Question

Insert six rational numbers between `5/6 and 8/9`.

Answer 1

LCM of denominator 6 and 9 is 18
Make, the denominator of each given rational number equal to 18 i.e the LCM

`5/6 = (5xx3)/(6xx3) = 15/18` and

`8/9= (8xx2)/(9xx2) = 16/18`

Since six rational numbers are required, multiply the numerator and denominator of each rational number by 6 + 1 = 7

`therefore 15/18 = (15xx7)/(18xx7) = 105/126` and

`16/18 = (16xx7)/(18xx7) = 112/126`

`therefore` Required rational numbers between `5/6` and

`8/9 "are" = 106/126, 107/126. 108/126. 109/126, 110/126, 111/126`

`= 53/63, 107/126, 6/7, 109/126, 55/63, 37/42`