Question

Find five rational numbers between $2$ and $3$

Answer 1

Since we want the five rational number between 2 and 3

The numbers of denominator $5+1=6$

So $2=\frac{2\times 6}{1\times 6}=\frac{12}{6}$

And $3=\frac{3\times 6}{1\times 6}=\frac{18}{6}$

We know that $12<13<14<15<17<18$

And $\frac{12}{6}<\frac{13}{6}<\frac{14}{6}<\frac{15}{6}<\frac{16}{6}<\frac{17}{6}<\frac{18}{6}$

Hence five rational number between 2 and 3 are

$\frac{13}{6},\frac{14}{6},\frac{15}{6},\frac{16}{6},\frac{17}{6}$