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,
8/10 – 3/10
= (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: 5/12 – 7/12 + 11/12
Solution:
We have,
5/12 – 7/12 + 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
Related Links:
● 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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