Question

Which of the two rational numbers is greater?

$\frac{9}{-13}or\frac{7}{-12}$

Answer 1

We have $\frac{9}{-13}and\frac{7}{-12}$

First, make both the denominators positive.

$\frac{9}{-13}=\frac{9\times (-1)}{-13\times (-1)}=\frac{-9}{13}$ and $\frac{7}{-12}=\frac{7\times (-1)}{-12\times (-1)}=\frac{-7}{12}$

The rational numbers are $\frac{-9}{13}and\frac{-7}{12}$

Now, to compare them we have to make their denominators equal.

$LCM(13,12)=156$

Now,$\frac{-9}{13}=\frac{-9\times 12}{13\times 12}=\frac{-108}{156}$ and $\frac{-7}{12}=\frac{-7\times 13}{12\times 13}=\frac{-91}{156}$

Since

$$\begin{gathered} \frac{108}{156}>\frac{91}{156} \\ \Rightarrow \frac{-108}{156}<\frac{-91}{156} \\ \Rightarrow \frac{-9}{13}<\frac{-7}{12} \\ \Rightarrow \frac{9}{-13}<\frac{7}{-12} \end{gathered}$$

Hence, $\frac{7}{-12}$is greater.