Question
Verify whether the given statement is true or false: $\Big\{(-16)\div\frac{6}{5}\Big\}\div\frac{-9}{10}=(-16)\div\Big\{\frac{6}{5}\div\frac{-9}{10}\Big\}$
✓
Answer
False.
Solution:
$\text{L.H.S.}=\Big\{(-16)\div\frac{6}{5}\Big\}\div\frac{-9}{10}$
$=\Big[(-16)\times\frac{5}{6}\Big]\times\frac{10}{-9}$
$=\frac{(-16)\times5\times10}{6\times(-9)}$
$=\frac{800}{54}$
$=\frac{400}{27}$
$\text{R.H.S.}=(-16)\div\Big\{\frac{6}{5}\div\frac{-9}{10}\Big\}$
$=(-16)\div\Big[\frac{6}{5}\times\frac{10}{-9}\Big]$
$=-16\div\Big(\frac{-60}{45}\Big)$
$=-16\times\Big(\frac{-45}{60}\Big)$
$=-16\times\Big(\frac{-3}{4}\Big)$
$=\frac{48}{4}$
$=12$
$\text{L.H.S}\neq\text{R.H.S}$
Solution:
$\text{L.H.S.}=\Big\{(-16)\div\frac{6}{5}\Big\}\div\frac{-9}{10}$
$=\Big[(-16)\times\frac{5}{6}\Big]\times\frac{10}{-9}$
$=\frac{(-16)\times5\times10}{6\times(-9)}$
$=\frac{800}{54}$
$=\frac{400}{27}$
$\text{R.H.S.}=(-16)\div\Big\{\frac{6}{5}\div\frac{-9}{10}\Big\}$
$=(-16)\div\Big[\frac{6}{5}\times\frac{10}{-9}\Big]$
$=-16\div\Big(\frac{-60}{45}\Big)$
$=-16\times\Big(\frac{-45}{60}\Big)$
$=-16\times\Big(\frac{-3}{4}\Big)$
$=\frac{48}{4}$
$=12$
$\text{L.H.S}\neq\text{R.H.S}$
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