Dividing whole numbers by unit fractions
Picturing things
A good way to understand what a question is asking us, is to imagine using pictures. We can use things like area models and number lines to picture things like division. When we want to divide a whole number by a unit fraction (a fraction with $1$1 as the numerator), it helps to imagine how many of those parts each whole ($1$1) contains.
Let's take a look at how we can visualise this, using number lines and fraction bars.
Need more?
If you're still a little unsure, watch this video using a clock. By thinking about how many $\frac{1}{4}$14 hour blocks there are in $1$1 hour, we see that multiplying the denominator of the unit fraction by the whole number works!
If we see a problem like $5$5 ÷ $\frac{1}{6}$16, it helps to think of how many sixths there are in $1$1 whole. Then, we can think about how many there are in 5 wholes.
Worked Examples
Question 1
The number line below shows $4$4 wholes split into $\frac{1}{3}$13 size pieces.
If $4$4 is divided into pieces that are $\frac{1}{3}$13 of a whole each, how many pieces are there in total?
How many pieces would there be if we had $5$5 wholes?
How many pieces would there be if we split up $10$10 wholes?
Question 2
This number line shows that each whole is divided up into thirds.
Write the fraction that shows how big each division is:
How many divisions are in $2$2 wholes?
What is the result of $2\div\frac{1}{3}$2÷13?
How many third size pieces are there in $5$5 wholes?
Question 3
$2\div\frac{1}{5}$2÷15 can be visualised using the following model:
How many $\frac{1}{5}$15 pieces are in $2$2 wholes?
How many $\frac{1}{5}$15 size pieces would be in $9$9 wholes?
How many $\frac{1}{5}$15 size pieces would be in $17$17 wholes?