Question

Find five rational numbers between $\frac{-5}{7}$ and $\frac{-3}{8}$.

Answer 1

We find we can firstly convert the rational numbers into their equivalent forms and then plot on the number line.
$\frac{-5}{7}$ and $\frac{-3}{8}$.
The LCM of $7$ and $8$ is $56$.
$\frac{-5}{7}=\frac{-5\times 8}{7\times 8}=\frac{-40}{56}$ and $\frac{-3}{8}=\frac{-3\times 7}{8\times 7}=\frac{-21}{56}$
Hence,
$\frac{-22}{56}$, $\frac{-23}{56}$, $\frac{-24}{56}$, $\frac{-25}{56}$, $\frac{-26}{56}$ are a few rational numbers lying between $\frac{-5}{7}$ and $\frac{-3}{8}$.