Question

List five rational number between:

$1)-1and0$

$2)-2and-1$

$3)\frac{-4}{5}and\frac{-2}{3}$

Answer 1

Five rational number between

A) $-1$ and $0$

$\Rightarrow \frac{-1}{1}\times \frac{6}{6}=\frac{-6}{6}$ and

$\Rightarrow \frac{0}{1}\times \frac{0}{6}=\frac{0}{6}$

Thus, 5 rational numbers between $\frac{-6}{6}$ and $\frac{0}{6}$ are,

$\frac{-1}{6},\frac{-2}{6},\frac{-3}{6},\frac{-4}{6},\frac{-5}{6}$

B) $-2$ and $-1$

$\Rightarrow \frac{-2}{1}\times \frac{6}{6}=\frac{-12}{6}$ and

$\Rightarrow \frac{-1}{1}\times \frac{6}{6}=\frac{-6}{6}$

Thus, 5 rational numbers between $\frac{-12}{6}$ and $\frac{-6}{6}$ are,

$\frac{-7}{6},\frac{-8}{6},\frac{-9}{6},\frac{-10}{6},\frac{-11}{6}$

C) $\frac{-4}{5}$ and $\frac{-2}{3}$

$\Rightarrow \frac{-4}{5}\times \frac{18}{18}=\frac{-72}{90}$ and

$\Rightarrow \frac{-2}{3}\times \frac{30}{30}=\frac{-60}{90}$

Thus, 5 rational numbers between $\frac{-72}{90}$ and $\frac{-60}{90}$.

$=\frac{-70}{90},\frac{-68}{90},\frac{-66}{90},\frac{-64}{90},\frac{-62}{90}$