Question

Evaluate :
$(3\frac{5}{12}+1\frac{2}{3})÷(3\frac{5}{12}-1\frac{2}{3})$

Answer 1

$(3\frac{5}{12}+1\frac{2}{3})÷(3\frac{5}{12}-1\frac{2}{3})$
It can be written as
$=[\frac{12\times 3+5}{12}+\frac{3\times 1+2}{3}]÷[\frac{12\times 3+5}{12}-\frac{3\times 1+2}{3}]$
$=[\frac{41}{12}+\frac{5}{3}]÷[\frac{41}{12}-\frac{5}{3}]$
LCM of $12$ and $3$ is $12$
$=\left[\frac{41+20}{12}\right]÷\left[\frac{41-20}{12}\right]$
By further calculation
$=\frac{61}{12}÷\frac{21}{12}$
We can write it as
$=\frac{61}{12}\times \frac{12}{21}$
$=\frac{61}{21}$
$=2\frac{19}{21}$