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

Take the median like that $\frac{\frac{1}{3} + \frac{1}{4}}{2} = \frac{7}{24}$

Dec 16, 2015

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

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

$\frac{1}{4} = 0.25$
and
$\frac{1}{3} = 0.33333$

Thus, $\frac{1}{4} = \frac{25}{100}$ and $\frac{1}{3} = \frac{33. \overline{3}}{100}$.

Fractions between these two fractions can be picked out easily.

$\frac{26}{100} = \frac{13}{50}$

$\frac{30}{100} = \frac{3}{10}$

$\frac{31}{100}$

All of these are found between $\frac{1}{3}$ and $\frac{1}{4}$.

You could also take the geometric mean.

$\sqrt{\left(\frac{1}{3}\right) \left(\frac{1}{4}\right)} = \sqrt{\frac{1}{12}} = \frac{1}{2 \sqrt{3}} = \frac{\sqrt{3}}{6}$

You could also find arbitrary common denominators.

$\frac{1}{3} \left(\frac{52}{52}\right)$ and $\left(\frac{1}{4}\right) \left(\frac{39}{39}\right)$

$\frac{52}{156}$ and $\frac{39}{156}$

Between these are plenty of fractions...

$\frac{50}{156} = \frac{25}{78}$

$\frac{397}{1560}$

May 11, 2018

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

$\frac{1 + 1}{3 + 4} = \frac{2}{7}$

We're assured

$\frac{1}{4} < \frac{2}{7} < \frac{1}{3}$