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

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Answer 1 · 2015-09-09T08:45:44

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

Answer 2 · 2015-12-16T04:20:21

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 · 2018-05-11T18:55:52

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

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

We're assured

$1/4 < 2/7 < 1/3$