Question

Divide the sum of $\frac{65}{12}$ and $\frac{8}{3}$ by thier difference.

Answer 1

Step 1: To find out the sum of $\frac{65}{12}$ and $\frac{8}{3}$is

$$\begin{gathered} =\frac{65}{12}+\frac{8}{3} \\ =\frac{65}{12}+\frac{8\times 4}{3\times 4} \\ =\frac{65}{12}+\frac{32}{12} \\ =\frac{65+32}{12}\Rightarrow \frac{97}{12} \end{gathered}$$

Step 2: To find out the difference of $\frac{65}{12}$and $\frac{8}{3}$is

$$\begin{gathered} =\frac{65}{12}-\frac{8}{3} \\ =\frac{65}{12}-\frac{8\times 4}{3\times 4} \\ =\frac{65}{12}-\frac{32}{12} \\ =\frac{65-32}{12}\Rightarrow \frac{33}{12} \end{gathered}$$

Step 3: Divide the sum $\frac{97}{12}$by the difference $\frac{33}{12}$

$$\begin{gathered} =\frac{97}{12}÷\frac{33}{12} \\ =\frac{97}{12}\times \frac{12}{33} \\ =\frac{97}{33} \end{gathered}$$

Hence, the final answer is $\frac{97}{33}.$