Question

On simplification of $4\frac{1}{12}-[1\frac{3}{4}+\{2\frac{1}{2}-(\frac{1}{2}-\frac{1}{3})\left\}\right]$, we get ___

Answer 1

$4\frac{1}{12}-[1\frac{3}{4}+\{2\frac{1}{2}-(\frac{1}{2}-\frac{1}{3})\left\}\right]$
$=\frac{49}{12}-[\frac{7}{4}+\{\frac{5}{2}-(\frac{1}{2}-\frac{1}{3})\left\}\right]$

$=\frac{49}{12}-[\frac{7}{4}+\{\frac{5}{2}-\frac{1}{2}+\frac{1}{3}\left\}\right]$
$=\frac{49}{12}-[\frac{7}{4}+2+\frac{1}{3}]$

$=\frac{49}{12}-[\frac{7}{4}+\frac{8}{4}+\frac{1}{3}]$ ( Adding the first two fractions inside the bracket, and taking LCM as 4)

$=\frac{49}{12}-[\frac{15}{4}+\frac{1}{3}]$
$=\frac{49}{12}-\left[\frac{45+4}{12}\right]$ (LCM of 3 and 4 is 12 )
$=\frac{49}{12}-\frac{49}{12}$
$=0$