Question

Use the method of mean to find $3$ rational numbers between $-1$ and $-2$.

Answer 1

A rational number between two numbers $a$ and $b=\frac{(a+b)}{2}$
So, a rational number between $-1$ and $-2=\frac{-1-2}{2}=\frac{-3}{2}$
Now, another rational number between $-1$ and $\frac{-3}{2}=\frac{-1+\frac{-3}{2}}{2}=\frac{-5}{4}$
And another rational numbers between $\frac{-3}{2}$ and $-2=\frac{\frac{-3}{2}-2}{2}=\frac{-7}{4}$