Question

Evaluate:
(ii) $\left[\right(\frac{5}{6}{)}^2\times \frac{9}{4}]÷[(-\frac{3}{2}{)}^2\times \frac{125}{216}]$

Answer 1

Given, $\left[\right(\frac{5}{6}{)}^2\times \frac{9}{4}]÷[(-\frac{3}{2}{)}^2\times \frac{125}{216}]$
On further simplificatiom we have:
$=\left[\right(\frac{5\times 5}{6\times 6})\times \frac{9}{4}]÷\left[\right(\frac{-3\times -3}{2\times 2})\times \frac{125}{216}]$

$=[\frac{25}{36}\times \frac{9}{4}]÷[\frac{9}{4}\times \frac{25}{216}]$

$=[\frac{25}{4}\times \frac{1}{4}]÷[\frac{1}{4}\times \frac{125}{24}]$

$=\left[\frac{25}{16}\right]÷\left[\frac{125}{96}\right]$

$=\frac{25}{16}\times \frac{96}{125}$

$=\frac{1}{1}\times \frac{6}{5}$

$=1\frac{1}{5}$

Hence , $\left[\right(\frac{5}{6}{)}^2\times \frac{9}{4}]÷[(-\frac{3}{2}{)}^2\times \frac{125}{216}]=1\frac{1}{5}$