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:
To subtract two or more like fractions we simply subtract their numerators and keep the same denominator.
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
4. Subtract \(\frac{3}{7}\) from \(\frac{5}{7}\).
Solution:
\(\frac{5}{7}\) - \(\frac{3}{7}\)
= \(\frac{5 - 3}{7}\)
= \(\frac{2}{7}\)
5. Emily has \(\frac{7}{12}\) hrs to reach her school. She takes \(\frac{5}{12}\) hrs to finish her breakfast. How much time is left with Emily to reach her school?
Solution:
We subtract \(\frac{5}{12}\) from \(\frac{7}{12}\).
\(\frac{7}{12}\) - \(\frac{5}{12}\)
= \(\frac{7 - 5}{12}\)
= \(\frac{2}{12}\) hrs is left with her.
For Example:
Add the following fractions.
1. 1/6 + 4/6Solution:
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
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