Find the difference: i. 5/6 - 1/4 ii. 11/18 - 3/4 Class 9

Find the difference: i. 5/6 - 1/4 ii. 11/18 - 3/4 Class 9

Question 1.

Find the difference: Class 9

i. $\frac{5}{6}-\frac{1}{4}$

ii. $\frac{11}{8}-\frac{3}{4}$

iii. $\quad-\frac{7}{9}-\left(-\frac{2}{3}\right)$

Solution:

i. $\frac{5}{6}-\frac{1}{4}$

L.C.M. of 6 and 4 is 12.

$\begin{aligned} \therefore \quad \frac{5}{6}-\frac{1}{4} & =\frac{5 \times 2}{6 \times 2}-\frac{1 \times 3}{4 \times 3} \\ & =\frac{10}{12}-\frac{3}{12} \\ & =\frac{10-3}{12} \\ \therefore \quad \frac{5}{6}-\frac{1}{4} & =\frac{7}{12}\end{aligned}$

ii. $\frac{11}{8}-\frac{3}{4}$

L.C.M. of 8 and 4 is 8.

$\begin{aligned} \therefore \quad \frac{11}{8}-\frac{3}{4} & =\frac{11}{8}-\frac{3 \times 2}{4 \times 2} \\ & =\frac{11}{8}-\frac{6}{8} \\ & =\frac{11-6}{8} \\ \therefore \quad \frac{11}{8}-\frac{3}{4} & =\frac{5}{8}\end{aligned}$

iii. $\quad-\frac{7}{9}-\left(-\frac{2}{3}\right)$

L.C.M. of 9 and 3 is 9.

$\begin{aligned} \therefore \quad-\frac{7}{9}-\left(-\frac{2}{3}\right) & =-\frac{7}{9}+\frac{2}{3} \\ & =-\frac{7}{9}+\frac{2 \times 3}{3 \times 3} \\ & =-\frac{7}{9}+\frac{6}{9} \\ & =\frac{-7+6}{9} \\ \therefore \quad-\frac{7}{9}-\left(-\frac{2}{3}\right) & =-\frac{1}{9}\end{aligned}$