# How do you find a fraction between 1/5 and 1/4?

Sep 16, 2015

Find the mean of the two numbers

$\frac{\frac{1}{5} + \frac{1}{4}}{2} = \frac{\frac{9}{20}}{\frac{2}{1}} = \frac{9 \cdot 1}{20 \cdot 2} = \frac{9}{40}$

this is always halfway between the two numbers

May 12, 2016

Convert to equivalent fractions with a common denominator and then choose a suitable numerator between the ones you have calculated..

#### Explanation:

Change to a common denominator.
$\frac{1}{5} \mathmr{and} \frac{1}{4}$ can be changed to $\frac{4}{20} \mathmr{and} \frac{5}{20}$

However, the only values between 4 and 5 are fractions.
for example: $\frac{4.5}{20} = \frac{9}{40}$
This would require further simplifying.

Use a different common denominator: $\frac{8}{40} \mathmr{and} \frac{10}{40}$
$\frac{9}{40}$is between them.

Similarly for any common denominator with a value higher than 40:

$\frac{12}{60} \mathmr{and} \frac{15}{60}$ or $\frac{16}{80} \mathmr{and} \frac{20}{80}$

The question does not ask for a fraction midway between them, so any of the following would be possible answers:

$\frac{13}{60} , \frac{14}{60} , \frac{17}{80} , \frac{18}{80} , \frac{19}{80}$etc.

Sep 25, 2016

See below.

#### Explanation:

If you have two numbers ${\lambda}_{1} < {\lambda}_{2}$

then you have infinite numbers in between them. You can construct them as

$\mu = {\lambda}_{1} + \eta \left({\lambda}_{2} - {\lambda}_{1}\right)$ or
$\mu = \eta {\lambda}_{1} + \left(1 - \eta\right) {\lambda}_{2}$

with $0 < \eta < 1$ so

${\lambda}_{1} < \mu < {\lambda}_{2}$

Example: choosing $\eta = \frac{3}{5}$

$\frac{1}{5} < \frac{3}{5} \times \frac{1}{5} + \left(1 - \frac{3}{5}\right) \times \frac{1}{4} < \frac{1}{4}$ or

$\frac{1}{5} < \frac{11}{50} < \frac{1}{4}$