Question

find two rational numbers between 1/10 and 9/4 by mean method

Answer 1

$We \:know \: that,$

$\blue{ Rational \: number \: between \: 'a'}$

$\blue {and\: 'b' \: is }\: \pink{\frac{a+b}{2} }$

$i) Rational \: number \: between \: \frac{1}{10}\\and \: \frac{9}{4}$

$= \frac{ \frac{1}{10}+\frac{9}{4}}{2}$

$= \frac{ \frac{2+45}{20}}{2}$

$= \frac{ \frac{47}{20}}{2}$

$= \frac{47}{20} \times \frac{1}{2}$

$= \frac{47}{40} \: --(1)$

$ii) Rational \: number \: between \: \frac{1}{10}\\and \: \frac{47}{40}$

$= \frac{ \frac{1}{10}+\frac{47}{40}}{2}$

$= \frac{ \frac{4+47}{40}}{2}$

$= \frac{ \frac{51}{40}}{2}$

$= \frac{51}{40} \times \frac{1}{2}$

$= \frac{51}{80} \: --(2)$

Therefore.,

$\green { \frac{51}{80}\: and \: \frac{47}{40} \:are}\\ \green { two \: rational \: numbers \: between}\\\green { \frac{1}{10} \:and \: \frac{9}{4}}$

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