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Division of a fraction - class-VIII
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Evaluate: $\dfrac{(3\dfrac{2}{3})^{2} -(2\dfrac{1}{2})^{2}}{(4\dfrac{3}{2})^{2} -(3\dfrac{1}{3})^{2}}$ $\div$ $\dfrac{3\dfrac{2}{3} -2\dfrac{1}{2}}{4\dfrac{3}{2} -3\dfrac{1}{3}}$
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A
$\dfrac{37}{53}$
💡 Explanation:
$\dfrac{(3\frac{2}{3})^2-(2\frac{1}{2})^2}{(4\frac{3}{2})^2-(3\frac{1}{3})^2} \div \dfrac{3\frac{2}{3}-2\frac{1}{2}}{4\frac{3}{2}-3\frac{1}{3}}$
$=\dfrac{(3\frac{2}{3}+2\frac{1}{2})(3\frac{2}{3}-2\frac{1}{2})}{(4\frac{3}{2}+3\frac{1}{3})(4\frac{3}{2}-3\frac{1}{3})} \div \dfrac{3\frac{2}{3}-2\frac{1}{2}}{4\frac{3}{2}-3\frac{1}{3}}$
$=\dfrac{3\frac{2}{3}+2\frac{1}{2}}{4\frac{3}{2}+3\frac{1}{3}}$
$=\dfrac{\dfrac{11}{3}+\dfrac{5}{2}}{\dfrac{11}{2}+\dfrac{10}{3}}$
$=\dfrac{\dfrac{22+15}{6}}{\dfrac{33+20}{6}}$
$=\dfrac{37}{53}$