 # Add and Subtract Fractions with Different Denominators

In this worksheet, students will add and subtract fractions which have different denominators by first finding a common denominator. 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

One of the golden rules when working with fractions is that you can only add and subtract fractions which have the same denominator.

So the question is: "What do we do when they don't have the same denominator?"

That's easy - we have to change the fractions so they do have the same denominator

e.g.

 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 that 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 as 3 x 4 = 12 and 4 x 3 = 12.

Step 1:

Convert the first fraction to have a denominator of 12.

This is done by multiplying both the numerator and denominator by 3.

 1 4
=
 3 12

Step 2:

Convert the second fraction to have a denominator of 12.

This is done by multiplying both the numerator and denominator by 4.

 1 3
=
 4 12

Step 3:

We can now rewrite our sum with our new fractions, then work it out as a normal addition with like denominators.

Our rule when adding fractions with the same denominator, is to 'add the top row and keep the bottom the same', like this:

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

Step 4:

Don't forget to simplify your answer into its simplest form if you can.

In this case, 7/12 cannot be simplified any further as 7 and 12 do not have any factors in common, except for 1.

In this activity, you will practise adding and subtracting fractions with different denominators by finding the Lowest Common Multiple (LCM) they have in common and converting them to have the same denominator.

What is the LCM of 3 and 7?

What is the LCM of 4 and 12?

4

12

48

Complete the sentence below to summarise what you have learnt about LCMs.

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 B

A
3
B
2
C
5
D
6

For each of these numbers, state if it is a common multiple, the lowest common multiple or not a common multiple for the numbers 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 B

A
15
B
3
C
13
D
10

 3 10
+
 2 5

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

 8 17
-
 1 34

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

 9 10
+
 2 5

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

Here's a find challenge.

 3 4
+
 5 6
-
 7 12

• Question 1

What is the LCM of 3 and 7?

21
EDDIE SAYS
Did you remember that LCM stands for 'Lowest Common Multiple'? If we write out the 3 and 7 times tables, what's the first number that's in both of them? It's 21, as 3 x 7 = 21 and 7 x 3 = 21. A top tip for finding the LCM is to multiply the denominators. This doesn't always work, particularly with even numbers, as you may not find the lowest multiple, but you will always find one you can work with.
• Question 2

What is the LCM of 4 and 12?

12
EDDIE SAYS
What number comes appears first in both the 4 and 12 times table? If we applied the tip in the previous question, we would think 48 as this is the answer to 4 x 12. However, this is not the lowest multiple. The lowest option is 12, as this appears earlier in the times tables and will be a simpler number to work with: 4 x 3 = 12 1 x 12 = 12 This skill of finding the LCM is going to come in handy later.
• Question 3

Complete the sentence below to summarise what you have learnt about LCMs.

EDDIE SAYS
The important thing to take from this is that the LCM is the first number which appears in the times tables of both denominators. Remember this rule as you work on the remainder of this activity.
• 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

## Column B

A
2
B
6
C
3
D
5
EDDIE SAYS
The first step here is to find the common denominator. We do this by finding the LCM of 3 and 2, which is 6. If we convert our fractions to numerators over 6, we get 2/6 and 3/6. Now these fractions have the same denominator, so we can add the numerators and leave the denominator the same. This leaves us with an answer of 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 numbers 8 and 5.

EDDIE SAYS
Which of these numbers aren't in both the 8 and 5 times tables? 8, 16, 20 So these are in the category of 'Not a common multiple'. Which of these numbers are in both the 8 and 5 times tables? 40, 80 So they are both 'Common multiples' but which is the lowest? Which of these is the first number in 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

## Column B

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

 3 10
+
 2 5

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

7/10
EDDIE SAYS
Did you write 35/50? This one was testing if you noticed that the LCM 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 the numerators. Note: If you got 35/50, that's fine! Just remember to simplify it down. If you divide both the numerator and denominator by 5, you will reach the same answer of 7/10.
• Question 8

 8 17
-
 1 34

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

15/34
EDDIE SAYS
Did you spot the minus sign here? You need to subtract not add. The LCM here is 34, so the second fraction can stay the same. We need to multiply the first fraction by 2, so it has a denominator of 34. 16/34 - 1/34 = 15/34 Can this be simplified further? No, as 15 and 34 do not have any common factors except 1.
• Question 9

 9 10
+
 2 5

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

13/10
1 3/10
EDDIE SAYS
The LCM of 5 and 10 (which we saw earlier) is 10. So we don't need to do anything to our first fraction as it already has a denominator of 10. We need to double the second. 9/10 + 4/10 = 13/10 Does it matter if the numerator gets bigger than the denominator? Nope, not a problem. But you can write this as a mixed number if you are feeling confident or the question asks you to.
• Question 10

Here's a find challenge.

 3 4
+
 5 6
-
 7 12

1
EDDIE SAYS
If a question has three fractions instead of two, just calculate in the same way, moving from left to right. We need to find the LCM of our three denominators: 4, 6 and 12. The LCM of 4, 6 and 12 is 12. This leaves us with the calculation: 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 know is the same as 1 in its simplest form. Well done if you got that correct, as you had to put lots of steps together!
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