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1. The product of two fractions is $\frac{14}{15}$ and their quotient is $\frac{35}{24}$ . The greater fraction is :

A. $\frac{4}{5}$

B. $\frac{7}{6}$

C. $\frac{7}{4}$

D. $\frac{7}{3}$

Solution:

Let the two fractions be a and b
Then,

\begin{aligned} a b = \frac{14}{15} & \frac{a}{b} = \frac{35}{24} \\ \Leftrightarrow \frac{a b}{(\frac{a}{b})} = (\frac{14}{15} \times \frac{24}{35}) \\ \Leftrightarrow b^{2} = \frac{16}{25} \\ \Leftrightarrow b = \frac{4}{5} \\ So, \\ \Leftrightarrow a b = \frac{14}{15} \\ \Leftrightarrow a = (\frac{14}{15} \times \frac{5}{4}) \\ \Leftrightarrow a = \frac{7}{6} \end{aligned}

Since a > b,
So, greater fraction is

\frac{7}{6}

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