Question

List three rational numbers between -2 and -1

Answer 1

Let us write -1 and -2 as rational numbers with denominator 5 (why?)
We have -1 = $\frac{-5}{5}$= -2= $\frac{-10}{5}$
so $\frac{-10}{5}$< $\frac{-9}{5}$< $\frac{-8}{5}$< $\frac{-7}{5}$< $\frac{-6}{5}$< $\frac{-5}{5}$

or -2< $\frac{-9}{5}$< $\frac{-8}{5}$< $\frac{-7}{5}$< $\frac{-6}{5}$<-1

The three rational numbers between -2 and -1 would be $\frac{-9}{5}$, $\frac{-8}{5}$, $\frac{-7}{5}$

(You can take any three of $\frac{-9}{5},$ $\frac{-8}{5}$, $\frac{-7}{5}$, $\frac{-6}{5}$)