When we divide a whole number by a unit fraction, such as $2\div\frac{1}{3}$2÷13, we ask the question "how many parts of size $\frac{1}{3}$13 fit into $2$2 wholes?"

For this example, the answer is $6$6, and we can get this result by multiplying the whole $2$2 by the denominator $3$3.

Dividing a unit fraction by a whole number is the reverse of this. Let's look at $\frac{1}{3}\div2$13÷2 as an example:

We start with $\frac{1}{3}$13 of a whole, shown as the shaded area in the image above. We then divide each of these thirds into $2$2 parts:

How big is the remaining shaded area? Well, there are now $6$6 parts of equal area and $1$1 of them is shaded, so this is equal to $\frac{1}{6}$16 of the whole.

We can think about this using multiplication, in a similar way to dividing by a unit fraction, but this time the multiplication happens in the denominator:

$\frac{1}{3}\div2$13÷2	$=$=	$\frac{1}{2\times3}$12×3
	$=$=	$\frac{1}{6}$16

Apply

Question

Let's use the image below to help us find the value of $\frac{1}{3}\div4$13÷4. This number line shows the number $1$1 split into $3$3 parts of size $\frac{1}{3}$13.

Which image shows that each $third$ has been divided into $4$4 parts?
A
B
C
What is the size of the part created when $\frac{1}{3}$13 is divided by $4$4?

Remember!

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

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.a

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

5.NF.7.b

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

8.11 Divide unit fractions by whole numbers

Are you ready?

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