# 4th Class Mathematics Fractions and Decimals Operation on the Fractions

## Operation on the Fractions

Category : 4th Class

### Operation on the Fractions

Addition of Like Fractions

$\text{Sum of like fractions}=\frac{\text{Sum of numerators}}{\text{common denominator}}$ In addition of like fractions, sum of the numerators will be the numerator for the resulting fraction and the common denominator will be the denominator. $\frac{P}{R}+\frac{Q}{R}=\frac{P+Q}{R}$

Add the following fractions.

Solution: $\frac{3}{11}+\frac{2}{11}+\frac{5}{11}=\frac{10}{11}$

Add the following fractions:

$\frac{3}{10}+\frac{2}{10}$

Solution:

$\frac{3}{10}+\frac{2}{10}=\frac{5}{10}$

Addition of Unlike Fractions

Add$\frac{5}{7}$ and$\frac{5}{8}$

Step 1:   Convert the fractions into like fractions. $\frac{5}{7}=\frac{5\times 8}{7\times 8}=\frac{40}{56}$ And $\frac{5}{8}=\frac{5\times 7}{8\times 7}=\frac{35}{56}$

Step 2:   Add numerator of the fractions$\text{4}0+\text{35}=\text{75}$.

Step 3:   Write the sum as numerator for the required fraction and common denominator as denominator$\frac{75}{56}$

Add$\frac{12}{19}$and$\frac{12}{11}$

Solution: $\frac{12}{19}=\frac{12\times 11}{19\times 11}=\frac{132}{209}$

$\frac{12}{11}=\frac{12\times 19}{19\times 19}=\frac{228}{209}$

$\frac{12}{19}+\frac{12}{11}=\frac{132}{209}+\frac{228}{209},=\frac{132+228}{209}=\frac{360}{209}$

Subtraction of Like Fractions

$\text{Difference of like fractions}=\frac{\text{Difference of numerators}}{\text{Common denominator}}$

In subtraction of like fractions, the difference of the numerators will be the numerator and the common denominator will be the denominator for the required fraction.

$\frac{p}{q}-\frac{r}{q}=\frac{p-r}{q}$

Solve the following:

$\frac{5}{7}-\frac{3}{7}$

Solution: $\frac{5}{7}-\frac{3}{7}=\frac{5-3}{7}=\frac{2}{7}$

Represent the shaded part in the above figures as a fraction and find their difference.

Solution:

$\frac{3}{5}-\frac{2}{5}=\frac{3-2}{5}=\frac{1}{5}$

Subtraction of Unlike

Fractions Subtract$\frac{5}{6}-\frac{4}{5}$

Step 1:   Convert the fractions into like fractions.

$\frac{5}{6}=\frac{5\times 5}{6\times 5}=\frac{25}{30}$

$\frac{4}{5}=\frac{4\times 6}{5\times 6}=\frac{24}{30}$

Step 2:  Find difference of the numerator.

$\text{25}-\text{24}=\text{1}$.

Step 3:   Write the difference as numerator and common denominator as denominator for the required fraction.

$\frac{1}{30}$

Solve$\frac{7}{9}-\frac{5}{8}$. Solution:

$\frac{7}{9}=\frac{7\times 8}{9\times 8}=\frac{56}{72}$

$\frac{5}{8}=\frac{5\times 9}{8\times 9}=\frac{45}{72}$

Now $\frac{56}{72}-\frac{45}{72}=\frac{56-45}{72}=\frac{9}{72}=\frac{1}{8}$

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