Question

Use the rules to determine which number is bigger and which is smaller.

(1) $\frac{-13}{8},\frac{5}{3}$

Answer 1

$\frac{-13}{8},\frac{5}{3}$

Let $\frac{-13}{8}=\frac{a}{b}\mathrm{and}\frac{5}{3}=\frac{c}{d}$ and
Then, a × d = −13 × 3 = −39
And b × c = 8 × 5 = 40
−39 < 40
∴ a × d < b × c
$$\begin{gathered} \therefore \frac{a}{b}<\frac{c}{d} \\ \therefore \frac{13}{8}<\frac{5}{3} \end{gathered}$$