Question

How do you find the fraction between 1/3 and 1/4?

Answer 1

Take the median like that `(1/3+1/4)/2=7/24`

Answer 2

There are an infinite amount of fractions between the two numbers.

Besides the other ways already mentioned, it's common knowledge that

`1/4=0.25`
and
`1/3=0.33333`

Thus, `1/4=25/100` and `1/3=(33.bar3)/100`.

Fractions between these two fractions can be picked out easily.

`26/100=13/50`

`30/100=3/10`

`31/100`

All of these are found between `1/3` and `1/4`.

You could also take the geometric mean.

`sqrt((1/3)(1/4))=sqrt(1/12)=1/(2sqrt3)=sqrt3/6`

You could also find arbitrary common denominators.

`1/3(52/52)` and `(1/4)(39/39)`

`52/156` and `39/156`

Between these are plenty of fractions...

`50/156=25/78`

`397/1560`

Answer 3

The mediant or freshman addition of fractions works great when we need one in between:

`{1 + 1}/{3 + 4} = 2/7`

We're assured

`1/4 < 2/7 < 1/3`