Find the sum: i. -2/5 + 3/10 ii. 7/12 + 5/8 iii. -4/7 + 3/14 Class 9

Find the sum: i. -2/5 + 3/10 ii. 7/12 + 5/8 iii. -4/7 + 3/14 Class 9

Question 1.

Find the sum: Class 9

i. $\quad \frac{2}{5}+\frac{3}{10}$

ii. $\frac{7}{12}+\frac{5}{8}$

iii. $\quad-\frac{4}{7}+\frac{3}{14}$

Solution:

i. $\quad \frac{2}{5}+\frac{3}{10}$

L.C.M. of 5 and 10 is 10.

$\begin{aligned} \therefore \quad \frac{2}{5}+\frac{3}{10} & =\frac{2 \times 2}{5 \times 2}+\frac{3}{10} \\ & =\frac{4}{10}+\frac{3}{10}=\frac{4+3}{10} \\ \therefore \quad \frac{2}{5}+\frac{3}{10} & =\frac{7}{10}\end{aligned}$

ii. $\quad \frac{7}{12}+\frac{5}{8}$

L.C.M. of 12 and 8 is 24.

$\begin{aligned} \therefore \quad \frac{7}{12}+\frac{5}{8} & =\frac{7 \times 2}{12 \times 2}+\frac{5 \times 3}{8 \times 3} \\ & =\frac{14}{24}+\frac{15}{24} \\ & =\frac{14+15}{24} \\ \therefore \quad \frac{7}{12}+\frac{5}{8} & =\frac{29}{24}\end{aligned}$

iii. $\quad-\frac{4}{7}+\frac{3}{14}$

L.C.M. of 7 and 14 is 14 .

$\begin{aligned} \therefore \quad-\frac{4}{7}+\frac{3}{14} & =\frac{-4 \times 2}{7 \times 2}+\frac{3}{14} \\ & =\frac{-8}{14}+\frac{3}{14} \\ & =\frac{-8+3}{14} \\ \therefore \quad-\frac{4}{7}+\frac{3}{14} & =-\frac{5}{14}\end{aligned}$