Question

Explain how to determine whether two ratios are equivalent

Answer 1

Ratios are fractions, right? Set the two fractions equal to each other and then cross-multiply them. If each side of the equation is equal, then the ratios are equal; if not, then the ratios are not equivalent.

Ex. 1

Comparing ratios 4:2 and 2:1

`(4)/(2) = (2)/(1)`

Cross-multiplying, we get 4 = 4, but we can also simplify each side of the equation to get 2 = 2.

Ex. 2

Comparing ratios 3:5 and 6:7

`(3)/(5) =? (6)/(7)`

Cross-multiply, we get 21 = 30, so the ratios are not equal. This is an example of a case where you can't simplify the ratios.

Ex. 3

Comparing rations 5:12 and 10:24

`(5)/(12) = (10)/(24)`

Cross-multiply, 120 = 120 so the ratios are equal.

Hope this helps!