 # Find Equivalent Fractions

In this worksheet, student will practise simplifying fractions and making equivalent fractions. 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

Equivalents fractions are simply fractions that are equal.

The golden rule you must remember when you are manipulating fractions is that;

Whatever you do to the numerator, you must do the same to the denominator.

Imagine these fractions as bar models.

 1 2
=
 4 8 Both have the same amount shaded so they must be equal.

Finding equivalent fractions

e.g.

 3 4
=
 ? 16

We need to notice that we have two denominators and we are missing a numerator.

The first denominator has been multiplied by 4 to become the second, so we must do the same for the numerator.

3 x 4 = 12

 3 4
=
 12 16

Simplifying a fraction

To simplify a fraction (make the numbers smaller), we have to find the highest common factor.

This is the largest number we can divide both numbers by.

When we have found this, we need to divide both the numerator and denominator by this amount.

e.g. Simplify:

 45 120

The highest common factor of these two numbers is 5, so we have to divide both numbers by 5:

 45 120
=
 45 ÷ 5 120 ÷ 5
=
 9 20

In this activity, you will find equivalent fractions and simplify fractions into their lowest possible components.

Make sure you have your times tables and knowledge of factors at the ready to support you!

Complete the sentence regarding the equation below:

 3 7
=
 ? 21

What is the missing number in the equivalent fraction below?

 4 9
=
 8 ?

What do we need to multiply by to find the missing number in the equation below?

 3 5
=
 ? 25
15

5

10

Imagine trying to find missing value in this equivalent fraction:

 3 ?
=
 12 16

Then complete the sentence below to summarise what you would do.

15

5

10

How would you find the missing number in the equation below?

 4 9
=
 ? 45
15

5

10

Complete the sentence regarding the equation below:

 15 20
15

5

10

What is the highest common factor (HCF) of the two numbers in the fraction below?

 21 28
1

2

7

14

Consider each of the numbers below in relation to this fraction:

 15 30

For each, state if it is a factor of this fraction or not by selecting the correct boxes below.

Imagine trying to simplify this fraction as far as possible:

 3 9

Then complete the sentence below to summarise what you would do.

How would you simplify the fraction below?

 125 1000
• Question 1

Complete the sentence regarding the equation below:

 3 7
=
 ? 21
EDDIE SAYS
We have two denominators but we are missing a numerator. To convert the first denominator into the second, we have multiplied by 3: 21 ÷ 7 = 3 This means we have to multiply our first denominator by 3 also: 3 x 3 = 9 So 3/7 is equivalent to 9/21.
• Question 2

What is the missing number in the equivalent fraction below?

 4 9
=
 8 ?
18
eighteen
EDDIE SAYS
We need to notice that we have both two numerators this time, and we are missing a denominator. The second numerator is double the first, so we have multiplied by 2 to find the equivalent fraction. This means we have to multiply 9 by 2 to find the missing denominator. 4/9 = 8/18
• Question 3

What do we need to multiply by to find the missing number in the equation below?

 3 5
=
 ? 25
5
EDDIE SAYS
This question was intentionally meant to catch you out! So don't feel disheartened if you got this one wrong. We asked for the number you multiply by, not what the missing number is. We have both the denominators here, and the second one is 5 times the first. It's really important to closely read the question and take your time.
• Question 4

Imagine trying to find missing value in this equivalent fraction:

 3 ?
=
 12 16

Then complete the sentence below to summarise what you would do.

EDDIE SAYS
We have both numerators here, and 12 ÷ 3 = 4. So we have multiplied the first by 4 to reach the second. This means we have to divide 16 by 4 to find the missing denominator. As the missing number is in the first fraction, we have to work backwards from the denominator we have been provided with. Did that catch you out? Well done if you spotted it!
• Question 5

How would you find the missing number in the equation below?

 4 9
=
 ? 45
EDDIE SAYS
We have both denominators here, and we are looking for a missing numerator in the second fraction. 45 ÷ 9 = 5 So the first denominator has been multiplied by 5 to become the second. This means we have to multiply the first numerator by 5 too: 4 x 5 = 20 So 4/9 = 20/45
• Question 6

Complete the sentence regarding the equation below:

 15 20
EDDIE SAYS
The largest number, which you can divide both these numbers by, is 5. Therefore, in order to simplify this fraction, we need to divide by the numerator and denominator by 5. If we do this, we reach an answer of 3/4. Did you get that same simplification?
• Question 7

What is the highest common factor (HCF) of the two numbers in the fraction below?

 21 28
7
EDDIE SAYS
The largest number that you can divide both these numbers by is 7. You can also divide them both by 1 but this wouldn't change the overall fraction.
• Question 8

Consider each of the numbers below in relation to this fraction:

 15 30

For each, state if it is a factor of this fraction or not by selecting the correct boxes below.

EDDIE SAYS
The largest number that you can divide both the numbers in this fraction by is 15. This means that 15 is the highest common factor (HCF) of the fraction 15/30. Remember that there can only be one HCF. Both 2 and 30 are not common factors, as they can't be divided into both the denominator and numerator of the fraction. 1, 3 and 5 are all factors of both the numerator and denominator in this fraction, but they are not the HCF.
• Question 9

Imagine trying to simplify this fraction as far as possible:

 3 9

Then complete the sentence below to summarise what you would do.

EDDIE SAYS
The largest number that you can divide both these numbers by is 3. We then divide both the numerator and the denominator by this number, in order to simplify the fraction. If we do this, we find that: 3/9 = 1/3
• Question 10

How would you simplify the fraction below?

 125 1000
EDDIE SAYS
This is a really common question, which pops up on exams a lot. So it's worth trying to remember this one. The largest number that you can divide both the numerator and denominator by is 125. If you didn't spot the HCF straight away, there's nothing wrong with dividing both numbers by 5 to start with and then keep cancelling. We then divide both the numerator and the denominator by the HCF to simplify the fraction to its simplest form. So 125/1000 = 1/8 Another activity completed! Why not practise more on HCFs or fractions if you want to revise more? If not, then consider moving on to adding and subtracting fractions.
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