Question

Simplify :

$2\frac{3}{4}-[3\frac{1}{8}÷\{5-(4\frac{2}{3}-\frac{11}{12})\}]$

Answer 1

Step 1: Converting the mixed fractions into improper fractions

$2\frac{3}{4}-[3\frac{1}{8}÷\{5-(4\frac{2}{3}-\frac{11}{12})\}]$
$=\frac{2\times 4+3}{4}-[\frac{3\times 8+1}{8}÷\{5-(\frac{4\times 3+2}{3}-\frac{11}{12})\}]$
$=\frac{8+3}{4}-[\frac{24+1}{8}÷\{5-(\frac{12+2}{3}-\frac{11}{12})\}]$
$=\frac{11}{4}-[\frac{25}{8}÷\{5-(\frac{14}{3}-\frac{11}{12})\}]$

Step 2: Solve the parentheses first

$\frac{11}{4}-[\frac{25}{8}÷\{5-(\frac{14}{3}-\frac{11}{12})\}]$
$=\frac{11}{4}-[\frac{25}{8}÷\{5-\left(\frac{14\times 4-11}{12}\right)\}]$
$\left[LCM\text{of}\right(3,12)=12]$
$=\frac{11}{4}-[\frac{25}{8}÷\{5-\left(\frac{56-11}{12}\right)\}]$
$=\frac{11}{4}-[\frac{25}{8}÷\{5-\left(\frac{45}{12}\right)\}]$
$=\frac{11}{4}-[\frac{25}{8}-\{5-\frac{45}{12}\}]$

Step 3: Solving the curly brackets

$\frac{11}{4}-[\frac{25}{8}-\{5-\frac{45}{12}\}]$
$=\frac{11}{4}-[\frac{25}{8}÷\left\{\frac{5\times 12-45}{12}\right\}]$
$=\frac{11}{4}-[\frac{25}{8}÷\left\{\frac{60-45}{12}\right\}]$.
$=\frac{11}{4}-[\frac{25}{8}÷\left\{\frac{15}{12}\right\}]$
$=\frac{11}{4}-[\frac{25}{8}÷\frac{15}{12}]$


Step 4: Solving the square brackets
$\frac{11}{4}-[\frac{25}{8}÷\frac{15}{12}]$
$=\frac{11}{4}-[\frac{25}{8}\times \frac{12}{15}]$
$=\frac{11}{4}-\left[\frac{5}{2}\right]$
$=\frac{11-5\times 2}{4}=\frac{11-10}{4}$
$=\frac{1}{4}$
Hence, the given expression is equal to $\frac{1}{4}$