How can you determine if ratios are equivalent?

Answer 1

The ratios are equal if and only if their cross products are equal.

That is a/b = c/d iff ad = bc

Answer 2

there are a few ways. let's look at 1/2 or the ratio 1 to 2 ( sometime written as 1:2) and compare it to 2 to 4 which I will write as 2/4 So one way is to multiply the bottom number on the first by the top number on the second. 2x2=4 and do the same with the remaining two numbers, 1x4=4 so they are the same and that means the ratios are the same. They used to call this multiplying the means and the extremes. In general a/b is equivalent to c/d if bc=ad. The other way is to put them both in lowest terms and compare. So 2/4 is 1/2 by dividing the numerator and denominator by 2.