Addition of Fractions

Addition of Fractions depends on one main factor which is the denominator of the fractions, to be added. There are different ways to add them depending on whether the denominators of the fractions to be added are like or unlike fractions. We need to make the bases of the denominators same in order to add the given fractions.

Let us learn here the addition of fractions with whole numbers and unlike fractions, adding mixed fractions along with examples.

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 tale 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.

Addition of 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.

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.

Adding Fractions with Co-prime Denominators

Co-prime denominators: The denominators which do not have common factors.

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:

  • Add : 3 ⅓  + 1 ¾

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

The denominators are 3 and 4, which are different and have no common factors,

so to calculate the numerator, you need to multiply 10 X 4 = 40 and  2 x 3 = 6, and add the results, 40 + 6 = 46, which would be the numerator of the answer.

Hence, the final answer to the addition is 46/12.

Add Fractions with a Denominator that is the Divisor of the Other

Let’s understand it with an example:

  • Add 10 / 20 + 3/ 4 = 10 / 20 + (3 × 5)(4 × 5) = 10 / 20 + 15/20 = (10 × 15)/(20) = 150/20 = 15 / 2
  • As the denominator of these fractions are different, but as 4 is a factor of 20, which is a multiple of 5.
  • Multiply both the numerator and the denominator of 3 / 4 by 5.
  • You will get 15/ 20.
  • Now find the sum of both fractions.
  • It will give the answer as 150 / 20  which can be simplified further to 15/2

Adding fractions with unlike denominators

Let’s understand it with an example:

Let’s add: 3/12 + 10/8

Steps:

  • The denominators of the added fractions are 12 and 8.
  • Both of these are different from common factors.
  • To determine the least common multiple, we need to factor the numbers.

            12 = 22 × 3

            8 = 23

  • Find the highest power of any common factors to find the LCM  – 24 = 23  × 3
  • So, 24 is the common denominator.

To calculate the numerator of the fractions for adding or subtracting, divide the calculated LCM into the denominator.

  • Next, Multiply the result with the numerator, 24/12 = 2 and 6 / 2 = 3
  • 24 / 8 = 3 and 30 / 3 = 10
  • The new fractions will be 3 / 12  × 2/2 and 10 / 8 × 3 / 3.
  • Resulting Fraction – 30 / 24
  • Now add the numerators.
  • The sum of the two fractions is 36 / 24
  • Simplify it by dividing the numerator and denominator by 12.

The answer is 3 / 2

Addition of Fractions Examples

Let us solve some problems based on adding fractions.

Example 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

Example 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

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