Question

What fraction is between `1/20 and 1/30`??

Answer 1

`1/25`

Answer 2

See below

Explanation:

There are a couple of ways to do this:

• See that, if we talk about the size of the slices we make (looking at the denominator - a value of 2 means we're slicing a whole pizza into 2 pieces, a value of 20 means we take that same pizza and slice it in to 20 pieces, and a value of 30 means we're slicing it into 30 pieces), we can pick any denominator between 20 and 30. And so possible answers are:

`1/21, 1/22, 1/23, 1/24,...1/29`

• See that we can also make the denominators equal:

`1/20(1), 1/30(1)=>1/20(3/3), 1/30(2/2)=>3/60, 2/60`

With 60 as a denominator, there is no room to make more fractions. But if we make the denominators even bigger, there will be:

`(3xx10)/(60xx10), (2xx10)/(60xx10)=>30/600,20/600`

Now there is room to make `21/600, 22/600, 23/600, 24/600,...29/600`

If we make the denominator even bigger, there will be even more opportunities to make more fractions between `1/20 and 1/30`