# Five rational numbers between1/2 and 2/3?

The given number

$\frac{1}{2} and \frac{2}{3} \\$

We can write as,

$\frac{1}{2} = \frac{1}{2} \times \frac{3}{3} = \frac{3}{6} \\ \frac{2}{3} = \frac{2}{3} \times \frac{2}{2} = \frac{4}{6}$

Now

$\frac{3}{6} = \frac{3}{6} \times \frac{10}{10} = \frac{30}{60} \\ \frac{4}{6} = \frac{4}{6} \times \frac{10}{10} = \frac{40}{60}$

then five rational number between

$\frac{30}{60} and \frac{40}{60}$  is given below

$\frac{31}{60}, \frac{32}{60}, \frac{34}{60}, \frac{35}{60}, \frac{36}{60}$

Hence, five rational number

$\frac{31}{60}, \frac{32}{60}, \frac{34}{60}, \frac{35}{60}, \frac{36}{60}$

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