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Finding Equivalent Fractions

In this worksheet, students practise finding equivalent fractions.

'Finding Equivalent Fractions' worksheet

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Simplify Algebraic Expressions to Maintain Equivalence

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

In this worksheet you must find equivalent fractions.

Equivalent fractions are the same size.


Example

 

In the diagram, the shaded section represents
1
3
or
2
6

 

You find equivalent fractions by multiplying the numerator and the denominator by the same number.

 
1
3
=
1 × 2
3 × 2
=
2
6
=
1 × 3
3 × 3
=
3
9
=
1 × 10
3 × 10
=
10
30

 

 

You could also divide the numerator and the denominator by the same number.

This is what you do when you reduce a fraction.

 
6
24
=
6 ÷ 2
24 ÷ 2
=
3
12
=
6 ÷ 3
24 ÷ 3
=
2
8

Choose appropriate values for A, B, C and D which will make these fractions equivalent.

A is smaller than C.

 

2
10
=
4

A
=
B

30

Choose appropriate values for A, B, C and D which will make these fractions equivalent.

 

1
7
=
2

A
=
3

B

 

 

Choose appropriate values for A, B, which will make these fractions equivalent.

 

1
6
=
A

12
=
B

24

 

Choose appropriate values for A, B, C and D which will make these fractions equivalent.

A is smaller than C.

 

20
40
=
A

B
=
C

D

 

Are the fractions below equivalent?

 

25
45
=
5

9
 
 

 

Yes

No

Are the fractions below equivalent?

 

20
40
=
1

3

 
 
Yes

No

Are the fractions below equivalent?

 

10
40
=
4

20
   

 

Yes

No

 

3
9
=

 
   

 

Which fractions below are equivalent?

1/3

9/27

3/27

6/18

Choose appropriate values for A, B, C and D which will make these fractions equivalent.

A is smaller than C.

 

12
40
=
3

A
   

 

1/3

9/27

3/27

6/18

Choose appropriate values for A, B, C and D which will make these fractions equivalent.

A is smaller than C.

 

5
30
=
10

A
=
B

90

 

1/3

9/27

3/27

6/18

  • Question 1

Choose appropriate values for A, B, C and D which will make these fractions equivalent.

A is smaller than C.

 

2
10
=
4

A
=
B

30
CORRECT ANSWER
EDDIE SAYS
How did you do with the first one? Did you look at the numbers that we had? The numerator here is five times the denominator
  • Question 2

Choose appropriate values for A, B, C and D which will make these fractions equivalent.

 

1
7
=
2

A
=
3

B

 

 

CORRECT ANSWER
EDDIE SAYS
Remember the rule! Whatever you do to the numerator you must do to the denominator to get an equivalent fraction. In the first fraction, both have been multiplied by 2 and then by 3. The numerator here is seven times the denominator
  • Question 3

Choose appropriate values for A, B, which will make these fractions equivalent.

 

1
6
=
A

12
=
B

24

 

CORRECT ANSWER
EDDIE SAYS
How did you do? Are you spotting the pattern and remembering the rule here? What ever we do to the numberator we must do to the denominator.
  • Question 4

Choose appropriate values for A, B, C and D which will make these fractions equivalent.

A is smaller than C.

 

20
40
=
A

B
=
C

D

 

CORRECT ANSWER
EDDIE SAYS
Sometimes these questions are easier if you are writing them as you go? We must do the same to the numerator and the denominator. How did you get from 20/40 to 4/? We divided 20 by 5 to get 4 So, we must divide 40 by 5 and we get 8. Did you follow this?
  • Question 5

Are the fractions below equivalent?

 

25
45
=
5

9
 
 

 

CORRECT ANSWER
Yes
EDDIE SAYS
Did you spot that these two fractions are equivalent? We need to divide both the numerator and the denominator by 5. Simplifying the fraction first (divide by 5) will give 5/9
  • Question 6

Are the fractions below equivalent?

 

20
40
=
1

3

 
 
CORRECT ANSWER
No
EDDIE SAYS
These fractions are not equivalent, did you spot that? 1/2 would be an equivalent fraction of 20/40 but you can see that the numbers can not be simplified.
  • Question 7

Are the fractions below equivalent?

 

10
40
=
4

20
   

 

CORRECT ANSWER
No
EDDIE SAYS
These are not equivalent fractions as the denominator has been divided by 2 but the numerator has not been divided by 2. You know the rules... what we do to the top, we must do to the bottom!
  • Question 8

 

3
9
=

 
   

 

Which fractions below are equivalent?

CORRECT ANSWER
1/3
9/27
6/18
EDDIE SAYS
Did you look for which fractions had applied the same rule to the numerator and denominator? Write it down if it helps.
  • Question 9

Choose appropriate values for A, B, C and D which will make these fractions equivalent.

A is smaller than C.

 

12
40
=
3

A
   

 

CORRECT ANSWER
EDDIE SAYS
Simplifying the fraction first (divide by 4) will give 3/10 (A/B) Did you get this?
  • Question 10

Choose appropriate values for A, B, C and D which will make these fractions equivalent.

A is smaller than C.

 

5
30
=
10

A
=
B

90

 

CORRECT ANSWER
EDDIE SAYS
That's another activity completed, great work! So, long as you remember when working with equivalent fractions you must do the same to the numerator and the denominator, you will not go wrong! Great work!
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