Find 6 rational numbers between 3 and 4.

Given,

Two numbers : 3 and 4.

To find 6 rational numbers, we can express 3 and 4 with a common denominator that is greater than 6.

Multiplying numerator and denominator by 7 :

$\Rightarrow 3 = \dfrac{3 \times 7}{1 \times 7} = \dfrac{21}{7} \\[1em] \Rightarrow 4 = \dfrac{4 \times 7}{1 \times 7} = \dfrac{28}{7}.$

So, the 6 rational numbers between $\dfrac{21}{7}$ and $\dfrac{28}{7}$ are :

$\Rightarrow \dfrac{22}{7}, \dfrac{23}{7}, \dfrac{24}{7}, \dfrac{25}{7}, \dfrac{26}{7}, \dfrac{27}{7}.$

Hence, 6 rational numbers between 3 and 4 are $\dfrac{22}{7}, \dfrac{23}{7}, \dfrac{24}{7}, \dfrac{25}{7}, \dfrac{26}{7}$ and $\dfrac{27}{7}$.