Question

List five rational numbers between :
i) $-1$ and $0$
ii) $-2$ and $-1$

Answer 1

To find $n$-number of rational numbers between the rational numbers $a$ and $b$,

Multiply each rational number by $\frac{n+1}{n+1}$.

Since, there exist $n$ number of integers between $a$ and $b$.

(i)

To find $5$ rational numbers between $-1$ and $0$ , multiply the numbers by $\frac{6}{6}$

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

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

Integers between $-6$ and $0$ are $-5,-4,-3,-2,-1$

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

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

i.e., $\frac{-5}{6},\frac{-2}{3},\frac{-1}{2},\frac{-1}{3},\frac{-1}{6}$

(ii)

To find $5$ rational numbers between $-2$ and $-1$ , multiply the numbers by $\frac{6}{6}$

$-2\times \frac{6}{6}=\frac{-12}{6}$

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

Integers between $-12$ and $-6$ are $-11,-10,-9,-8,-7$

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

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

i.e., $\frac{-11}{6},\frac{-5}{3},\frac{-3}{2},\frac{-4}{3},\frac{-7}{6}$
Note: There exist infinite number of rational numbers between any two distinct rational numbers.