Question

Insert five rational numbers between `3/5` and `2/3`.

Answer 1

LCM of denominators 5 and 3 is 15.

make the denominator of each given rational number equal to 15 i.e., the LCM.

`3/5 = (3 xx 3)/(5 xx 3) = 9/15 ` and 

Since five rational numbers are required, multiply the numerator and denominator of each rational number by 5 + 1 = 6.

∴ `9/15 = (9 xx 6)/(15 xx 6) = 54/90` and `10/15 = (10 xx 6)/(15 xx 6 ) = 60/90`

∴ Required rational numbers between `3/5` and  `2/3` are `55/90, 56/90,57/90, 58/90`, and `59/90`.

=`11/18, 28/45,19/35,29/45` and `59/90`