Addition and Subtraction 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:

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,

8/103/10

= (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

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:

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

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