Unit 20 Section 4 : Dividing Fractions

To divide two fractions, we turn over the fraction we are dividing by and then multiply instead.

 a ÷ c = a × d b d b c

It is very important that only the fraction we are dividing by is turned over, not the first fraction.

If there are whole numbers or mixed numbers, these can be converted into top-heavy fractions and divided in the same way.

Example 1

 Work out: 4 ÷ 3 7 5

 This becomes: 4 × 5 7 3

 The answer is 4 × 5 = 20 7 × 3 21

Example 2 (with cancelling down before multiplying)

We can't cancel down a division, but we can cancel it down once it has changed into a multiplication.

 Work out: 6 ÷ 3 25 10

 This becomes: 6 × 10 25 3

At this stage we can cancel numerators with denominators.
For example, 10 and 25 are both divisible by 5, so we can divide them both by 5.
Also, 6 and 3 are both divisible by 3, so we can divide them both by 3.

 6 2 ÷ 10 2 25 5 3 1

Now the fractions can be multiplied:

 The answer is 2 × 2 = 4 5 × 1 5

Example 3 (with a whole number in the question)
 NOTE: If a whole number appears in a question, it can be converted to a top-heavy fraction because N = N 1
 Work out: 5 ÷ 3 7 This becomes: 5 ÷ 3 1 7 Then change to a multiplication: 5 × 7 1 3

In this case the multiplication can not be pre-cancelled, so we just do the multiplication:

 The answer is 5 × 7 = 35 = 11 2 1 × 3 3 3

NOTE: Remember that you can just leave your answer as a top-heavy fraction if you wish.

Example 4 (with mixed numbers in the question)

If there is a mixed number in the question, it must be converted into a top-heavy fraction before multiplying.

 Work out: 1 5 ÷ 2 2 6 3 This becomes: 11 ÷ 8 6 3 Then change to a multiplication: 11 × 3 6 8

We can now pre-cancel and carry out the multiplication as normal:

 11 × 3 = 11 × 3 1 = 11 6 8 6 2 8 16

Practice Question

Work out the answer to each of these questions then click on the button marked to see whether you are correct.

 (a) 2 ÷ 5 3 7

 (b) 3 ÷ 7 10 15

 (c) 4 ÷ 3 5

 (d) 3 1 ÷ 2 1 2 5

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Question 1
Work out the answers to the questions below. Simplify your answers and leave as a top-heavy fraction where necessary.
(a)
 1 ÷ 1 2 3
(b)
 3 ÷ 1 8 2
(c)
 3 ÷ 2 4 3
(d)
 4 ÷ 2 5 3
(e)
 3 ÷ 4 1 5
(f)
 3 ÷ 1 8 2
(g)
 5 ÷ 2 7 5
(h)
 5 ÷ 5 7 9
(i)
 1 ÷ 2 8 9
(j)
 3 ÷ 1 4 9
(k)
 1 ÷ 1 7 3
(l)
 4 ÷ 5 5 8
Question 2
Work out the answers to the questions below. Simplify your answers and leave as a top-heavy fraction where necessary.
(a)
 5 ÷ 2 3
(b)
 4 ÷ 3 4
(c)
 5 ÷ 3 7
(d)
 4 ÷ 6 7
(e)
 9 ÷ 2 5
(f)
 1 ÷ 4 11
(g)
 1 ÷ 3 2
(h)
 3 ÷ 2 4
(i)
 1 ÷ 2 8
(j)
 3 ÷ 4 4
(k)
 5 ÷ 3 8
(l)
 4 ÷ 2 5
Question 3
Work out the answers to the questions below. Simplify your answers and leave as a top-heavy fraction where necessary.
(a)
 3 1 ÷ 1 1 4 2
(b)
 3 1 ÷ 1 1 2 4
(c)
 1 5 ÷ 5 8 7
(d)
 3 1 ÷ 1 1 2 2
(e)
 5 1 ÷ 2 2 3
(f)
 4 1 ÷ 5 5 7
 Question 4Ahmed purchased 3 kg of sweets. He divides these into 3 equal parts to share with his brothers. 4
What fraction of a kilogram does each boy get?
 kg

 Question 5A large cake uses 3 times as much flour as a small cake. A large cake needs 1 1 kg of flour. 8
How much flour does a small cake need?
 kg

Question 6
A piece of leather is 45cm long and 20cm wide.
 Work out how many bookmarks, 2 1 cm wide, can be made if the leather is: 2
 (a) cut as shown above, to make bookmarks 20cm long bookmarks (b) cut the other way, to make bookmarks 45cm long bookmarks

You have now completed Unit 20 Section 4
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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