Question

Find the rational number between -5/7 and -3/ 8

Answer 1

To find : rational number between $\frac{-5}{7}$  and $\frac{-3}{8}$

Solution:

• According question we have to find four rational numbers between $\frac{-5}{7}$  and $\frac{-3}{8}$  for this we need to equalize denominators of the rational numbers by taking LCM.
• Therefore, LCM = $56$
• Now, multiplying numerators by same numbers as multiplied by denominator to make LCM .
• We get, $\frac{-5}{7}=\frac{-5 \times 8}{56}=\frac{-40}{56} and \frac{-3}{8}=\frac{-3 \times 7}{56}=\frac{-21}{56}$
• Now, we can find rational numbers between $\frac{-40}{56}$ and $\frac{-3}{8}$

• They are : $\frac{-4}{56}, \frac{-5}{56}, \frac{-6}{56}, \frac{-7}{56}$  and so on till $\frac{-40}{56}$

Hence, rational number between  $\frac{-5}{7}$  and $\frac{-3}{8}$ is  $\frac{-4}{56}$  and  so on  till $\frac{-40}{56}$ .  

Note  : it was not mentioned how many rational numbers we had to find .