Question

Insert two rational number between $\frac{-1}{3}$ and $\frac{-1}{2}$ and arrange in ascending order

Answer 1

We can write the rational numbers as

$\frac{-1\times 2}{3\times 2}=\frac{-2}{6}=\frac{-2\times 3}{6\times 3}=\frac{-6}{18}$

and $\frac{-1\times 3}{2\times 3}=\frac{-3}{6}=\frac{-3\times 3}{6\times 3}=\frac{-9}{18}$

Two rational numbers between $\frac{-1}{3}$ and $\frac{-1}{2}$ are $\frac{-7}{18},\frac{-8}{18}$

The ascending order is $\frac{-1}{3}>\frac{-7}{18}>\frac{-8}{18}>\frac{-1}{2}$