Add, Subtract, Multiply and Divide Fractions

Example 1: Add $\frac{5}{8}$ and $\frac{6}{8}$
As the denominator is 8 and add numerator of both fractions only
= $\frac{5}{8}+\frac{6}{8}$
= $\frac{5+6}{8}=\frac{11}{8}$

Example 2: Add $\frac{1}{4},\frac{2}{4},\frac{6}{4}$
Here, the denominator is 4 for all fractions, so add numerators of all fractions only.
= $\frac{1}{4}+\frac{2}{4}+\frac{6}{4}$
= $\frac{1+2+6}{4}=\frac{9}{4}$

Example 1: Add $\frac{3}{4},\frac{5}{6}$
Step 1: Take LCM of denominators of fractions. $\frac{3}{4}$ and $\frac{5}{6}$ .

Step 2: Multiply both fractions numerator and denominators by the same numbers such that the denominators become equal to LCM 12.
$\frac{3}{4}\times \frac{3}{3}=\frac{9}{12}$
$\frac{5}{6}\times \frac{2}{2}=\frac{10}{12}$
Step 3: Add the like fractions $\frac{9}{12}$ and $\frac{10}{12}$ .
= $\frac{9}{12}+\frac{10}{12}$
= $\frac{9+10}{12}=\frac{19}{12}$
∴ $\frac{3}{4}+\frac{5}{6}=\frac{19}{12}$

Example 2: Add $\frac{2}{3},\frac{4}{6},\frac{1}{4}$
Step 1: Take LCM of denominators of fractions $\frac{2}{3},\frac{4}{6}$ and $\frac{1}{4}$

Step 2: Multiply numerators and denominators of all fractions by the same numbers such that their denominators become equal to LCM 12.
$\frac{2}{3}\times \frac{4}{4}=\frac{8}{12}$
$\frac{4}{6}\times \frac{2}{2}=\frac{8}{12}$
$\frac{1}{4}\times \frac{3}{3}=\frac{3}{12}$
Step 3: Add the like fractions $\frac{8}{12},\frac{8}{12}$ and $\frac{3}{12}$
= $\frac{8}{12}+\frac{8}{12}+\frac{3}{12}$
= $\frac{8+8+3}{12}=\frac{19}{12}$
∴ $\frac{2}{3}+\frac{4}{6}+\frac{1}{4}=\frac{19}{12}$

Example 1: Subtract $\frac{8}{9}$ from $\frac{10}{9}$
As these are like fractions with their same denominators of 9.
So, subtract numerator of both fractions only.
$\frac{10}{9}-\frac{8}{9}$
$\frac{10-8}{9}=\frac{2}{9}$

Example 2: Subtract $\frac{11}{12}$ from $\frac{15}{12}$
Here, the two fractions are like fractions and their denominator is 12.
So, subtract numerators of both fractions only.
= $\frac{15}{12}-\frac{11}{12}$
$\frac{15-11}{12}=\frac{4}{12}$
= $\frac{1}{3}$

Subtract $\frac{6}{4}$ from $\frac{8}{3}$
Step 1: Take LCM of denominators of fractions.

LCM of 4 and 3 is 12
Step 2: Convert unlike fractions into like fractions by multiplying a number which makes denominators equal to LCM 12.
$\frac{8}{3}\times \frac{4}{4}=\frac{32}{12}$
$\frac{6}{4}\times \frac{3}{3}=\frac{18}{12}$
Step 3: Subtract $\frac{18}{12}$ from $\frac{32}{12}$
= $\frac{32}{12}-\frac{18}{12}$
= $\frac{32-18}{12}=\frac{14}{12}$
∴ $\frac{8}{3}-\frac{6}{4}=\frac{14}{12}=\frac{7}{6}$

Example 1: $\frac{7}{5}\times 2$
Here, $\frac{7}{5}$ is a fraction and 2 is a whole number.
2 is written as $\frac{2}{1}$
= $\frac{7}{5}\times \frac{2}{1}$
= $\frac{7\times 2}{5\times 1}=\frac{14}{5}$

Example 2: $\frac{6}{5}\times 4$
= $\frac{6}{5}\times \frac{4}{1}$
= $\frac{6\times 4}{4\times 1}=\frac{24}{5}$

Example 1: Multiply fraction $\frac{7}{5}$ by $\frac{3}{4}$
Here, multiply numerators 7 and 3. Also, multiply their denominators 5 and 4.
$\frac{7}{5}\times \frac{3}{4}$
= $\frac{7\times 3}{5\times 4}=\frac{21}{20}$

Example 2: Multiply fractions $\frac{2}{5},\frac{4}{6},\frac{3}{2}$
$\frac{2}{5}\times \frac{4}{6}\times \frac{3}{2}$
multiply numerators 2, 4 and 3 and also multiply denominators 5, 6 and 2.
= $\frac{2\times 4\times 3}{5\times 6\times 2}=\frac{24}{60}$
Now $\frac{24}{60}$ should be reduced to its lowest term by dividing with the common factor 12.
$\frac{24}{60}=\frac{2}{5}$

Example 1: Divide $\frac{2}{3}$ by $\frac{5}{7}$
= $\frac{2}{3}÷\frac{5}{7}$
= $\frac{2}{3}\times \frac{7}{5}$
= $\frac{2\times 7}{3\times 5}=\frac{14}{15}$

Example 2: Divide fraction $\frac{4}{5}$ by whole number 6
= $\frac{4}{5}÷\frac{6}{1}$
= $\frac{4}{5}\times \frac{1}{6}$
= $\frac{4\times 1}{5\times 6}=\frac{4}{30}$
$\frac{4}{30}$ should be reduced into its the lowest term by dividing with common factor 2
= $\frac{2}{15}$

Example 3: Divide 5 by $\frac{6}{7}$
= $5÷\frac{6}{7}$
= $\frac{5\times 7}{1\times 6}=\frac{35}{6}$