Question

Which of the following forms a pair of equivalent rational numbers?

• A. $\frac{-8}{15}$ and $\frac{-24}{48}$
• B. $\frac{24}{40}$ and $\frac{35}{50}$
• C. $\frac{9}{72}$ and $\frac{-3}{21}$
• D. $\frac{-25}{35}$ and $\frac{55}{-77}$

Answer 1

The correct option is D

$\frac{-25}{35}$ and $\frac{55}{-77}$

When we have to compare two rational numbers, we first make their denominators equal and then compare their numerators.
Consider $\frac{24}{40}$ and $\frac{35}{50}.$ LCM of 40 and 50 is 200.
$⟹\frac{(24\times 5)}{(40\times 5)}=\frac{120}{200}$
and $\frac{(35\times 4)}{(50\times 4)}=\frac{140}{200}\ne \frac{120}{200}$.
Thus, $\frac{24}{40}$ and $\frac{35}{50}$ are not equivalent.
Considering $\frac{-25}{35}$ and $\frac{55}{-77},$ LCM of 35 and 77 is 385.
$⟹\frac{(-25\times 11)}{(35\times 11)}=\frac{-275}{385}$
and $\frac{(55\times 5)}{(-77\times 5)}=\frac{-275}{385}.$
Thus, $\frac{-25}{35}$ and $\frac{55}{-77}$ are equivalent rational numbers.

Similarly, on checking the remaining options we find that $\frac{-25}{35}$ and $\frac{55}{-77}$ is the only pair of equivalent rational numbers.