Question

Divide the sum of $\frac{5}{8}$ and $\frac{-11}{12}$ by the difference of $\frac{3}{7}$ and $\frac{5}{14}$.

Answer 1

$\text{Sum of}\frac{5}{8}and\frac{-11}{2}=\frac{5}{8}+\left(\frac{-11}{12}\right)=\frac{5}{8}-\frac{11}{12}=\frac{(5\times 3)-(11\times 2)}{24}(\because \text{LCM of 8 and 12 is 24})=\frac{15-22}{24}=\frac{-7}{24}\text{Now, divide}\frac{3}{7}and\frac{5}{14}=\frac{3}{7}-\frac{5}{14}or\frac{5}{14}-\frac{3}{7}(\because \text{LCM of 7 and 13=14}=\frac{6-5}{14}or\frac{5-6}{14}=\frac{1}{14}or\frac{-1}{14}\text{Now divide}\frac{-7}{24}by\frac{1}{14}or\frac{-1}{14}=\frac{\frac{-7}{24}}{\frac{1}{14}}or\frac{\frac{-7}{24}}{\frac{-1}{14}}=\frac{-7}{24}\times \frac{14}{1}or\frac{-7}{24}\times \frac{-14}{1}=\frac{-49}{12}or\frac{49}{12}=-4\frac{1}{12}or4\frac{1}{12}$