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Add and Subtract Fractions with Different Denominators

In this worksheet, students will add and subtract fractions that have different denominators.

'Add and Subtract Fractions with Different Denominators' worksheet

Key stage:  KS 4

Curriculum topic:  

Curriculum subtopic:  

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

One of the main rules for fractions is that you can only add and subtract fractions that have the same denominator.

So the question becomes, "what do we do when they don't have the same denominator?"

Easy. Change them so they do.

 

Example 1:

 

1
4
+
1
3

 

The first thing we need to do is think what we are going to change the denominators to. To do this we find the Lowest Common Multiple (LCM) of 3 and 4.

All this means is we want to know the first number that is in both the 3 and 4 times tables. If we write them out, we find that this is 12.

Step 1: Change the first fraction to a number over 12. This is done by multiplying both the numerator and denominator by 3

 

1
4
=
3
12

 

Step 2: Change the second fraction to a number over 12. This is done by multiplying both the numerator and denominator by 4

 

1
3
=
4
12

 

We can now rewrite our sum and work it out.

 

1
4
+
1
3
=
3
12
+
4
12
=
7
12

 

What is the LCM of 3 and 7?

What is the LCM of 4 and 12?

4

12

48

Complete the following sentence;

 

4

12

48

Find the values of A, B, C and D that satisfy this equation.

1
3
+
1
2
=
A
B
+
C
B
=
D
B

Column A

Column B

A
6
B
2
C
5
D
3

For each of these numbers, state if it is a common multiple, the lowest common multiple or not a common multiple for the number 8 and 5.

Find the values of A, B, C and D that satisfy this equation;

 

1
5
+
2
3
=
A
B
+
C
B
=
D
B

Column A

Column B

A
10
B
13
C
15
D
3

Find the answer to...

3
10
+
2
5

Give your answer in the form a/b in its simplest form.

Find the answer to; 

 

8
17
-
1
34

 

 

Give your answer in the form a/b in it's simplest form.

Find the answer to;

 

9
10
+
2
5

 

 

Give your answer in the form a/b in its simplest form.

CHALLENGE:

Find the answer to;

 

3
4
+
5
6
-
7
12

 

 

Give your answer in its simplest form.

  • Question 1

What is the LCM of 3 and 7?

CORRECT ANSWER
21
EDDIE SAYS
If we write out the 3 and 7 times tables, what's the first number that's in both of them?
  • Question 2

What is the LCM of 4 and 12?

CORRECT ANSWER
12
EDDIE SAYS
What number comes appears first in both the 4 and 12 times table? This skill is going to come in handy later...
  • Question 3

Complete the following sentence;

 

CORRECT ANSWER
EDDIE SAYS
The important thing to take from this is that the LCM is the first number in both times tables.
  • Question 4

Find the values of A, B, C and D that satisfy this equation.

1
3
+
1
2
=
A
B
+
C
B
=
D
B
CORRECT ANSWER

Column A

Column B

A
2
B
6
C
3
D
5
EDDIE SAYS
The first step is to find the common denominator. We get this by finding the LCM of 3 and 2 which is 6. If we change our fractions to numbers over 6, we get 2/6 and 3/6. Now these have the same denominator, we can add the numerators which leaves us with 5/6.
  • Question 5

For each of these numbers, state if it is a common multiple, the lowest common multiple or not a common multiple for the number 8 and 5.

CORRECT ANSWER
EDDIE SAYS
Which of these numbers aren't in both times tables? (8, 16, 20) Which of these numbers are in both times tables (40, 80) Which of these is the first number on both times tables? (40)
  • Question 6

Find the values of A, B, C and D that satisfy this equation;

 

1
5
+
2
3
=
A
B
+
C
B
=
D
B
CORRECT ANSWER

Column A

Column B

A
3
B
15
C
10
D
13
EDDIE SAYS
The first step is to find the common denominator. We get this by finding the LCM of 5 and 3 which is 15. If we change our fractions to numbers over 15, we get 3/15 and 10/15. Now these have the same denominator, we can add the numerators.
  • Question 7

Find the answer to...

3
10
+
2
5

Give your answer in the form a/b in its simplest form.

CORRECT ANSWER
7/10
EDDIE SAYS
Did you put 35/50? This one was testing if you noticed that the lowest common multiple of 5 and 10 is 10. If we use this as our new common denominator, our fractions become 3/10 and 4/10 which we can then add. Note: If you got 35/50, that's fine, just remember to simplify it down.
  • Question 8

Find the answer to; 

 

8
17
-
1
34

 

 

Give your answer in the form a/b in it's simplest form.

CORRECT ANSWER
15/34
EDDIE SAYS
Did you spot the negative? For these, we do just the same, but instead of adding the numerators, we just subtract them.
  • Question 9

Find the answer to;

 

9
10
+
2
5

 

 

Give your answer in the form a/b in its simplest form.

CORRECT ANSWER
13/10
EDDIE SAYS
The LCM of 5 and 10 (which we saw earlier) is 10. If we use this our fractions become 9/10 and 4/10 which we can add. Does it matter if the numerator is bigger than the denominator? Nope, not a problem.
  • Question 10

CHALLENGE:

Find the answer to;

 

3
4
+
5
6
-
7
12

 

 

Give your answer in its simplest form.

CORRECT ANSWER
1
EDDIE SAYS
If a question has three numbers instead of two, just do it the same way. The LCM of 4,6 and 12 is 12. If we change our three fractions, we get (9/12 + 10/12) - 7/12 We can now add the numerators of the first two and then subtract the third. Doing this gives 12/12 which we all know is the same as 1.
---- OR ----

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