Question

Which of the two rational numbers $\frac{5}{-12}$ and $\frac{-4}{9}$ is greater?

Answer 1

The given rational numbers are $\frac{5}{-12}$ and $\frac{-4}{9}$ or $\frac{-5}{12}$ and $\frac{-4}{9}$
LCM of $12$ and $9$ is $108$
$\frac{-5}{12}=\frac{(-5)\times 9}{12\times 9}=\frac{-45}{108}$
Again, $\frac{-4}{9}=\frac{(-4)\times 12}{9\times 12}=\frac{-48}{108}$
Since, $-48<-45$, we have
$\frac{-48}{108}<\frac{-45}{108}$ or $\frac{-4}{9}<\frac{-5}{12}$ or $\frac{-4}{9}<\frac{5}{-12}$