Question

Find four rational numbers between $\frac{-2}{5}$ and $\frac{-3}{4}$.

Answer 1

Given fractions have denominators of $5$ and $4$.

$L.C.M$ of $5$ and $4$ is $5\times 4=20$

Making the denominators of both the fractions same :

multiply $-\frac{2}{5}$ by $\frac{4}{4}$

$\Rightarrow -\frac{2}{5}\times \frac{4}{4}=-\frac{8}{20}$

multiply $-\frac{3}{5}$ by $\frac{5}{5}$

$\Rightarrow -\frac{3}{4}\times \frac{5}{5}=-\frac{15}{20}$

There are infinite rational numbers between the $-\frac{8}{20}$ and $-\frac{15}{20}$ as we can find many equivalent rational number by multiplying or dividing any number in the numerator and denominator.

Four rational numbers between $-\frac{2}{5}$ and $-\frac{3}{4}$ are $-\frac{10}{20},-\frac{12}{20},-\frac{13}{20},-\frac{14}{20}$