Addition of Fractions

The addition of fractions can discuss in a few categories

  1. Unit fraction addition
  2. Improper fraction addition
  3. Mixed number addition

There is only one golden rule that we have to follow when the adding  fractions,

There should be a common denominator between the fractions

Unit Fraction Addition

Example 01:

Like Denominators

Unit Fraction Addition 1

Yellow color area :

ufa 2

Green color area :

ufa3

Let’s express the shaded area as a fraction,

Here we have a common denominator which is 10.

ufa4

Write the common denominator.

ufa 5

Add the numerators 3 + 5 = 8

In our answer 8 is the numerator and 10 is the denominator. We can also verify the answer by looking at the above figure. 

ufa 6

Example 02:

Unlike Denominators

ufa 7

Here we have an unlike denominator, Which means we have a common denominator, So we have to make one.

Denominators are 8 and 4. We can convert 4 into 8 by multiplying 4 by 2.

We have to multiply both numerator and denominator by the same number.

By doing so we will get an equivalent fraction for 1/4 with the denominator 8. 

Unlike Denominators

Example 03:

unlike denominators 2

In this example, we have to change both the denominators, because we can’t change 3 to 5 or 5 to 3.

Denominators are 3 and 5. Let’s find the Least Common Multiple (LCM) of 3 and 5.

There are a few methods to find LCM. Here we have mentioned only one way. Here you can learn about other methods of finding LCM.

Multiples of 3:    3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33

Multiples of 5:    5, 10, 15, 20, 25, 30, 35, 40, 45

LCM is 15.

Our new denominator is 15.

Unit Fraction Addition 2

Improper Fraction Addition

Addition of Improper Fractions with Like Denominator

Example 01:

improper fraction addition 1

We cannot keep answer as an improper fraction. Convert it into a mixed number.

ifa 1

Example 02:

Addition of Improper Fractions with Unlike Denominators

improper fraction addition 2

Example 03:

improper fraction addition 3

Mixed Number Addition

When we are doing an addition on mixed numbers, first you have to convert the mixed number to an improper fraction.

mixed number addition 1

We have another method of adding mixed numbers. Let’s see the same example.

mna 1

Here we separately add the whole number parts and fractional part and finally join them to take the answer.

mixed number addition 2

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