Question

Find a rational number exactly halfway between:

`1/15` and `1/12`

Answer 1

We know that, a rational number, which is halfway between two rational number i.e. a and b = `(a + b)/2`

Given rational numbers are `1/15` and `1/12`

Here, a = `1/15` and b = `1/12`

∴ `(a + b)/2 = (1/15 + 1/12)/2`

= `((1 xx 4)/(15 xx 4) + (1 xx 5)/(12 xx 5))/2`  ...[∵ LCM of 15 and 12 = 60]

= `(4/60 + 5/60)/2`

= `((4  +  5)/60)/2`

= `9/(60 xx 2)`

= `9/120`

= `3/40`

Hence, the exactly halfway between `1/15` and `1/12` is `3/40`.