Question

find the rational number between 2/3 and 4/5 ?

Answer 1

$2 \times 5 \div 3 \times 5 \\ = 10 \div 15 \\ \\ 4 \times 3 \div 5 \times 3 \\ = 12 \div 15 \\ \\ 11 \div 15 \: is \: your \: required \: answer$

Answer 2

SOLUTION :  

Given : Two rational numbers ⅔ & ⅘

L.C.M of 3 & 5 is 15

2/3 = 2 x5 / 3 x 5  = 10 / 15

4/5 = 4 x3 / 5 x3 = 12 / 15  

To insert five rational numbers we multiply the numerator and denominator of about the fractions by 6 (5 +1 = 6) so that the difference between enumerators is at least 6.

10 ×6/ 15 × 6  

= 60 / 90  

12 ×6/ 15x 6

= 72 / 90  

The required 5 rational numbers between ⅔ & 4/5 are 61/ 90  , 62/90 , 63 /90 , 64/90, 65/90 , 66/90, 67 /90  

Hence, the 5 rational numbers are 61/ 90  , 62/90 , 63 /90 , 64/90, 65/90 , 66/90, 67 /90

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