Question

Find four rational numbers between $\frac{-7}{8}$ and $\frac{-8}{7}$.

Answer 1

Given rational numbers are $\frac{-7}{8}$ and $\frac{-8}{7}$.

To compare the given ratio, lets make their denominators equal as follows:
LCM of $7$ and $8$ is $56$.

$\Rightarrow \frac{-7}{8}\times \frac{7}{7}=\frac{-49}{56}$

$\Rightarrow \frac{-8}{7}\times \frac{8}{8}=\frac{-64}{56}$

Since, in like fractions, the fraction which has smallest numerator is the smallest fraction.

So, $\frac{-64}{56}<\frac{-49}{56}$ [Since, $-64<-49$]

Now integers between $-64$ and $-49$ are $-63,-62,-61,....-48$

Thus, $\frac{-63}{56},\frac{-62}{56},\frac{-61}{56},\frac{-60}{56}$ are four rational numbers among the infinite rational numbers.

Note: There exist infinite many rational numbers between any two rational numbers.