The fraction is defined as a numerical part of a whole number. Sometimes we want to add or subtract two fractions to find out the total number. It can be identified by the Addition and Subtraction of Fractions. For example, Malini ate 1 ½ roties for lunch and 2 ½ roties for dinner. What is the total number of roties Malini ate? In the above example, it is necessary to add the fractions. How do add or subtract fractions? What are the steps involved to add or subtract fractions? Let us take an overview of the Addition and Subtraction of Fractions.

## Addition and Subtraction of Fraction Methods

All fractions cannot be added or subtracted easily. The following methods are available to add or subtract fraction.

- Add or subtract fraction with the same denominator
- Add or subtract fraction with different denominator
- Add or subtract mixed number fraction

### Addition or Subtraction of Fractions with the Same Denominator

In this method, the addition or subtraction of fraction is very easy. Because the denominators of the two fractions are the same.

Example: ^{2}/_{4} + ^{3}/_{4} = ?

In the above fractions, the denominators are the same.

^{2}/_{4 }=

1 | 2 |

^{ }^{3}/_{4} =

1 | 2 | 3 |

In the above fractions, the box is divided into four parts. For ^{2}/_{4 } and ^{3}/_{4}, take 3 and 1 numerator parts respectively out of 4 equal parts.

Steps involved adding fractions if denominators are the same.

Step 1: Check the given fractions, if denominators are same or not.

Step 2: If denominators are same, take the numerators of two fractions and add or subtract it.

Step 3: Give a final answer with denominator.

Example 1: ^{5}/_{8} + ^{2}/_{8} = ?

Step 1: Denominators are same.

Step 2: Take the numerators 5 and 2 respectively and add it

^{ }= ^{(5+2)}/_{8}

Step 3: Give the final answer.

= ^{7}/_{8}

Example 2: ^{5}/_{8} – ^{2}/_{8} =?

Step 1: Denominators are same.

Step 2: Take the numerators 5 and 2 respectively and subtract the smaller from the bigger numerator.

^{ }= ^{(5-2)}/_{8}

Step 3: Give the final answer.

= ^{3}/_{8}

### Addition or Subtraction of Fractions with the Different Denominator

In this method, the denominators are not the same in two fractions. So we need to make the same.

In this method, the numerators and denominators are different in the two fractions.

Let us add two fractions, ^{3}/_{8 }and ^{5}/_{12}.

In the above fractions, numerators and denominators are different.

Solution:

Step 1: Take LCM for denominators of above fractions. i.e. 8 and 12 respectively.

(LCM is the smallest number which is used as a common multiple of two numbers)

24 is a common multiple for 8 and 12.

Step 2: Convert denominators 8 and 12 into 24.

In ^{3}/_{8}, multiply numerator and denominator by 3 = ^{3}/_{8} x^{3}/_{3} = ^{9}/_{24}

In ^{5}/_{12}, multiply numerator and denominator by 2 = ^{5}/_{12}x ^{2}/_{2} = ^{10}/_{24}

(Note: We must do to the numerator what we do to the denominator)

Step 3: Now, the denominators of the two fractions are the same.

^{9}/_{24}, ^{10}/_{24}

Step 4: Take the numerators 9 and 10 respectively and add it

= ^{(9+10)}/_{24}

Step 5 : Give a final answer

= ^{19}/_{24}

Example: ^{3}/_{8 }– ^{5}/_{12} =?

Solution: Denominators are different. So, take the Least Common Multiple (LCM).

24 is a common multiple of 8 and 12.

^{3}/_{8} => ^{3}/_{8} x^{3}/_{3} = ^{9}/_{24}

^{5}/_{12} => ^{5}/_{12}x ^{2}/_{2} = ^{10}/_{24}

^{3}/_{8} – ^{5}/_{12} = ^{9}/_{24} – ^{10}/_{24}

= ^{9-10}/_{24 }(subtract the smaller numerator from the bigger)

Answer = ^{-1}/_{24 }

## Addition and Subtraction of Mixed Fractions

A *mixed fraction* is defined as a fraction and a whole number combined into one “*mixed*” *number*.

Depends on the denominator, two following methods of available for add or subtract of mixed fraction.

- If the same denominators are present in the mixed fraction.
- If different denominators are present in the mixed fraction.

### Addition or Subtraction of Mixed Fractions with the Same Denominator

In this method, the mixed fraction consists of the same denominators. The following steps are involved to add or subtract the mixed fraction.

Step 1: Add the whole number of two fractions separately.

Step 2: Add the fractions separately.

Step 3: Combine the whole number and the fraction both

Step 3: Convert improper fraction into a mixed fraction.

Example: 3 ^{2}/_{5} + 1 ^{4}/_{5} = ?

Step 1 : Add the whole number of two fraction separately

= 3+1 = 4 — (1)

Step 2: Add the fractions separately

= ^{2}/_{5} + ^{4}/_{5} = ^{6}/_{5} —– (2)

Step 3 : Combine the both equation (1) and (2)

= 4 ^{6}/_{5} —— (3)

In 4 ^{6}/_{5}, ^{6}/_{5} is an improper fraction. So, convert into proper mixed fraction.

Equation (2) —–> ^{6}/_{5} = 1 ^{1}/_{5} —– (3)

Step 4: Now, add equation (1) and (3)

4 + 1 ^{1}/_{5} = 5 ^{1}/_{5}

Answer = 5 ^{1}/_{5}

### Addition or Subtraction of Mixed Fractions with the Different Denominator

In this method, the mixed fraction consists of different denominators. The following steps are involved to add or subtract the mixed fraction.

Example: 6 ^{3}/_{4} + 3 ^{5}/_{8} = ?

Solution: In the above-mixed fractions, the denominators are different. So we need to make the same.

Step 1: Take LCM for denominators of above fractions. i.e. 4 and 8 respectively.

(LCM is the smallest number which is used as a common multiple of two numbers)

8 is a common multiple for 4 and 8.

Step 2: Convert denominators 4 and 8 into 8.

In ^{3}/_{4}, multiply numerator and denominator by 2 = ^{3}/_{4} x^{2}/_{2} = ^{6}/_{8}

In ^{5}/_{8}, multiply numerator and denominator by 1 = ^{5}/_{8}x ^{1}/_{1} = ^{5}/_{8}

(Note: We must do to the numerator what we do to the denominator)

Now, denominators are same in the mixed fraction.

6 ^{3}/_{4} + 3 ^{5}/_{8} = 6 ^{6}/_{8} + 3 ^{5}/_{8}

Step 3: Add the whole number of two fractions separately

= 6+3 = 9 ———— (1)

Step 4: Add the fractions separately

= ^{6}/_{8} + ^{5}/_{8}= ^{11}/_{8} —– (2)

^{11}/_{8} is an improper fraction. So, convert into a proper fraction.

^{11}/_{8} = 1 ^{3}/_{8 }————(3)

Step 5: Combine both equation (1) and (3)

9+ 1 ^{3}/_{8 }= 10 ^{3}/_{8}

Answer: 10 ^{3}/_{8}

We have thus seen this basic introduction of Addition and Subtraction of Fractions. For the complete understanding of the topic please visit our site or download the Byjus learning app.

This link helped me a lot.Thank you.

I have a little child of class 6