Equivalent Ratios

Equivalent ratios

Equivalent ratios describe the same comparison between two quantities, even when the numbers are different. Two ratios are equivalent if one can be made from the other by multiplying or dividing both parts by the same nonzero number.

How to solve

1. Read the ratio carefully. It may be written with a colon, a fraction, or words.
2. Look for the missing value. Decide whether you need to scale up or scale down.
3. Use the same factor on both parts. If one part is multiplied by 3, the other part must also be multiplied by 3.
4. Simplify when needed. If the answer can be reduced, write it in simplest form.

Useful method

If you know one part of an equivalent ratio, find the scale factor by comparing the known numbers. Then apply that factor to the other part. For example, if one ratio is 2:5 and a matching ratio has first term 6, the scale factor is 3, so the second term is 15.

Check your answer

Make sure the two ratios represent the same relationship. A quick check is to divide the first number by the second in both ratios; the results should match. If fractions appear, reduce them fully before submitting.