Question

Which of the two rational numbers is greater?

$\frac{2}{-3}or\frac{-4}{5}$

Answer 1

We have $\frac{-2}{3}and\frac{-4}{5}$

To compare them we have to equate the denominators of both rational numbers.

Since $LCM(3,5)=15$

Now,

$\frac{2}{-3}=\frac{2\times (-5)}{-3\times (-5)}=\frac{-10}{15}$and $\frac{-4}{5}=\frac{-4\times 3}{5\times 3}=\frac{-12}{15}$

Since,

$$\begin{gathered} \frac{10}{15}<\frac{12}{15} \\ \Rightarrow \frac{-10}{15}>\frac{-12}{15} \end{gathered}$$

Therefore, $$\begin{gathered} \frac{-2}{3}>\frac{-4}{5} \\ or,\frac{2}{-3}>\frac{-4}{5} \end{gathered}$$

Hence, $\frac{2}{-3}$is greater than $\frac{-4}{5}$