Addition of Fractions

Addition of fractions depends on two major conditions: 

  • Same denominators
  • Different denominators

If denominators are same, then such fractions are said to be like fractions and can be added directly. But if the denominators are different, (such fractions are called unlike fractions) then we need to rationalise the denominators and then add the numerators, keeping the denominators of the fractions common. Learn like or unlike fractions, here.

Adding fractions with Different Denominators

We have already learned to add two fractions when the denominators are like or same. Here we are going to discuss, how to add the fractions when the denominators are unlike or different.

To add two fractions, whose denominators are different, we need to rationalise the denominator first, by taking the LCM. Now we need to multiply fractions, numerator and denominator, in such a way that the denominators of both fractions become equal to the LCM value. 

After the denominators have become equal, we can add the numerators, keeping the denominator common.

Let’s understand it with an example:

Example: 3/12 + 5/2

Solution: Let us write the fraction into the more simplified form:

¼ + 5/2

Now, we can see here the denominators of the two fractions are different, i.e. 4 and 2.

Step 1: Rationalise the denominator by taking the LCM

LCM of 4 and 2 = 2

Step 2: Multiply and divide the second fraction by 2, to make its denominator equal to 4

5/2 x (2/2) = 10/4

Step 3: Since the denominator is same for both the fractions, therefore we can add them:

¼ + 10/4

Step 4: Add the numerator, keeping the denominator common.

(1+10)/4 

= 11/4

Therefore, the addition of 3/12 + 5/2 is 11/4.

Adding fractions with whole numbers

It is easy to add the fractions with whole numbers than to add mixed fractions. Let us understand it with an example. If the denominator of both the numbers is the same, we take the denominator as common and add the numerators. Here in the given example to show how to add fractions with whole numbers say a/b and c/b, we will follow the following steps.

  1. Denominator for both the fractions, b is the same.
  2. So, keep b as the denominator and add the numerators.
  3. The resultant will be the addition of both the fractions.

Example:

  • Add 7/2 + 4/2 = 11/2

In the above example, if we add 7/2 and 4/2, we leave the denominator 2 as it is and add the numerators 7 and 4, i.e 7 + 4 = 11. The result of the fraction is 11/2.

Adding Fractions with Co-prime Denominators

Co-prime denominators: The denominators which do not have common factors, other than 1.

Let’s study how to add co-prime factors?

Steps:

  • You need to multiply the denominator to find the denominator of the resulting fraction.
  • Multiply the numerator of one of the fractions by the denominator of the other or vice versa to get the numerator.
  • Add the result now.

Also, see:

Adding Mixed Fractions

Let’s understand how to add mixed fractions with an example:

Example: Add : 3 ⅓  + 1 ¾

          10/3 + 7/4 = [(10 × 4) / (3 × 4)] + [(7 × 3) /(4 × 3)] = (40 / 12)  + (21 / 12) = 61 / 12

Addition of Fraction Worksheet

Fraction addition is one of the important topics in class 6, 7 and 8. We have provided a worksheet for the addition of fractions here. After practising the questions given in this worksheet, you’ll be able to solve ant fraction addition sum easily. Practice from the given addition of fraction worksheet link here and score well in exams.

Subtraction of Fractions

As we know, addition and subtraction are similar operations in Maths. In addition, we add two or more numbers, whereas, in subtraction, we subtract a number from another. Therefore, subtraction of fractions also follows the same rule as addition of fractions. 

If the denominators are the same for given fractions, then we can directly subtract the numerator, keeping the denominator same.

If the denominators of fractions are different, we need to rationalise them first and then perform subtraction. 

Some examples are:

Example 1: Subtract ⅓ from 8/3.

Solution: We need to find,

8/3 – ⅓ = ?

Since the denominator of two fractions ⅓ and 8/3 is common, therefore, we can directly subtract them:

8/3 – ⅓ = (8-1)/3 = 7/3

Example 2: Subtract ½ from ¾. 

Solution: We need to subtract ½ from ¾, i.e.,

¾ – ½ = ?

Since the denominators of two fractions are different, therefore, we need to rationalise them by taking the LCM.

LCM (4,2) = 4

Now multiply the ½ by 2/2, to get 2/4

Therefore,

¾ – 2/4 = (3-2)/4 = ¼

Hence, ¾ – ½ = ¼

Solved Examples

Let us solve some problems based on adding fractions.

Q. 1: Add 1/2 and 7/2.

Solution: Given fractions: 1/2 and 7/2
Since the denominators are same, hence we can just add the numerators here, keeping the denominator as it is.

Therefore,

1/2 + 7/2

= (1+7)/2

= 8/2

=4

Q. 2: Add 3/5 and 4.

Solution: We can write 4 as 4/1

Now, 3/5 and 4/1 are the two fractions to be added.

Since the denominators here are different, thus we need to simplify the denominators first, before adding the fractions.

Hence,

3/5 + 4/1

Taking LCM of 5 and 1, we get;

LCM(5,1) = 5

Therefore, multiplying the second fraction, 4/1 by 5 both in numerator and denominator, we get;

(4×5)/((1×5) = 20/5

Now 3/5 and 20/5 have a common denominator, i.e. 5, therefore, adding the fractions now;

3/5 + 20/5

= 23/5

Practice Questions

  1. ⅜ + ⅝ = 
  2. 1(⅓) + 3(5/2) = 
  3. 2(¾) + ___ = 7
  4. ⅖ + ⅔ = 
  5. 3/7 + 2 + 4/3 =

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Frequently Asked Questions – FAQs

How to add two fractions with different denominators?

To add two fractions, with different denominators, we need to rationalise the denominators by taking out the LCM and make the denominator same. Then add the numerators of the fractions, keeping the denominator, common. For example, ½ + ⅗
LCM of 2 and 5 = 10
= (5/5) x (½) + (⅗) x (2/2)
= (5+6)/10
= 11/10

What are the rules to add and subtract fractions?

There are two simple rules to add and subtract fractions. If the denominators are the same, then we can directly add and subtract fractions. But if denominators are different then we need to rationalise the denominators by finding LCM of the two and then add the fractions.

How to add whole numbers and fractions?

If we add a whole number and a fraction, then we need to first write the whole number in the form of fraction. For example, adding 3 and ½ we get,
3+½ = 3x(2/2) + ½ = 6/2 + ½ = 7/2

How to add large fractions?

Let us take two fractions: 11/24 and 9/60
LCM of 24 and 60 = 120
Therefore,
= (11/24)x(5/5) + (9/60)x(2/2)
= (55+18)/120
= 73/120

How to add fractions with like denominators?

Let us say, ⅗ and 7/5 are two fractions. Since ⅗ and 7/5 are two like fractions, having same denominator, we can add the numerators directly.
Therefore,
⅗ + 7/5 = (3+7)/5 = 10/5 = 2

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