Question

Write five rational no. in between 2 and 3 ​

Answer 1

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For any rational number between "a" and "b" is a+b/2

so,

first rational number lies between 2 and 3

$\frac{2 + 3}{2} = \frac{5}{2}$

second number lies between 2 and 5/2

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

third number lies between 5/2 and 3

$\frac{ \frac{5}{2} + 3}{2} = \frac{ \frac{5 + 6}{2} }{2} = \frac{11}{2} \div \frac{2}{1} = \frac{11}{2} \times \frac{1}{2} = \frac{11}{4}$

fourth number lies between 9/4 and 5/2

$\frac{ \frac{9}{4} + \frac{5}{2} }{2} = \frac{ \frac{9 +10}{4} }{2} = \frac{19}{4} \div \frac{2}{1} = \frac{19}{4} \times \frac{1}{2} = \frac{19}{8}$

fifth number lies between 5/2 and 11/4

$\frac{ \frac{5}{2} + \frac{11}{4} }{2} = \frac{ \frac{10 + 11}{4} }{2} = \frac{21}{4} \div \frac{2}{1} = \frac{21}{4} \times \frac{1}{2} = \frac{21}{8}$

hope this is useful..