Question

Which of the two rational numbers in each of the following pairs of rational numbers is smaller?
(i) $\frac{-6}{-13},\frac{7}{13}$
(ii) $\frac{16}{-5},3$
(iii) $\frac{-4}{3},\frac{8}{-7}$
(iv) $\frac{-12}{5},-3$

Answer 1

(i) $\frac{-6}{-13}=\frac{6}{13}<\frac{7}{13}$
(ii) $\frac{16}{-5}<3$
(iii)
$$\begin{gathered} \frac{-4}{3}=\frac{-4\times 7}{3\times 7}=\frac{-28}{21}\mathrm{and}\frac{8}{-7}=\frac{-8\times 3}{7\times 3}=\frac{-24}{21} \\ \mathrm{Therefore},\frac{-4}{3}<\frac{8}{-7} \end{gathered}$$
(iv)
$$\begin{gathered} \frac{-12}{5}\mathrm{and}-3=\frac{-3\times 5}{1\times 5}=\frac{-15}{5} \\ \mathrm{Therefore}\frac{-12}{5}>-3 \end{gathered}$$