Question

You are comparing apples to oranges in a fruit bowl. Is the ratio 2:3 the same as the ratio 3:2?

Answer 1

No, the two ratios are not the same.

Explanation:

When we are saying "apples to oranges", mathematically it means:

`(Apples)/(Oranges)`,

Which could be 2:3 or 3:2, which in fractional from are written as
`(2)/(3)` and
`(3)/(2)` respectively.

We see that

`(2)/(3) \\eq (3)/(20).`

In words the ratio 2:3 says "for every two apples there are three oranges", and 3:2 says "for every three apples there are two oranges". Again we see that the two sentences are not saying the same thing, therefore the ratio 2:3 is not same as 3:2.