Ratios are considered equivalent when they represent the same relationship between two quantities. In other words, two ratios are equivalent if they can be simplified to have the same value. The definition of equivalent ratios is as follows:
Two ratios, a/b and c/d, are equivalent if and only if ad = bc.
This means that if the product of the means (a and d) is equal to the product of the extremes (b and c), the ratios are equivalent. You can also think of it as reducing both ratios to their simplest form; if they result in the same simplified ratio, they are equivalent.
For example, the ratios 2/4 and 6/12 are equivalent because 2 * 12 = 4 * 6, which follows the definition of equivalent ratios.