Question
Verify whether the given statement is true or false:
$\frac{-8}{9}\div\frac{-4}{3}=\frac{-4}{3}\div\frac{-8}{9}$
$\frac{-8}{9}\div\frac{-4}{3}=\frac{-4}{3}\div\frac{-8}{9}$
✓
Answer
False.
Solution:
$\text{L.H.S.}=\frac{-8}{9}\div\frac{-4}{3}$
$=\frac{-8}{9}\times\frac{3}{-4}$
$=\frac{-8\times3}{9\times(-4)}$
$=\frac{-24}{-36}=\frac{24}{36}$
$=\frac{24\div12}{36\div12}$
$=\frac{2}{3}$
$\text{R.H.S.}=\frac{-4}{3}\div\frac{-8}{9}$
$=\frac{-4}{3}\times\frac{9}{-8}$
$=\frac{-36}{-24}=\frac{36}{24}$
$=\frac{36\div12}{24\div12}$
$=\frac{3}{2}$
$\text{L.H.S}\neq\text{R.H.S}$
$\therefore$ It is false.
Solution:
$\text{L.H.S.}=\frac{-8}{9}\div\frac{-4}{3}$
$=\frac{-8}{9}\times\frac{3}{-4}$
$=\frac{-8\times3}{9\times(-4)}$
$=\frac{-24}{-36}=\frac{24}{36}$
$=\frac{24\div12}{36\div12}$
$=\frac{2}{3}$
$\text{R.H.S.}=\frac{-4}{3}\div\frac{-8}{9}$
$=\frac{-4}{3}\times\frac{9}{-8}$
$=\frac{-36}{-24}=\frac{36}{24}$
$=\frac{36\div12}{24\div12}$
$=\frac{3}{2}$
$\text{L.H.S}\neq\text{R.H.S}$
$\therefore$ It is false.
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