# How do I find a fraction between 7/56 and 8/56?

May 29, 2017

There are infinitely many fractions (possible answer $\frac{15}{112}$)

#### Explanation:

The fractions given are $\frac{1}{\textcolor{red}{7}}$ and $\frac{1}{\textcolor{b l u e}{8}}$

Multiply $\frac{1}{\textcolor{red}{7}}$ by $\frac{\textcolor{b l u e}{8}}{\textcolor{b l u e}{8}}$, and multiply $\frac{1}{\textcolor{b l u e}{8}}$ by $\frac{\textcolor{red}{7}}{\textcolor{red}{7}}$

The answer will be $\frac{8}{56}$, and $\frac{7}{56}$

A fraction between them will be $\frac{7.5}{56}$ or $\frac{15}{112}$

Or $\frac{7.1}{56} \implies \textcolor{red}{\frac{71}{560}}$. Or $\frac{7.2}{56} \implies \textcolor{red}{\frac{9}{70}}$

Or $\frac{7.22}{56} \implies \textcolor{red}{\frac{361}{2800}}$...

May 29, 2017

Use equivalent fractions of $\frac{8}{56} \mathmr{and} \frac{7}{56}$

For example, it is easy to write down fractions between

$\frac{72}{504} \mathmr{and} \frac{63}{504.}$

#### Explanation:

There are infinitely many fractions between these two fractions.
$\frac{1}{7} \mathmr{and} \frac{1}{8}$

Find a common denominator first: It is$56$

Find a fraction between $\frac{8}{56} \mathmr{and} \frac{7}{56}$

We could answer $\frac{7.1}{56} \mathmr{and} \frac{7.4}{56} \mathmr{and} \frac{7.8}{56}$ etc,

but it is not good practice to use decimals combined with fractions.

If the denominator is not the Lowest Common Denominator, it becomes easier.

Use equivalent fractions of $\frac{8}{56} \mathmr{and} \frac{7}{56}$

It is then easier to find any number of fractions.

$\frac{16}{112} \mathmr{and} \frac{14}{112}$ leads to an answer of $\frac{15}{112}$

$\frac{32}{224} \mathmr{and} \frac{28}{224}$ allows us to find:

$\frac{29}{224} , \frac{30}{224} , \frac{31}{224}$ as being fractions between.