8.11 Divide unit fractions by whole numbers
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Do you remember how to divide whole numbers by unit fractions?
What is $4\div\frac{1}{14}$4÷114?
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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?"
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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 |
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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?
ABCWhat is the size of the part created when $\frac{1}{3}$13 is divided by $4$4?
Dividing a unit fraction by a whole number is the same as multiplying the denominator of that fraction by the whole.