Question

Find a rational number exactly halfway between:

`5/(-13)` and `(-7)/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 `5/(-13)` and `(-7)/9`

Here, a = `-5/13` and b = `-7/9`

∴ `(a + b)/2 = ((-5)/13 + (-7/9))/2`

= `((-5)/13 - 7/9)/2`

= `((-5 xx 9)/(13 xx 9) - (7 xx 13)/(9 xx 13))/2`

= `((-45)/177 - 91/177)/2`

= `((-45  -  91)/177)/2`

= `(-136)/(117 xx 2)`

= `(-136)/234`

Hence, the exactly of halfway between `5/(-13)` and `(-7)/9` is `-136/234`.