8.11 Divide unit fractions by whole numbers

Are you ready?

Do you remember how to divide whole numbers by unit fractions?

Learn

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