# Add and Subtract Fractions with the Same Denominator

In this worksheet, students will add and subtract fractions which share the same denominator, simplifying answers into the simplest forms.

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 you are adding or subtracting fractions, there is one golden rule which you need to remember over everything else:

Fractions must have the same denominator before you can add or subtract them.

When you have fractions that have the same denominator, adding and subtracting them is simple.

All you have to do is add (or subtract) the numerator and leave the denominator alone.

That's right! You don't need to do a single thing to the denominator.

e.g.

 3 5
+
 1 5

Let's compare these fractions using bar models so we can see what is happening visually:

We can now clearly see that adding 3/5 and 1/5 will give us 4/5.

If you track this process in the sum alone, we have added the top row (numerators) and kept the bottom number (the denominator) the same, like this:

 3 5
+
 1 = 4 5 5

In this activity, you will practise adding and subtracting fractions with the same denominators, whilst simplifying your answers into their simplest form.

Work out the following sum:

 2 5
+
 1 5

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

Simplify your answer as far as possible.

For the following sum:

 3 8
+
 2 8

What will the numerator of the answer be?

5

8

1

For the following sum:

 4 5
-
 1 5

What will the denominator of the answer be?

5

0

10

Work out the following sum:

 3 7
+
 2 7

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

Simplify your answer as far as possible.

Work out the following sum:

 4 9
-
 1 9

Simplify your answer as far as possible.

3/9

1/3

4/9

Calculate the following sum:

 5 8
-
 3 8

Simplify your answer as far as possible.

Then complete the sentence below to summarise your answer.

3/9

1/3

4/9

Work out the following sum:

 3 8
+
 3 8

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

Simplify your answer as far as possible.

Consider this calculation:

 5 12
+
 1 12

Can you match the fractions below to the correct description of their role in this calculation?

## Column B

6/24
The simplified, correct answer
6/12
An incorrect addition
1/2
A correct addition

Work out the following sum:

 4 5
-
 4 5

Simplify your answer as far as possible.

8/5

0

0/5

Consider the algebraic fraction below:

 a b
+
 c b

In what circumstance is it true that:

 a  +  c b
Always

Sometimes

Never

• Question 1

Work out the following sum:

 2 5
+
 1 5

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

Simplify your answer as far as possible.

CORRECT ANSWER
3/5
EDDIE SAYS
As the denominator is the same here, we just need to add the numerators. 2 + 1 = 3 Great start, let's continue!
• Question 2

For the following sum:

 3 8
+
 2 8

What will the numerator of the answer be?

CORRECT ANSWER
5
EDDIE SAYS
Remember that if the denominator (bottom number) is the same, we can simply add the numerators in the top row. 3 + 2 = 5 Hopefully you spotted that the question asked for the numerator of the answer fraction, not the denominator, which would have been 8.
• Question 3

For the following sum:

 4 5
-
 1 5

What will the denominator of the answer be?

CORRECT ANSWER
5
EDDIE SAYS
Did you spot that we had a subtraction here? Does that matter? No! When we are adding and subtracting fractions, remember that we leave the denominators alone in both cases. So as our denominator was 5 in the question fractions, it will be 5 in the answer. Simple!
• Question 4

Work out the following sum:

 3 7
+
 2 7

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

Simplify your answer as far as possible.

CORRECT ANSWER
5/7
EDDIE SAYS
As the denominator is the same here, we can just add the numerators and leave the denominator alone. 3 + 2 = 5 So 3/7 + 2/7 = 5/7 Great focus, let's move on to some subtractions now.
• Question 5

Work out the following sum:

 4 9
-
 1 9

Simplify your answer as far as possible.

CORRECT ANSWER
1/3
EDDIE SAYS
As the denominator is the same, we can subtract the numerators to reach our answer. 4 - 1 = 3 So 3/9 is the correct answer BUT we tried to catch you out! Did you remember to cancel down your fraction? Whenever a fraction can be simplified, you should do so. It is also explicitly mentioned in the question here. With 3/9, we can divide both the numerator and denominator by 3, to reach 1/3. Great work if you spotted that!
• Question 6

Calculate the following sum:

 5 8
-
 3 8

Simplify your answer as far as possible.

Then complete the sentence below to summarise your answer.

CORRECT ANSWER
EDDIE SAYS
We need to subtract the numerators here: 5 - 3 = 2 So our first answer is 2/8, but can this be simplified? It can, as both the numerator and denominator can be divided by 2. This means that our simplified answer is 1/4. Students often lose marks in these questions by forgetting to cancel, so always check in the exam if the question asks for it and don't get caught out!
• Question 7

Work out the following sum:

 3 8
+
 3 8

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

Simplify your answer as far as possible.

CORRECT ANSWER
3/4
EDDIE SAYS
As the denominator is the same, we can add the numerators here: 3 + 3 = 6 So our first answer is 6/8, can this be simplified? Both the numerator and denominator can be divided by 2, which gives us a simplified answer of 3/4. Did you remember to cancel?
• Question 8

Consider this calculation:

 5 12
+
 1 12

Can you match the fractions below to the correct description of their role in this calculation?

CORRECT ANSWER

## Column B

6/24
An incorrect addition
6/12
A correct addition
1/2
The simplified, correct answer
EDDIE SAYS
How did you get on with this one? As the denominator is the same, we can add the numerators: 5 + 1 = 6 So our first answer is 6/12 so we can define this as 'A correct addition' but it can be simplified further so it is not 'The simplified, correct answer'. We can divide both the numerator and denominator in 6/12 by 6, so we reach 1/2 as our final answer. 6/24 was a red herring and totally incorrect, so it is best described as 'An incorrect addition'.
• Question 9

Work out the following sum:

 4 5
-
 4 5

Simplify your answer as far as possible.

CORRECT ANSWER
0
EDDIE SAYS
If you subtract any number from itself, you will reach zero. If you chose 8/5 you added the fractions by mistake! If you put 0/5 you hadn't noticed that nothing divided by 5 is still nothing. Believe it or not, this answer can be simplified to just '0'.
• Question 10

Consider the algebraic fraction below:

 a b
+
 c b

In what circumstance is it true that:

 a  +  c b
CORRECT ANSWER
Always
EDDIE SAYS
This question may look more challenging than it is. As both the denominators are b, they are the same. What is our rule when the denominators are the same? That's right, we can simply add the numerators. In this case the numerators are 'a' and 'c'. So this statement is always true. It may help you to imagine numbers in the place of the letters. Great work on completing this activity! If you found simplifying fractions to be challenging, it would be useful to revise these before you move on.
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