Addition and Subtraction of Like Fractions


Here we will learn about addition and subtraction of like fractions.


Addition of Like Fractions:

In order to add two or more like fractions, we may follow the following steps:

Step I:

Obtain the fractions.


Step II:

Add the numerators of all fractions.


Step III:

Retain the common denominator of all fractions.


Step IV:

Write the fraction as Result in Step II / Result in Step III.





For Example:

Add the following fractions.

1. 1/6 + 4/6

Solution:

We have,

1/6 + 4/6

= (1+4)/6

= 5/6



2. 2/7 + 3/7 + 4/7

Solution:

We have,

2/7 + 3/7 + 4/7

= (2+3+4)/7

= 9/7



3. 23/5 + 4/5 + 12/5

Solution:

We have,

23/5 + 4/5 + 12/5

= (2 × 5 + 3)/5 + 4/5 + (1 × 5 + 2)/5

= (10 + 3)/5 + 4/5 + (5 + 2)/5

= 13/5 + 4/5 + 7/5

= (13 + 4 + 7)/5

= 24/5



4. 11/4 + 23/4 + 71/4

Solution:

We have,

11/4 + 23/4 + 71/4

= (1 × 4 + 1)/4 + (2 × 4 + 3)/4 + (7 × 4 + 1)/4

= (4 + 1)/4 + (8 + 3)/4 + (28 + 1)/4

= 5/4 + 11/4 + 29/4

= (5 + 11 + 29)/4

= 45/4


Subtraction of Like Fractions:



In order to subtract two like fractions, we may follow the following steps:



Step I:

Obtain the two fractions and their numerators.



Step II:

Subtract the smaller numerator from the bigger numerator.



Step III:

Retain the common denominator.



Step IV:

Write the fraction as Result in Step II / Result in Step III.



For Example:

1. Subtract 3/10 from 8/10

Solution:

We have to find,

8/103/10

= (8 – 3)/10

= 5/10

= (5 ÷ 5)/(10 ÷ 5) [Dividing the numerator and denominator by their HCF (highest common factor) 5].

= 1/2



2. Compute: 5/127/12 + 11/12

Solution:

We have,

5/127/12 + 11/12

= (5-7+11)/12

= (11-2)/12

= 9/12

= (9 ÷ 3)/(12 ÷ 3) [Dividing the numerator and denominator by their HCF (highest common factor) 3].

= 3/4



3. Simplify: 42/3 + 1/3 – 41/3

Solution:

We have,

42/3 + 1/3 – 41/3

= (4 × 3 + 2)/3 + 1/3 - (4 × 3 + 1)/3

= (12+2)/3 + 1/3(12+1)/3

= 14/3 + 1/3 - 13/3

= (14 + 1 – 13)/3

= (15 – 13)/3

= 2/3




For Example:

Add the following fractions.

1. 1/6 + 4/6

Solution:

We have,

1/6 + 4/6

= (1+4)/6

= 5/6



2. 2/7 + 3/7 + 4/7

Solution:

We have,

2/7 + 3/7 + 4/7

= (2+3+4)/7

= 9/7



3. 23/5 + 4/5 + 12/5

Solution:

We have,

23/5 + 4/5 + 12/5

= (2 × 5 + 3)/5 + 4/5 + (1 × 5 + 2)/5

= (10 + 3)/5 + 4/5 + (5 + 2)/5

= 13/5 + 4/5 + 7/5

= (13 + 4 + 7)/5

= 24/5



4. 11/4 + 23/4 + 71/4

Solution:

We have,

11/4 + 23/4 + 71/4

= (1 × 4 + 1)/4 + (2 × 4 + 3)/4 + (7 × 4 + 1)/4

= (4 + 1)/4 + (8 + 3)/4 + (28 + 1)/4

= 5/4 + 11/4 + 29/4

= (5 + 11 + 29)/4

= 45/4


● Fraction

Representations of Fractions on a Number Line

Fraction as Division

Types of Fractions

Conversion of Mixed Fractions into Improper Fractions

Conversion of Improper Fractions into Mixed Fractions

Equivalent Fractions

Interesting Fact about Equivalent Fractions

Fractions in Lowest Terms

Like and Unlike Fractions

Comparing Like Fractions

Comparing Unlike Fractions

Addition and Subtraction of Like Fractions

Addition and Subtraction of Unlike Fractions

Inserting a Fraction between Two Given Fractions







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