# Multiply Fractions

In this worksheet, students will practise multiplying fractions and simplifying answers by finding the Greatest Common Factor (GCF).

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

When working with fractions, multiplying them may seem daunting, but don't worry!

It is actually one of the simplest processes if you follow the rules.

The rules are straightforward and, as long as you can multiply and divide whole numbers, you should have no trouble.

The Rules:

1) Multiply the numerators (top numbers);

2) Multiply the denominators (bottom numbers);

3) Cancel down the answer to its simplest form.

That's it... easy peasy!

e.g. Multiply the following fractions:

 1 5
x
 2 3

If we follow the rules, we need to work out:

1) 1 x 2 = 2

2) 5 x 3 = 15

3) 2/15 cannot be simplified, as the numbers 2 and 15 do not have any common factors (except for 1).

Let's see this as the sum:

 1 5
x
 2 3
=
 2 15

Let's try another...

e.g. Multiply the following fractions:

 3 5
x
 5 11

If we follow the rules, we reach:

 3 5
x
 5 11
=
 15 55

If we now look at our new fraction, we need to find the largest number which we can divide both 11 and 55 by.

As the biggest number is 5, this means we divide both the numerator and denominator by 5:

 15 55
=
 15 ÷ 5 55 ÷ 5
=
 3 11

In this activity, you will practise multiplying fractions and simplifying the answer you reach when possible.

Work out the answer to:

 3 5
x
 1 2

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

Simplify your answer into its lowest form.

Work out the answer to:

 6 7
x
 2 15

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

Simplify your answer into its lowest form.

Imagine that your friend is trying to calculate the following sum:

 1 2
x
 3 4

They have written the workings below:

 1 x 3 2 x 4
=
 3 6

 3 6
= 2

You know that their answer is incorrect

Which of the statements below describes where they made an error?

They added the denominators instead of multiplying them

They added the numerators instead of multiplying them

They divided the fraction the wrong way round

They added the fractions instead of multiplying them

If we worked out:

 3 8
x
 4 5

What is the largest factor we could use to simplify our answer?

1

2

4

8

Work out the answer to:

 7 4
x
 8 14

Simplify your answer into its lowest form.

Complete the sentence below to explain how to multiply fractions.

If we worked out:

 2 5
x
 15 16

What is the Greatest Common Factor (GCF) we could use to simplify our answer?

Find the answer to:

 7 10
x
 15 28

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

Simplify your answer into its lowest form.

Find the answer to:

 5 12
x
 18 25

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

Simplify your answer into its lowest form.

Find the answer to:

 7 9
x
 18 35

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

Simplify your answer into its lowest form.

• Question 1

Work out the answer to:

 3 5
x
 1 2

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

Simplify your answer into its lowest form.

3/10
EDDIE SAYS
Let's follow our three rules: 1) 3 x 1 = 3 2) 5 x 2 = 10 3) Can 3/10 be simplified? 3 and 10 do not have any common factors (except 1), so this fraction cannot be simplified further.
• Question 2

Work out the answer to:

 6 7
x
 2 15

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

Simplify your answer into its lowest form.

4/35
EDDIE SAYS
If we multiply the top row (numerators), we reach 12. If we multiply the bottom row (denominators), we reach 105. Did you notice that both these numbers are in the three times table? So we can simplify 12/105 by dividing the numerator and denominator by 3, to reach 4/35.
• Question 3

Imagine that your friend is trying to calculate the following sum:

 1 2
x
 3 4

They have written the workings below:

 1 x 3 2 x 4
=
 3 6

 3 6
= 2

You know that their answer is incorrect

Which of the statements below describes where they made an error?

They added the denominators instead of multiplying them
They divided the fraction the wrong way round
EDDIE SAYS
Did you spot that there were two errors here? The first error is in line 2 of your friend's workings. Is 2 x 4 = 6? No, it's 8. The second comes in the last line. Is 3 ÷ 6 really 2? No, it's 1/2. The easiest way to spot mistakes in maths is to actually work out the sums and then compare your answer with the one you are given.
• Question 4

If we worked out:

 3 8
x
 4 5

What is the largest factor we could use to simplify our answer?

4
EDDIE SAYS
The easiest way to work this out is to do the sum and then compare the numbers in the fraction answer. If we multiply the numerators and denominators, we reach 12/40. 12 and 40 are both numbers in the 1,2 and 4 times tables. Of these, 4 is the largest factor. Using the Greatest Common Factor (GCF) ensures that we are simplifying a fraction to its smallest possible form.
• Question 5

Work out the answer to:

 7 4
x
 8 14

Simplify your answer into its lowest form.

1
EDDIE SAYS
If we multiply both the numerators and the denominators, we get 56/56. Did you spot that any number divided by itself is the same as 1? 1 is the simplest way to write 56/56.
• Question 6

Complete the sentence below to explain how to multiply fractions.

EDDIE SAYS
Remember our golden rule: Multiply the top row (numerators), then the bottom row (denominators), and simplify if you can. If you follow this rule, you can't go wrong!
• Question 7

If we worked out:

 2 5
x
 15 16

What is the Greatest Common Factor (GCF) we could use to simplify our answer?

10
EDDIE SAYS
If we multiply the numerators and denominators here, we reach 30/80. The numbers 30 and 80 both appear in the 1, 2, 5 and 10 times tables. The largest number is 10, so this is our GCF.
• Question 8

Find the answer to:

 7 10
x
 15 28

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

Simplify your answer into its lowest form.

3/8
EDDIE SAYS
If we multiply the numerators and the denominators, we reach 105/280. Both of these numbers appear in the 1, 5 and 7 times tables. So our GCF is 7 x 5 = 35, as any factor of these numbers will automatically be a factor of our target numbers. This is a useful tip to remember to find the GCF with larger numbers.
• Question 9

Find the answer to:

 5 12
x
 18 25

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

Simplify your answer into its lowest form.

3/10
EDDIE SAYS
If we multiply the top and bottom rows, we reach 90/300. Both of these numbers appear in the 1 2, 3, 5, 6, 10, 15 and 30 times tables. So our GCF is 30. If we divide the numerator and denominator by 30, the simplest form of this fraction is 3/10.
• Question 10

Find the answer to:

 7 9
x
 18 35

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

Simplify your answer into its lowest form.

2/5
EDDIE SAYS
Multiply the numerators and denominators to reach 126/315. Both of these numbers appear in the 1, 7 and 9 times tables. Our GCF is 9 x 7 = 63. If we divide the numerator and denominator by 63, we reach the answer 2/5. Well done if you spotted that GCF as that was challenging! You could also have divided by 9 (to reach 14/35) and then by 7.
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