Question

Which of the following rational numbers lie between $\frac{-5}{7}$ and $\frac{-4}{9}$?

• A. $\frac{-34}{63}$
• B. $\frac{-54}{63}$
• C. $\frac{-25}{63}$
• D. None of the above

Answer 1

The correct option is A $\frac{-34}{63}$

To find rational numbers between any two rational numbers, we have to first convert the given rational numbers into rational numbers having the same denominator.
This can be done by finding the LCM of the denominators.
The LCM of $7$ and $9$ is $9\times 7=63$

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 option only$\frac{-34}{63}$, lies between$\frac{-45}{63}$ and $\frac{-28}{63}$, that is it lies between$\frac{-5}{7}$ and $\frac{-4}{9}$.