Question

Mark the correct alternative in each of the following:

Which of the following is correct?

(a) $\frac{5}{9}>\frac{-3}{-8}$ (b) $\frac{5}{9}<\frac{-3}{-8}$ (c) $\frac{2}{-3}<\frac{-8}{7}$ (d) $\frac{4}{-3}>\frac{-8}{7}$

Answer 1

Consider the rational numbers $\frac{5}{9}$ and $\frac{-3}{-8}$.

We write the rational number $\frac{-3}{-8}$ with positive denominator.
$\frac{-3}{-8}=\frac{-3\times \left(-1\right)}{-8\times \left(-1\right)}=\frac{3}{8}$

Now, we write the rational numbers so that they have a common denominator.

LCM of 8 and 9 = 72

So, $\frac{5}{9}=\frac{5\times 8}{9\times 8}=\frac{40}{72}$ and $\frac{3}{8}=\frac{3\times 9}{8\times 9}=\frac{27}{72}$

Now,

$$\begin{gathered} 40>27 \\ \Rightarrow \frac{40}{72}>\frac{27}{72} \\ \Rightarrow \frac{5}{9}>\frac{3}{8} \\ \Rightarrow \frac{5}{9}>\frac{-3}{-8} \end{gathered}$$

It can also be checked that $\frac{2}{-3}>\frac{-8}{7}$ and $\frac{4}{-3}<\frac{-8}{7}$.

Hence, the correct answer is option (a).