8. Multiply and divide fractions

United States of America

Grade 5

Lesson

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

What is $4\div\frac{1}{14}$4÷114?

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 |

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?

ABCWhat 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.