Question

Three rational numbers between 5/31 and 6/31

Answer 1

Answer:

$\dfrac{26}{155}$, $\dfrac{27}{155}$, and $\dfrac{28}{155}$.

Step-by-step explanation:

What is a rational number? By definition, a rational number can be represented as the fraction of two integers.

The goal is to find three fractions in the form $\dfrac{p}{q}$ between $\dfrac{5}{31}$ and $\dfrac{6}{31}$.

$\dfrac{5}{31} < \dfrac{p}{q} < \dfrac{6}{31}$.

At this moment, there doesn't seems to be a number that could fit. The question is asking for three of these numbers. Multiple the numerator and the denominator by a number greater than three (e.g., five) to obtain

$\dfrac{25}{155} < \dfrac{p}{q} < \dfrac{30}{155}$.

Since $p$ and $q$ can be any integers, let $q = 155$.

$\dfrac{25}{155} < \dfrac{p}{155} < \dfrac{30}{155}$.

$\implies 25 < p < 30$.

Possible values of $p$ are 26, 27, and 28. That corresponds to the fractions

$\dfrac{26}{155}$, $\dfrac{27}{155}$, and $\dfrac{28}{155}$.

These are all rational numbers for they are fractions of integers.