Question

List five rational numbers between:
$-2$ and $-1$.

Answer 1

Given numbers $-2$ and $-1$
Let us write $-2$ and $-1$ as rational numbers with denominator $6$
$\Rightarrow -2\times \frac{6}{6}=\frac{-12}{6}$and$-1\times \frac{6}{6}=\frac{-6}{6}$
Therefore, insert the required five rational numbers between $\frac{-12}{6}$ and $\frac{-6}{6}$ as
$\frac{-12}{6}$<$\frac{-11}{6}$<$\frac{-10}{6}$<$\frac{-9}{6}$< $\frac{-8}{6}$<$\frac{-7}{6}$<$\frac{-6}{6}$
$\Rightarrow -2$ <$\frac{-11}{6}$<$\frac{-5}{3}$<$\frac{-3}{2}$<$\frac{-4}{3}$<$\frac{-7}{6}<-1$
Therefore, five rational numbers between $-2$ and $-1$ would be
$\frac{-11}{6},\frac{-5}{3},\frac{-3}{2},\frac{-4}{3},\frac{7}{6}$