Question

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

For example `4/5 divide 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.

Answer 1

See the construction tips in the explanation.

Explanation:

`color(red)("Measuring is counting")`

`color(blue)("Step 1")`

Draw a number line ( A to B) of some easily divisible length. Perhaps 15 lots of `1/2` cm. We will end up counting in `15^("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^("ths")` from A to B

Count `4/5` from A towards B and mark that point (H).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Step 2")`

In the same way as in Step 1 divide AH into 3 parts
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 3")`

In the same way divide AB into `15^("th")`. You only need to subdivide AJ to make your point. You will have `4/15` matching:

`4/5-:3->4/5xx1/3= 4/15`