Question

Which one of the following numbers lies between $\frac{5}{7}$ and $\frac{4}{9}$?

• A. $\frac{29}{63}$
• B. $\frac{46}{63}$
• C. $\frac{19}{63}$
• D. $\frac{49}{63}$

Answer 1

The correct option is A $\frac{29}{63}$

To find rational numbers between any two rational numbers, we have to first convert the given rational numbers into equivalent rational numbers having the same denominator.

So, $\frac{5}{7}=\frac{5\times 9}{7\times 9}=\frac{45}{63}$
and $\frac{4}{9}=\frac{4\times 7}{9\times 7}=\frac{28}{63}$

Hence, among the given options, $\frac{29}{63}$ lies between $\frac{28}{63}$ and $\frac{45}{63}$.

That means, $\frac{29}{63}$ lies between $\frac{5}{7}$ and $\frac{4}{9}$.