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.

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.

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Tony B Share
Mar 24, 2018

Answer:

See the construction tips in the explanation.

Explanation:

Tony B

#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#

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