Question

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

Answer 1

$[{\left(\frac{5}{6}\right)}^2\times \frac{9}{4}]÷[(-\frac{3^2}{2})\times \frac{125}{216}]$
$=[\frac{5\times 5}{6\times 6}\times \frac{9}{4}]÷[\frac{-3\times -3}{2\times 2}\times \frac{125}{216}]$
$=[\frac{25}{36}\times \frac{9}{4}]÷[\frac{9}{4}\times \frac{125}{216}]$
$=[\frac{25}{4}\times \frac{1}{4}]÷[\frac{1}{4}\times \frac{125}{24}]$
$=\left[\frac{25}{16}\right]÷\left[\frac{125}{96}\right]$
$=\frac{25}{16}\times \frac{96}{125}$
$=\frac{1}{1}\times \frac{6}{5}=1\frac{1}{5}$