Maths / Fractions and Decimals / Division of Fractions

QUESTION

If $\dpi{120} \fn_jvn \large x=\frac{2}{3}+\frac{3}{4}\;and\; y= \frac{3}{4}+\frac{5}{6},$  then the value of $\fn_jvn \large \frac{1}{x}\div\frac{1}{y}$ is

 OPTIONS A. $\frac{11}{38}$ B. $\frac{17}{38}$ C. $\frac{22}{17}$ D. $\frac{19}{17}$
Right Option : D

EXPLANATION
Explain TypeExplanation Content
Text

Given             $x=\frac{2}{3}+\frac{3}{4},y=\frac{3}{4}+\frac{5}{6}$

$A=\frac{1}{\frac{2}{3}+\frac{3}{4}}=\frac{1}{\frac{8+9}{12}}=\frac{12}{17}$

$B=\frac{1}{\frac{3}{4}+\frac{5}{6}}=\frac{1}{\frac{18+20}{24}}=\frac{24}{38}$

So, A $\div$ B

$=\frac{12}{17}\div\frac{24}{38}=\frac{12}{17}\times \frac{38}{24}=\frac{19}{17}$

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