Question

write three rational numbers between 6/7 and 2/5​

Answer 1

➲CORRECT QUESTION :

Find three rational numbers between $\sf{ \dfrac{2}{5} }$ and $\sf{ \dfrac{6}{7} }$.

☯GIVEN :

• $\bf{ \dfrac{2}{5} }$ and $\bf{ \dfrac{6}{7} }$.

☯TO FIND :

• Three rational numbers between $\bf{ \dfrac{2}{5} }$ and $\bf{ \dfrac{6}{7} }$.

☯KNOWLEDGE REQUIRED :

• Rational numbers can be found between two rational numbers (m and n) , when m is less than n (m< n).

☯FORMULA REQUIRED :

• $\bigstar \underline{ \pink{\boxed{ \bf{ Rational \: Number = \dfrac{m+ n}{2} }}}}$

➲SOLUTION :

• 1)

$\implies{ \sf{ Rational \: Number =\dfrac{m + n}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac{\dfrac{2}{5} + \dfrac{6}{7}}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{14+ 30}{35}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{44}{35}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac{44}{35} \div2 }}$

$\implies{ \sf{ Rational \: Number = \dfrac{\cancel{44}}{35} \times \dfrac{1}{\cancel{2}} }}$

$\implies{ \boxed{ \green{ \bf{ Rational \: Number = \dfrac{22}{35} }}}}$

• 2)

$\implies{ \sf{ Rational \: Number =\dfrac{m + n}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac{\dfrac{2}{5} + \dfrac{22}{35}}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{14 + 22}{35}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{36}{35}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac{36}{35} \div 2 }}$

$\implies{ \sf{ Rational \: Number = \dfrac{\cancel{36}}{35} \times \dfrac{1}{\cancel{2}} }}$

$\implies{ \boxed{ \green{ \bf{ Rational \: Number = \dfrac{18}{35} }}}}$

• 3)

$\implies{ \sf{ Rational \: Number =\dfrac{m+ n}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac{\dfrac{22}{35} + \dfrac{6}{7}}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{22 + 30}{35}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{52}{35}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac{52}{35} \div 2 }}$

$\implies{ \sf{ Rational \: Number = \dfrac{\cancel{52}}{35} \times \dfrac{1}{\cancel{2}} }}$

$\implies{ \boxed{ \green{ \bf{ Rational \: Number = \dfrac{26}{35} }}}}$