Question

Find four rational number between 1/2 and 1/3​

Answer 1

➲CORRECT QUESTION :

• Find four rational numbers between $\sf{ \dfrac{1}{3} }$ and $\sf{ \dfrac{1}{2} }$.

☯GIVEN :

• $\bf{ \dfrac{1}{3} }$ and $\bf{ \dfrac{1}{2} }$.

☯TO FIND :

• Four rational numbers between $\bf{ \dfrac{1}{3} }$ and $\bf{ \dfrac{1}{2} }$.

☯KNOWLEDGE REQUIRED :

1. Rational numbers can be found between two rational numbers (a and b) , when a is less than b (a < b).

☯FORMULA REQUIRED :

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

➲SOLUTION :

• 1)

$\implies{ \sf{ Rational \: Number =\dfrac{a + b}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac{\dfrac{1}{3} + \dfrac{1}{2}}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{2 + 3}{6}}{2}} }$

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

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

$\implies{ \sf{ Rational \: Number = \dfrac{5}{6} \times \dfrac{1}{2} }}$

$\implies{ \boxed{ \green{ \bf{ Rational \: Number = \dfrac{5}{12} }}}}$

• 2)

$\implies{ \sf{ Rational \: Number =\dfrac{a + b}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac{\dfrac{1}{3} + \dfrac{5}{12}}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{4 + 5}{12}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{9}{12}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac{9}{12} \div 2 }}$

$\implies{ \sf{ Rational \: Number = \dfrac{9}{12} \times \dfrac{1}{2} }}$

$\implies{ \sf{ Rational \: Number = \cancel{\dfrac{9}{24}} }}$

$\implies{ \boxed{ \green{ \bf{ Rational \: Number = \dfrac{3}{8} }}}}$

• 3)

$\implies{ \sf{ Rational \: Number =\dfrac{a + b}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac{\dfrac{5}{12} + \dfrac{1}{2}}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{5 + 6}{12}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{11}{12}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac{11}{12} \div 2 }}$

$\implies{ \sf{ Rational \: Number = \dfrac{11}{12} \times \dfrac{1}{2} }}$

$\implies{ \boxed{ \green{ \bf{ Rational \: Number = \dfrac{11}{24} }}}}$

• 4)

$\implies{ \sf{ Rational \: Number =\dfrac{a + b}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac{\dfrac{3}{8} + \dfrac{5}{12}}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{9 + 10}{24}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{19}{24}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac{19}{24} \div 2 }}$

$\implies{ \sf{ Rational \: Number = \dfrac{19}{24} \times \dfrac{1}{2} }}$

$\implies{ \boxed{ \green{ \bf{ Rational \: Number = \dfrac{19}{48} }}}}$