Question

Evaluate:
$(\frac{32}{15}+\frac{8}{5})÷(\frac{32}{15}-\frac{8}{5})$

Answer 1

Step 1: Simplifying the given terms
Given,
$(\frac{32}{15}+\frac{8}{5})÷(\frac{32}{15}-\frac{8}{5})$
Consider : $\frac{32}{15}+\frac{8}{5}$
$=\frac{32}{15}+\frac{8\times 3}{5\times 3}[\because \text{LCM of}5,15=15]$
$=\frac{32}{15}+\frac{24}{15}$
$=\frac{32+24}{15}=\frac{56}{15}$
Consider: $\frac{32}{15}-\frac{8}{5}$
$=\frac{32}{15}-\frac{8\times 3}{5\times 3}[\because \text{LCM of}5,15=15]$
$=\frac{32}{15}-\frac{24}{15}=\frac{32-24}{15}=\frac{8}{15}$

Step 2: Finding the required value
$(\frac{32}{15}+\frac{8}{5})÷(\frac{32}{15}-\frac{8}{5})$
$\left(\frac{56}{15}\right)÷\left(\frac{8}{15}\right)$
$=\frac{56}{15}\times \left(\text{multiplicative inverse of}\frac{8}{15}\right)$
$=\frac{56}{15}\times \frac{15}{8}$
$=\frac{56\times 15}{15\times 8}$
$=7$
Hence, required value is $7$.