Question

How do you determine whether the ratios are equivalent: 12/5 and 36/15?

Answer 1

`"ratios are equivalent"`

Explanation:

`"The ratio " 12/5` is in `color(blue)"simplest form".` That is no other factor except 1 will divide into them.

`"If we now simplify the ratio " 36/15`

36 and 15 both have a `color(blue)"common factor"` of 3 which we can divide them by.

`rArr36/15=(36÷3)/(15÷3)=12/5`

Usually written using `color(blue)"cancelling"` as follows.

`36/15=cancel(36)^(12)/cancel(15)^5=12/5`

`"Since " 36/15" reduces to the same value " 12/5" then the ratios are equivalent"`