Question

Write three rational numbers between -4/5
and - 2/3.​

Answer 1

Answer:

These rational numbers are: 21/30, 22/30, 23/30.

Answer 2

☯GIVEN :

• $\bf{ \dfrac{-4}{5}}$ and $\bf{ \dfrac{-2}{3}}$.

☯TO FIND :

• Three rational numbers between $\bf{ \dfrac{-4}{5}}$ and $\bf{ \dfrac{-2}{3} }$.

☯KNOWLEDGE REQUIRED :

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

☯FORMULA REQUIRED :

• $\bigstar \underline{ \purple{\boxed{ \bf{ Rational \: Number = \dfrac{x+ y}{2} }}}}$

➲SOLUTION :

• 1)

$: \implies{ \sf{ Rational \: Number =\dfrac{x + y}{2} }}$

$: \implies{ \sf{ Rational \: Number = \dfrac{\dfrac{-4}{5} + \dfrac{ - 2}{3}}{2} }}$

$: \implies{ \sf{ Rational \: Number = \dfrac { \dfrac{ - 12 + (- 10)}{15}}{2}} }$ .

$: \implies{ \sf{ Rational \: Number = \dfrac { \dfrac{ - 12- 10}{15}}{2}} }$ .

$:\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{ - 22}{ 15}}{2}} }$ .

$:\implies{ \sf{ Rational \: Number = \dfrac{ - 22}{15} \div 2 }}$ .

$:\implies{ \sf{ Rational \: Number = \dfrac{\cancel{ - 22}}{15} \times \dfrac{1}{\cancel{2}} }}$

$:\implies{ \underline{ \boxed{ \red{ \bf{ Rational \: Number = \dfrac{ - 11}{15} }}}}}$

• 2)

$: \implies{ \sf{ Rational \: Number =\dfrac{x + y}{2} }}$

$: \implies{ \sf{ Rational \: Number = \dfrac{\dfrac{-4}{5} + \dfrac{ - 11}{15}}{2} }}$

$: \implies{ \sf{ Rational \: Number = \dfrac { \dfrac{ - 12 + (- 11)}{15}}{2}} }$

$: \implies{ \sf{ Rational \: Number = \dfrac { \dfrac{ - 12- 11}{15}}{2}} }$

$:\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{ - 23}{ 15}}{2}} }$

$:\implies{ \sf{ Rational \: Number = \dfrac{ - 23}{15} \div 2 }}$ .

$:\implies{ \sf{ Rational \: Number = \dfrac{ - 23}{15} \times \dfrac{1}{2} }}$ .

$:\implies{ \underline{ \boxed{ \blue{ \bf{ Rational \: Number = \dfrac{ - 23}{30} }}}}}$ .

• 3)

$: \implies{ \sf{ Rational \: Number =\dfrac{x + y}{2} }}$

$: \implies{ \sf{ Rational \: Number = \dfrac{ \dfrac{ - 11}{15} + \dfrac{-2}{3}}{2}}}$

$: \implies{ \sf{ Rational \: Number = \dfrac { \dfrac{ - 11 + (- 10)}{15}}{2}} }$

$: \implies{ \sf{ Rational \: Number = \dfrac { \dfrac{ - 11- 10}{15}}{2}} }$

$:\implies{ \sf{ Rational \: Number = \dfrac { \dfrac{ - 21}{ 15}}{2}} }$

$:\implies{ \sf{ Rational \: Number = \dfrac{ - 21}{15} \div 2 }}$

$:\implies{ \sf{ Rational \: Number = \dfrac{ - \cancel{ 21}}{ \cancel{15}} \times \dfrac{1}{2} }}$

$:\implies{ \underline{ \boxed{ \pink{ \bf{ Rational \: Number = \dfrac{ - 7}{10} }}}}}$