Question

Find a rational number exactly halfway between:

`1/6` and `1/9`

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 `1/6` and `1/9`

Here, a = `1/6` and b = `1/9`

∴ `(a + b)/2 = (1/6 + 1/9)/2`

= `((1 xx 3)/(6 xx 3) + (1 xx 2)/(9 xx 2))/2`  ...[∵ LCM of 6 and 9 = 18]

= `(3/18 + 2/18)/2`

= `((3 + 2)/18)/2`

= `(5/18)/2`

= `5/(18 xx 2)`

= `5/36`

Hence, the exactly halfway between `1/6` and `1/9` is `5/36`.