8.10 Divide whole numbers by unit fractions

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Do you remember how a fraction can represent division?

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When we divide by a whole number, such as $$12÷​4, we ask the question "how many groups of $$4 fit into $$12?" It's just like thinking about "what number fills in the blank: $$4×=12".

In this case, there are $$3 whole groups of $$4 in $$12, so the result is $$3.

We can think about dividing by a unit fraction in a similar way. The division $$2÷​13​ is equivalent to asking the question "how many parts of size $$13​ fit into $$2 wholes?"

If we split two wholes up into thirds, we can see that there are $$3 thirds in each whole, and so there are $$2×3=6 thirds in total.

The same thing happens for dividing by other unit fractions. If we calculated $$3÷​15​ this time, each of the three wholes will be divided into $$5 fifths:

So $$3÷​15​ is the same as $$3×5=15.

Notice that this is just like thinking about "what number fills in the blank: $$15​×=3". We know that $$15​×15=3, so it makes sense that $$3÷​15​=15.

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