Question

What is `1/17 + 31/85`?

Answer 1

`1/17 + 31/85 = 36/85`

Explanation:

We have been asked to find the sum `1/17 + 31/85`.

To add (or subtract) fractions, we need the fractions to have the same denominator.
We could use `17xx85` for the common denominator, but we can use a smaller number if `17` is a factor of `85`. So we'll check that first.

Obviously, `5` is a factor of `85`, so do the division,

We find that `85 = 5xx17`.

So we will use `85` as our common denominator.

`1/17 = 5/5 xx 1/17 = 5/85`, so

`1/17 + 31/85 = 5/85 + 31/85`

`= 36/85`

Check to see if we can reduce the answer.
The only prime factors of `85` are `5` and `17`. Neither of these is a factor of `36`, (`2xx17=34` is too small and `3xx17 = 51` is too big) so the fraction cannot be reduced.