Question

Simplify: $\frac{\left(8\frac{1}{3}\times \frac{1}{5}\right)-\left(2\frac{1}{3}÷3\frac{1}{2}\right)}{\left(\frac{7}{10}of1\frac{1}{4}\right)+1\frac{1}{10}-\left(\frac{2}{5}÷\frac{5}{6}\right)}$

• A. $1\frac{3}{40}$
• B. $2\frac{38}{49}$
• C. $1\frac{40}{47}$
• D. $\frac{41}{49}$

Answer 1

The correct option is C $1\frac{40}{47}$

Given, $\frac{(8\frac{1}{3}\times \frac{1}{5})-(2\frac{1}{3}÷3\frac{1}{2})}{\left(\frac{7}{10}0f1\frac{1}{4}\right)+1\frac{1}{10}-(\frac{2}{5}÷\frac{5}{6})}$

First we solve all terms individually

$8\frac{1}{3}\times \frac{1}{5}$ = $\frac{25}{3}\times \frac{1}{5}$ = $\frac{5}{3}$

$2\frac{1}{3}÷3\frac{1}{3}$ = $\frac{7}{3}\times \frac{3}{10}$ = $\frac{7}{10}$

$\frac{7}{10}of1\frac{1}{4}$ = $\frac{7}{10}\times \frac{5}{4}$ = $\frac{7}{8}$

$\frac{2}{5}÷\frac{5}{6}$ = $\frac{2}{5}\times \frac{5}{6}$ = $\frac{1}{3}$

Now, we can put all the simplified fractions in equation

$=\frac{\frac{5}{3}-\frac{7}{10}}{\frac{7}{8}+\frac{11}{10}-\frac{1}{3}}$

$=\frac{\frac{50-21}{30}}{\frac{210+264-80}{240}}$

$=\frac{\frac{29}{30}}{\frac{394}{240}}$

$=\frac{29}{30}\times \frac{240}{394}$

$=1\frac{40}{47}$