Question

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

(5) $-10,\frac{-83}{9}$

Answer 1

$$\begin{gathered} -10,\frac{-83}{9} \\ -10=\frac{-10}{1} \\ \mathrm{Let}\frac{-10}{1}=\frac{a}{b}\mathrm{and}\frac{-83}{9}=\frac{c}{d} \end{gathered}$$
Then, a × d = −10 × 9 = −90
And b × c = 1 × −83 = −83
−90 < −83
∴ a × d < b × c
$$\begin{gathered} \therefore \frac{a}{b}<\frac{c}{d} \\ \therefore \frac{-10}{1}<\frac{-83}{9} \\ \therefore -10<\frac{-83}{9} \end{gathered}$$