: 6×4 : 7×4 = 24:28
Now we compare the given choices to our calculated ratios. We find that:
- 108:126 is equivalent (36×3 : 42×3 = 108:126)
- 6:7 is equivalent (already simplified)
- 72:84 is equivalent (36×2 : 42×2 = 72:84)
