Question

Find $12$ rational numbers between $-1$ and $2$.

Answer 1

Evaluate the required Rational Numbers

We need to find $12$ rational numbers greater than $-1$ and smaller than $2$.

The difference between $2$ and $-1$ is: $2–(-1)=3$

Now, we need to divide the difference into $13$ equal parts as $2$ should not be included i.e. $\frac{3}{13}$

Thus, with a difference of $\frac{3}{13}$, we can find the twelve rational numbers between $-1$ and $2$.

Therefore, the rational numbers can be given as,

$\frac{-9}{13},\frac{-6}{13},\frac{-3}{13},\frac{0}{13},\frac{3}{13},\frac{6}{13},\frac{9}{13},\frac{12}{13},\frac{15}{13},\frac{18}{13},\frac{21}{13},\frac{24}{13}$

Hence, $12$ rational numbers between $-1$ and $2$ are $\frac{-9}{13},\frac{-6}{13},\frac{-3}{13},\frac{0}{13},\frac{3}{13},\frac{6}{13},\frac{9}{13},\frac{12}{13},\frac{15}{13},\frac{18}{13},\frac{21}{13},\frac{24}{13}$