# What is the fraction between 1/3 and 1/5?

Oct 1, 2017

The fraction exactly between them is $\frac{4}{15}$

There are many, many fractions between $\frac{1}{3} \mathmr{and} \frac{1}{5}$.
Using a larger number as the denominator allows you to find some.

#### Explanation:

'The' fraction implies the fraction exactly halfway between them.
The obvious answer would seem to be $\frac{1}{4}$. However, it is wrong.

Find equivalent fractions for $\frac{1}{3} \mathmr{and} \frac{1}{5}$ with the same denominator:

$L C M = 15$
$\frac{1}{3} \mathmr{and} \frac{1}{5} \text{ "rarr 5/15 and 3/15" } \therefore \frac{4}{15}$ is exactly between them. (But this is not $\frac{1}{4}$!)

However, if you choose a larger denominator you will easily see how many other fractions there are.

Denominator of $60$

$\frac{1}{3} \mathmr{and} \frac{1}{5} \text{ } \rightarrow \frac{20}{60} \mathmr{and} \frac{12}{60}$

$\therefore \frac{13}{60} \text{ "14/60" "15/60" "16/60" "17/60" "18/60" } \frac{19}{60}$ are all between

Denominator of $75$

$\frac{1}{3} \mathmr{and} \frac{1}{5} \text{ } \rightarrow \frac{25}{75} \mathmr{and} \frac{15}{75}$

$\frac{16}{75} \text{ "17/75" "18/75" "19/75" "20/75" "21/75" "22/75" "23/75" } \frac{24}{75}$
are all between $\frac{1}{3} \mathmr{and} \frac{1}{5}$