Question

Find six rational number between $3$ and $4$.

Answer 1

We know that there exists infinite number of rational numbers between two rational numbers.

Now, to find some of many rational numbers, we follow these steps.

Step I: Make the denominator of the concerned rational numbers same.

Since, $3=\frac{3}{1}$ and $4=\frac{4}{1}$. Therefore, the denominators are same. But since we cannot simply find six rational numbers between them, therefore, we move to second step.

Step II: Multiply the denominator and numerator of both the rational numbers by a same rational number.

$\Rightarrow \frac{3}{1}\times \frac{10}{10}=\frac{30}{10}$ and

$\Rightarrow \frac{4}{1}\times \frac{10}{10}=\frac{40}{10}$

Now, $\frac{30}{10},\frac{31}{10},\frac{32}{10}...\frac{38}{10},\frac{39}{10},\frac{40}{10}$

Thus, we can choose any six rational numbers.

Hence, six rational numbers between $3$ and $4$ are $\frac{31}{10},\frac{32}{10},\frac{35}{10},\frac{36}{10},\frac{38}{10},\frac{39}{10}$