Question

rational number lie between 3/5and 4/5

Answer 1

RATIONAL NUMBER BETWEEN
$\frac{3}{5} \: \: and \: \frac{4}{5}$


so
$\frac{3 \times 6}{5 \times 6} = \frac{18}{30}$


and
$\frac{4 \times 6}{5 \times 6} = \frac{24}{30}$



WE KNOW THAT

$18 < 19 < 20 < 21 < 22 < 23 < 24$


===>


$\frac{18}{30 } < \frac{19}{30} < \frac{20}{30} < \frac{21}{30} < \frac{22}{30 } < \frac{23}{30} < \frac{24}{30}$
Hence five rational numbers between


$\frac{3}{5} and \frac{4}{5}$

Answer 2

Hey !!



X = 3/5 and Y = 4/5.




Then, 3/5 < 4/5 , since ( 3 × 5 ) < ( 5 × 4 )



Therefore,


X < Y and n = 5


Let D = ( Y - X / n + 1 ) = ( 4/5 - 3/5 ) / ( 5 + 1 ) = ( 1/5 × 1/6 ) = 1/30.





Then, required rational numbers are :


( X + D ) , ( X + 2D ) , ( X + 3D ) , ( X +4D ) and ( X + 5D ).



I.e , ( 3/5 + 1/20 ) , ( 3/5 + 2/20 ) , ( 3/5 + 3/20 ) , ( 3/5 + 4/20 ) and ( 3/5 , 5/20 ) .



I.e , 19/30 , 20/30 , 21/30 , 22/30 , 23/30.

i.e 19/30 , 2/3 , 7/10 , 11/15 , 23/30.


Hence,

The required rational numbers between 3/5 and 4/5 are : 19/30 , 2/3 , 7/10 , 11/15 and 23/30.