Question

Which of the following pairs represents the same rational number?

• A. $\frac{2}{3}$, $\frac{-12}{-9}$
• B. $\frac{3}{7}$, $\frac{-21}{49}$
• C. $\frac{-20}{25}$, $\frac{24}{-30}$
• D. $\frac{8}{-5}$, $\frac{-32}{24}$

Answer 1

The correct option is C $\frac{-20}{25}$, $\frac{24}{-30}$

• $\frac{-12}{-9}$ can be reduced to its standard form by dividing its numerator and denominator by $-3$ to get $\frac{4}{3}$, which is not equal to the first number. Hence, $\frac{2}{3}$ and $\frac{-12}{-9}$ cannot represent the same rational number.


• $\frac{3}{7}$ is a positive number, while $\frac{-21}{49}$ is a negative one. Thus, they cannot represent the same rational number.


• Both $\frac{-20}{25}$ and $\frac{24}{-30}$ when reduced, have the same standard form of $\frac{-4}{5}$. Thus, they represent the same rational number.


• $\frac{-32}{24}$ can be reduced to its standard form by dividing its numerator and denominator by $8$ to get $\frac{-4}{3}$, which is not the same as $\frac{-8}{5}$.