# Divide Fractions

In this worksheet, students will practise dividing two fractions by applying the KSF (Keep, Swap, Flip) process and simplifying answers if possible.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Number, Fractions, Decimals and Percentages

Curriculum subtopic:   Structure and Calculation, Fractions

Difficulty level:

### QUESTION 1 of 10

If you are confident with multiplying fractions, dividing fractions should be a walk in the park!

There is just one more step to add to the process of multiplying fractions.

A neat way to remember this process is with the acronym: KSF, which stands for Keep, Swap, Flip.

This little trick tells you precisely what to do to divide two fractions:

Keep the first fraction;

Swap the division sign to a multiply;

Flip the second fraction upside down.

Once you've done this, multiply your two fractions as usual and cancel your answer down if possible.

e.g. Complete the sum:

 2 7
÷
 1 3

If we apply KSF, we will reach the following sum:

Keep Swap Flip
 2 7
÷
 1 3
 2 7
x
 3 1

We can now work out this new sum and it will give the same answer as the original one:

 2 7
x
 3 1
=
 6 7

Clever right?!

In this activity, you will practise dividing two fractions by applying the KSF (Keep, Swap, Flip) process and simplifying your answer if you can.

 1 10
÷
 1 4

Give your answer in the form a/b, with no spaces and using the / key to provide your fraction bar.

 1 10
÷
 1 7

Give your answer in the form a/b, with no spaces and using the / key to provide your fraction bar.

Imagine you are checking a friend's work on this question:

 1 5
÷
 1 3

In which line of their working have they made a mistake?

1/5 x 3/1

1/5 x 3/1 = 3/6

3/6 = 1/2

Consider the calculation:

 15 30
÷
 2 5

Which of the fractions below is the simplest form of the answer to this question?

5/4

75/60

18/250

What single, simplified fraction is the same as:

 2 5
÷
 3 8

Give your answer in the form a/b, with no spaces and using the / key to provide your fraction bar.

Complete the sentence to summarise how to divide fractions.

If we divide these fractions:

 3 7
÷
 9 14

We will reach a fraction that needs to be cancelled.

Which of the numbers in the list are factors of both the numerator and denominator in our answer?

3

5

7

14

21

Which of the division sums in the table have been calculated correctly?

 2 9
÷
 10 27

Be careful with this one when you're cancelling.

 4 5
÷
 8 15

• Question 1

 1 10
÷
 1 4

Give your answer in the form a/b, with no spaces and using the / key to provide your fraction bar.

2/5
EDDIE SAYS
Did you follow the Keep, Swap, Flip process? We need to Keep 1/10, so that stays the same. We need to Swap the division sign to multiplication. Then we need to Flip the second fraction, so 1/4 becomes 4/1. So in summary we have: 1/10 x 4/1 We can calculate this multiplication as normal by multiplying the numerators and the denominators, to reach 4/10. Can this fraction be cancelled down? Yes, as 4 and 10 can both be divided by 2. So our final, simplified answer is 2/5. Is it getting easier to grasp this process? Let's practise some more.
• Question 2

 1 10
÷
 1 7

Give your answer in the form a/b, with no spaces and using the / key to provide your fraction bar.

7/10
EDDIE SAYS
Let's apply KSF again: Keep: 1/10 Swap: x Flip: 7/1 Put it together, and we have: 1/10 x 7/1 = 7/10 The numbers 7 and 10 do not have any common factors (except 1), so this fraction cannot be simplified further.
• Question 3

Imagine you are checking a friend's work on this question:

 1 5
÷
 1 3

In which line of their working have they made a mistake?

1/5 x 3/1 = 3/6
EDDIE SAYS
Did you spot the error in your friend's second line of working? They had applied KSF correctly, but then they added the denominators instead of multiplying them. This is an easy mistake to make, so try to avoid this trap yourself. I did then cancel the fraction correctly.
• Question 4

Consider the calculation:

 15 30
÷
 2 5

Which of the fractions below is the simplest form of the answer to this question?

5/4
EDDIE SAYS
If a question asks for the simplest form (especially for fraction questions), you MUST cancel down. If we apply KSF, we reach the calculation: 15/30 x 5/2 = 75/60 Option 2 was the un-cancelled answer - whoops! Option 3 was a complete red herring. Option 1 was the correct answer, as we could divide 75/60 by its GCF of 15 to reach 5/4.
• Question 5

What single, simplified fraction is the same as:

 2 5
÷
 3 8

Give your answer in the form a/b, with no spaces and using the / key to provide your fraction bar.

16/15
1 1/15
EDDIE SAYS
Did you remember KSF? It's a common mistake to forget the flip so keep an eye on that one. If we apply this, we reach the calculation: 2/5 x 8/3 = 16/15 Does it matter that the answer we got is a top-heavy fraction? Absolutely not, there's nothing wrong with that. Although, you can split into a mixed number if you are feeling confident or the question asks you to.
• Question 6

Complete the sentence to summarise how to divide fractions.

EDDIE SAYS
Always remember to Keep, Swap, Flip when dividing fractions. Trust us, it always works! The multiply the fractions as normal and, finally, always try to simplify your answer if you can.
• Question 7

If we divide these fractions:

 3 7
÷
 9 14

We will reach a fraction that needs to be cancelled.

Which of the numbers in the list are factors of both the numerator and denominator in our answer?

3
7
21
EDDIE SAYS
If we use KSF, we reach a calculation of: 3/7 x 14/9 = 42/63 So what can we divide both 42 and 63 by? If you spotted that they are both in the 3 and the 7 times tables, then that's awesome! If they are both in the 3 and 7 times tables, they will also be in the 21 (3 x 7) times tables. Remember this quick trick for the rest of the activity.
• Question 8

Which of the division sums in the table have been calculated correctly?

EDDIE SAYS
Well done if you spotted the two correct sums here! The first two have been done correctly, but the third one is incorrect. In the third sum, the 'flip' part of the working out has been missed. So instead of calculating 4/5 x 7/3 (28/15), this student has calculated 4/5 x 3/7 (12/35). This is something you need to watch out for in your own work. Always remember to apply all 3 steps before treating the sum as a multiplication.
• Question 9

 2 9
÷
 10 27

Be careful with this one when you're cancelling.

3
EDDIE SAYS
Did we manage to catch you out? We were hoping you would see that the simplest answer is a whole number, rather than a fraction. If you applied KSF correctly, you should have reached: 2/9 x 27/10 = 54/18 This can be simplified to 3/1 which is simply 3!
• Question 10

 4 5
÷
 8 15

1.5
EDDIE SAYS
Did you spot the cheeky little addition here? Examiners love throwing in an extra step that you weren't expecting to really push you. This question asked for your answer as a decimal. Applying KSF would give you: 4/5 x 15/8 = 60/40 Cancelling this fraction gets us to 3/2, which is the same as 1 and a half. As a decimal, this is written as 1.5. Always closely read the question. Great work, you've completed another activity! You may want to practise multiplying or simplifying fractions if you found this challenging.
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