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Rational Numbers — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsRational Numbers4 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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