# Addition and Subtraction of Unlike Fractions

In addition and subtraction of unlike fractions, we first convert them into corresponding equivalent like fractions and then they are added or subtracted.

Following steps are used to do the same.

Step I:

Obtain the fractions and their denominators.

Step II:

Find the LCM (least common multiple) of the denominators.

Step III:

Convert each fraction into an equivalent fraction having its denominator equal to the LCM (least common multiple) obtained in Step II.



Step IV:

Add or subtract like fractions obtained in Step III.

For Example:

Solution:

The LCM (least common multiple) of the denominators 3 and 7 is 21.

So, we convert the given fractions into equivalent fractions with denominator 21.

We have,

2/3 + 3/7

= (2 × 7)/(3 × 7) + (3 × 3)/(7 × 3)

[since 21 ÷ 3 = 7 and 21 ÷ 7 = 3]

= 14/21 + 9/21

= (14 + 9)/21

= 23/21

2. 1/6 + 3/8

Solution:

The LCM (least common multiple) of the denominators 6 and 8 is 24.

So, we convert the given fractions into equivalent fractions with denominator 24.

We have,

= 1/6 = (1 × 4)/(6 × 4)= 4/24 [since 24 ÷ 6 = 4]

and, 3/8 = (3 × 3)/(8 × 3) = 9/24 [since 24 ÷ 8 = 3]

Thus, 1/6 + 3/8 = 4/24 + 9/24

= (4 + 9)/24

= 13/24

Solution:

We have,

24/5 = (2 × 5 + 4)/5 = (10 + 4)/5 = 14/5

and, 35/6 = (3 × 6 + 5)/6 = 23/6

Now, we will compute 14/5 + 23/6

The LCM (least common multiple) of the denominators 5 and 6 is 30.

So, we convert the given fractions into equivalent fractions with denominator 30.

We have,

= 14/5 = (14 × 6)/(5 × 6) = 84/30 [since 30 ÷ 5 = 6]

and, 23/6 = (23 × 5)/(6 × 5) = 115/30 [since 30 ÷ 6 = 5]

Thus, 14/5 + 23/6 = 84/30 + 115/30

= (84 + 115)/30

= 199/30

= 6¹⁹/₃₀

4. Find the difference of ¹⁷/₂₄ and ¹⁵/₁₆.

Solution:

The LCM (least common multiple) of the denominators 24 and 16 is 48.

[Therefore, LCM = 2 × 2 × 2 × 2 × 3 = 48]

So, we convert the given fractions into equivalent fractions with denominator 48.

We have,

= 17/24 = (17 × 2)/(24 × 2) = 34/48 [since 48 ÷ 24 = 2]

and, 15/16 = (15 × 3)/(16 × 3) = 45/48 [since 48 ÷ 16 = 3]

Clearly, 45/48 > 34/48

Therefore, 15/16 > 17/24

Hence, difference = 15/1617/24

= 45/4834/48

= (45 – 34)/48

= 11/48.

5. Simplify: 42/3 – 31/4 + 2 1/6

Solution:

We have,

42/3 – 31/4 + 21/6

= (4 × 3 + 2)/3(3 × 4 + 1)/4 + (2 × 6 +1)/6

= (12 + 2)/3(12 +1)/4 + (12+1)/6

= 14/313/4 + 13/6

The LCM (least common multiple) of the denominators 3, 4 and 6 is 12.

[Therefore, LCM = 2 × 2 × 3 = 12]

So, we convert the given fractions into equivalent fractions with denominator 12.

We have,

= (14 × 4)/(3 × 4)(13 × 3)/(4 × 3) + (13 × 2)/(6 × 2)

= 56/1239/12 + 26/12

= (56 – 39 + 26)/12

= (82 – 39)/12

= 43/12

= 3⁷/₁₂

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

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