Are the ratios 9:14 and 1:2 equivalent

Are the ratios 9:14 and 1:2 equivalent?

The correct answer and explanation is:

No, the ratios 9:14 and 1:2 are not equivalent.

To determine whether two ratios are equivalent, you compare their values by cross-multiplying or simplifying them. Here’s how you can do that:

1. Simplify the first ratio, 9:14:
   The ratio 9:14 cannot be simplified further because 9 and 14 do not have any common factors other than 1. This ratio is already in its simplest form.
2. Simplify the second ratio, 1:2:
   The ratio 1:2 is already in its simplest form. It cannot be simplified further since the greatest common divisor (GCD) of 1 and 2 is 1.
3. Cross-multiply to compare the ratios:
   To check if the ratios are equivalent, you can cross-multiply them:
   • Multiply the first term of the first ratio by the second term of the second ratio:
     9 × 2 = 18
   • Multiply the first term of the second ratio by the second term of the first ratio:
     1 × 14 = 14
   Since 18 does not equal 14, the two ratios are not equivalent.

In conclusion, the ratios 9:14 and 1:2 are not equivalent because the products of their cross-multiplication are not the same. Therefore, 9:14 represents a different proportion than 1:2.