Question

insert two rational numbers between 1/2 and 2/5​

Answer 1

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We know that a rational number between "a" and "b" is a+b/2

so an rational number between 1/2 and 2/5 is

$\frac{ \frac{1}{2} + \frac{2}{5} }{2} = \frac{ \frac{5 + 4}{10} }{2} = \frac{9}{10} \div \frac{2}{1} = \frac{9}{10} \times \frac{1}{2} = \frac{9}{20}$

so second number lies between 1/2 and 9/20

$\frac{ \frac{1}{2} + \frac{9}{20} }{2} = \frac{ \frac{20 + 9}{20} }{2} = \frac{29}{20} \div \frac{2}{1} = \frac{29}{20} \times \frac{1}{2} = \frac{29}{40}$

The two rational number are ,

9/20 and 29/40

Hope this is useful..