Question

Determine whether the following ratios are equivalent or not. a) 3:4 and 15:20 b) 4:5 and 27:35 c) 7:4 and 49:28

Answer 1

To determine if ratios are equivalent, we simplify them and check if they yield the same value. The ratios 3:4 and 15:20 are equivalent, 4:5 and 27:35 are not equivalent, and 7:4 and 49:28 are equivalent.

Step-by-step explanation:

To determine whether two ratios are equivalent, we need to simplify them and check if they yield the same value. Let's check each pair of ratios:

1. 3:4 and 15:20: Both ratios can be simplified to 3/4 and 15/20. If we cross-multiply, we get 3x20 = 4x15, which simplifies to 60 = 60. Since the cross-products are equal, the ratios 3:4 and 15:20 are equivalent.
2. 4:5 and 27:35: We can simplify 4/5 to 8/10 and 27/35 to 27/35. Cross-multiplying, we get 8x35 = 10x27, which does not simplify to equal expressions. Therefore, the ratios 4:5 and 27:35 are not equivalent.
3. 7:4 and 49:28: Simplifying 7/4 gives us 7/4 and simplifying 49/28 gives us 7/4. Cross-multiplying, 7x28 = 4x49, which simplifies to 196 = 196. The cross-products are equal, so the ratios 7:4 and 49:28 are equivalent.

In summary, the ratios a) 3:4 and 15:20 and c) 7:4 and 49:28 are equivalent, while b) 4:5 and 27:35 are not equivalent.

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