Addition of Fractions

Addition of Fractions depends on one main factor that is the denominator of the fraction 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. We need to make the bases of the denominators same in order to add the given fractions. Here, we will study how to add:

  • Add fractions with whole numbers
  • Add Fractions with co-prime denominators
  • Add Mixed fractions
  • Fractions with a Denominator that is the Divisor of the Other:
  • Fractions with unlike denominators

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 leave it as it is and add the numerators.

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.

Add Fractions with Co-prime Denominators

  • What are Co-prime Factors?

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.

Adding Mixed Fractions

Let’s understand it with an example:

  • Add : 3 ⅓  + 1 ¾

          10/3 + 7/4 = (10 X 4) / (3 x 4) + (7 X 3) (4 X 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 X 5)(4 X 5) = 10 / 20 + 15/20 = (10 X 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 X 3

            8 = 23

  • Find the highest power of any common factors to find the LCM  – 24 = 23  x 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

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Practise This Question

If g(x)dx=g(x), then g(x)1f(x)+f(x)}dx is equal to