Question

What is the fraction between `1/3 and 1/5`?

Answer 1

The fraction exactly between them is `4/15`

There are many, many fractions between `1/3 and 1/5`.
Using a larger number as the denominator allows you to find some.

Explanation:

'The' fraction implies the fraction exactly halfway between them.
The obvious answer would seem to be `1/4`. However, it is wrong.

Find equivalent fractions for `1/3 and 1/5` with the same denominator:

`LCM =15`
`1/3 and 1/5" "rarr 5/15 and 3/15" ":. 4/15` is exactly between them. (But this is not `1/4`!)

However, if you choose a larger denominator you will easily see how many other fractions there are.

Denominator of `60`

`1/3 and 1/5" "rarr 20/60 and 12/60`

`:. 13/60" "14/60" "15/60" "16/60" "17/60" "18/60" "19/60` are all between

Denominator of `75`

`1/3 and 1/5" "rarr 25/75 and 15/75`

`16/75" "17/75" "18/75" "19/75" "20/75" "21/75" "22/75" "23/75" "24/75`
are all between `1/3 and 1/5`