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Rational Numbers — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSRational Numbers5 Marks
Question
Verify whether the given statement is true or false: $\Big(\frac{5}{9}\div\frac{1}{3}\Big)\div\frac{5}{2}=\frac{5}{9}\div\Big(\frac{1}{3}\div\frac{5}{2}\Big)$
✓

Answer

False.
Solution:
$\text{L.H.S.}=\Big(\frac{5}{9}\div\frac{1}{3}\Big)\div\frac{5}{2}$
$=\Big(\frac{5}{9}\times\frac{3}{1}\Big)\times\frac{2}{5}$
$=\frac{5\times3\times2}{9\times1\times5}$
$=\frac{30}{45}$
$=\frac{2}{3}$
$\text{R.H.S.}=\frac{5}{9}\div\Big(\frac{1}{3}\div\frac{5}{2}\Big)$
$=\frac{5}{9}\div\Big(\frac{1}{3}\times\frac{2}{5}\Big)$
$=\frac{5}{9}\div\Big(\frac{2}{15}\Big)$
$=\frac{5}{9}\times\Big(\frac{15}{2}\Big)$
$=\frac{75}{18}$
$=\frac{25}{6}$
$\text{L.H.S}\neq\text{R.H.S}$

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