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8.10 Divide whole numbers by unit fractions

Lesson

Are you ready?

Do you remember how a fraction can represent division?

Rewrite the fraction $\frac{5}{8}$58 as a division statement.

Learn

When we divide by a whole number, such as $12\div4$12÷​4, we ask the question "how many groups of $4$4 fit into $12$12?" It's just like thinking about "what number fills in the blank: $4\times\editable{}=12$4×=12".

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

We can think about dividing by a unit fraction in a similar way. The division $2\div\frac{1}{3}$2÷​13 is equivalent to asking the question "how many parts of size $\frac{1}{3}$13 fit into $2$2 wholes?"

If we split two wholes up into thirds, we can see that there are $3$3 thirds in each whole, and so there are $2\times3=6$2×3=6 thirds in total.

The same thing happens for dividing by other unit fractions. If we calculated $3\div\frac{1}{5}$3÷​15 this time, each of the three wholes will be divided into $5$5 fifths:

So $3\div\frac{1}{5}$3÷​15 is the same as $3\times5=15$3×5=15.

Notice that this is just like thinking about "what number fills in the blank: $\frac{1}{5}\times\editable{}=3$15×=3". We know that $\frac{1}{5}\times15=3$15×15=3, so it makes sense that $3\div\frac{1}{5}=15$3÷​15=15.

Apply

Question

The number line below shows $4$4 wholes split into $\frac{1}{3}$13 sized parts.

  1. If $4$4 is divided into parts that are $\frac{1}{3}$13 of a whole each, how many parts are there in total?

  2. How many parts would there be if we had $5$5 wholes?

  3. How many parts would there be if we split up $10$10 wholes?

Remember!

Dividing by a unit fraction is the same as multiplying by the denominator of that fraction.

Outcomes

5.NF.7

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Use strategies to divide fractions by reasoning about the relationship between multiplication and division. Division of a fraction by a fraction is not a requirement at this grade.

5.NF.7.b

Interpret division of a whole number by a unit fraction, and compute such quotients.

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