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# Find six rational numbers between 3 and 4.

There can be infinitely many rational numbers between 3 and 4, one way to take them is

3=$$\frac{21}{(6+1)}$$, 4=$$\frac{28}{(6+1)}$$ .

The rational numbers between 3 and 4 therefore, will become
$$\frac{22}{7} ,\frac{23}{7} ,\frac{24}{7} ,\frac{25}{7} ,\frac{26}{7} ,\frac{27}{7}.$$

Another way to find middle rational number between two number
$$\Rightarrow$$ $$\frac{\frac{21}{7} + \frac{28}{7} }{2}$$
= $$\frac{\frac{49}{7} }{2}$$
= $$\frac{7}{2}$$.

As,$$\frac{ 21}{7} < \frac{7}{2} < \frac{28}{7}$$.

Rational no. between$$\frac{21}{7}$$ and $$\frac{7}{2}$$ will become

$$\Rightarrow$$ $$\frac{\frac{21}{7} + \frac{7}{2} }{2}$$
= $$\frac{\frac{91}{14} }{2}$$
= $$\frac{91}{28}$$ .

As,$$\frac{21}{7} < \frac{91}{28} < \frac{7}{2} < \frac{28}{7}$$.

Similarly, the other group of rational numbers between 3 and 4 will become

$$\frac{175}{56} , \frac{91}{28} , \frac{7}{2} , \frac{203}{56} , \frac{105}{28} , \frac{217}{56}$$ .