Question

find five rational numbers between 3/5 and 5/6

Answer 1

Step-by-step explanation:

LCM of 5 and 6 is 30.

3×6=18

5×6=30

18/30

5×5=25

6×5=30

25/30

hence, the five rational no. are 19/30, 20/30, 21/30, 22/30 and 23/30.

Answer 2

☯GIVEN :

• $\bf{ \dfrac{3}{5} }$ and $\bf{ \dfrac{5}{6} }$.

☯TO FIND :

• Five rational numbers between $\bf{ \dfrac{3}{5} }$ and $\bf{ \dfrac{5}{6} }$.

☯KNOWLEDGE REQUIRED :

• 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)

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

$\implies{ \sf{ Rational \: Number = \dfrac{\dfrac{3}{5} + \dfrac{5}{6}}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{18 + 25}{30}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{43}{30}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac{43}{30} \div 2 }}$

$\implies{ \sf{ Rational \: Number = \dfrac{43}{30} \times \dfrac{1}{2} }}$

$\implies{ \boxed{ \green{ \bf{ Rational \: Number = \dfrac{43}{60} }}}}$

• 2)

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

$\implies{ \sf{ Rational \: Number = \dfrac{\dfrac{3}{5} + \dfrac{43}{60}}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{36 + 43}{60}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{79}{60}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac{79}{60} \div 2 }}$

$\implies{ \sf{ Rational \: Number = \dfrac{79}{60} \times \dfrac{1}{2} }}$

$\implies{ \boxed{ \green{ \bf{ Rational \: Number = \dfrac{79}{120} }}}}$

• 3)

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

$\implies{ \sf{ Rational \: Number = \dfrac{\dfrac{43}{60} + \dfrac{5}{6}}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{43+ 50}{60}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{93}{60}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac{93}{60} \div 2 }}$

$\implies{ \sf{ Rational \: Number = \dfrac{93}{60} \times \dfrac{1}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac{\cancel{93}}{\cancel{60}} \times \dfrac{1}{2} }}$

$\implies{ \boxed{ \green{ \bf{ Rational \: Number = \dfrac{31}{40} }}}}$

• 4)

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

$\implies{ \sf{ Rational \: Number = \dfrac{\dfrac{79}{120} + \dfrac{43}{60}}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{79 + 86}{120}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{165}{120}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac{165}{120} \div 2 }}$

$\implies{ \sf{ Rational \: Number = \dfrac{\cancel{165}}{\cancel{120}} \times \dfrac{1}{2} }}$

$\implies{ \boxed{ \green{ \bf{ Rational \: Number = \dfrac{11}{16} }}}}$

• 5)

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

$\implies{ \sf{ Rational \: Number = \dfrac{\dfrac{43}{60} + \dfrac{31}{40}}{2} }}$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{86+93}{120}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{179}{120}}{2}} }$

$\implies{ \sf{ Rational \: Number = \dfrac{179}{120} \div 2 }}$

$\implies{ \sf{ Rational \: Number = \dfrac{179}{120} \times \dfrac{1}{2} }}$

$\implies{ \boxed{ \green{ \bf{ Rational \: Number = \dfrac{179}{240} }}}}$