# How do you use a number line to divide a fraction by a whole number?

## For example $\frac{4}{5} \div i \mathrm{de} 3$ I know how to get the answer without a number line but I don't understand how to get the answer with a number line or how to prove my answer with a number line.

Mar 24, 2018

See the construction tips in the explanation.

#### Explanation:

$\textcolor{red}{\text{Measuring is counting}}$

$\textcolor{b l u e}{\text{Step 1}}$

Draw a number line ( A to B) of some easily divisible length. Perhaps 15 lots of $\frac{1}{2}$ cm. We will end up counting in ${15}^{\text{ths}}$

Draw the line BG of some length that is easily divided into 5 equal parts. The angle does not matter as long as it is sensible.

Draw the line GA. Then the parallel lines from F,E,D and C

This has provided a full set of ${5}^{\text{ths}}$ from A to B

Count $\frac{4}{5}$ from A towards B and mark that point (H).
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$\textcolor{b l u e}{\text{Step 2}}$

In the same way as in Step 1 divide AH into 3 parts
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$\textcolor{b l u e}{\text{Step 3}}$

In the same way divide AB into ${15}^{\text{th}}$. You only need to subdivide AJ to make your point. You will have $\frac{4}{15}$ matching:

$\frac{4}{5} \div 3 \to \frac{4}{5} \times \frac{1}{3} = \frac{4}{15}$