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Addition and Subtraction of Fractions

Addition and subtraction of Fraction can be done only when fraction have same denominators. When fractions have different denominators they can be added or subtracted in their equivalent fractions with common denominator.

Addition and subtraction of like fractions

Like fractions are fractions having same denominators.

Steps for addition and subtraction of like fraction-

1. Add or subtract the numerator

2. Write the sum over common denominator

3. Reduce the fraction .


Example of Addition and Subtraction of Fractions

Examples-

1) Find $ \frac{3}{7} + \frac{5}{7} $

Here, both the fraction have common denominator of 7. So simply add the numerators

$ \frac{3}{7} + \frac{5}{7}$ =$ \frac{8}{7} = 1 \frac{1}{7} $ [Reduce the fraction in proper fraction]

2) Find $\frac{4}{5} - \frac{1}{5}$

$\frac{4}{5} - \frac{1}{5}$ = $\frac{4-1}{5}$ = $\frac{3}{5}$

Addition and Subtraction of Unlike Fraction

Here denominator of fractions is different. Before addition and subtraction of such fraction,we must first change them to equivalent fraction so that they have common denominator.

Steps for finding equivalent fraction.

1. Find the LCM of both denominators.

2. Rewrite the fraction with LCM as a common denominator for both fraction.

As the equivalent fraction have common denominator so we can add or subtract fraction easily.

Examples

1) Find $\frac{3}{4} + \frac{1}{3}$

Since both the fraction have different denominators.We have to find equivalent fraction.

find LCM of 4 and 3

4 = 2 X 2

3 = 3

Taking each factors maximum number of times in either number.

So, LCM = 2 X 2 X 3 = 12

Equivalent fraction of $\frac{3}{4} = \frac{3 X3}{4 X 3} = \frac{9}{12}$

Equivalent fraction of $\frac{1}{3} = \frac{1 X 4}{3 X 4} = \frac{4}{12}$

$\frac{3}{4} + \frac{1}{3} = \frac{9}{12} + \frac{4}{12} = \frac{9 + 4}{12} = \frac{13}{12} = 1\frac{1}{12}$

2) Find $\frac{3}{8} + \frac{5}{6}$

LCM of 8 and 6:

8 = 2 X 2 X 2

6 = 2 X 3

LCM = 2 X 2 X 2 X 3 = 24

$\frac{3}{8} = \frac{3 X 3}{8 X 3} = \frac{9}{24}$

$\frac{5}{6} = \frac{5 X 4}{6 x 4} = \frac{20}{24}$

$\frac{3}{8} + \frac{5}{6} = \frac{9}{24} + \frac{20}{24} = \frac{29}{24} = 1\frac{5}{24}$

Addition and Subtraction of Mixed Fraction

To add or subtract mixed fractions add whole parts of add whole parts separately and fraction part separately.

Example:

1) Find $2\frac{3}{5} + 1\frac{2}{5}$

$2\frac{3}{5} + 1\frac{2}{5}$ = $(2 + 1) + (\frac{3}{5} + \frac{2}{5})$ = $3 + (\frac{3 + 2}{5})$ = $3 + \frac{5}{5}$ = 3 + 1 = 4

2) Find $7\frac{3}{8} - 3\frac{5}{8}$

$7\frac{3}{8} - 3\frac{5}{8} = (7 - 3) + (\frac{3}{8} - \frac{5}{8}) = 4 + (\frac{3}{8} - \frac{5}{8})$

[ Here $\frac{3}{8} < \frac{5}{8}$, so take 1 from whole part ]

= 3 + $(\frac{8}{8} + \frac{3}{8} - \frac{5}{8})$ [ Since 1 can be written as $\frac{8}{8}$ ]

= 3 + $(\frac{8 + 3}{8} - \frac{5}{8}) = 3 + (\frac{11}{8} -\frac{5}{8}) = 3 + (\frac{11-5}{8})$

= 3 + $\frac{6}{8} = 3 + \frac{3}{4} = 3\frac{3}{4}$