Ticks in forex/ interest rate futures

I personally find the use of ticks confusing. Now without using ticks the profit or loss from a future arises from multiplying:
number of future contracts x contract size x difference in contract price.
Using ticks, the formula changes to:
number of future contracts x P/L per tick x difference in contract price.
P/L per tick = contract size x tick size
As an example see example 11 and example 12 from chapter 18 of the study book.
In the example the 2 methods are equal, but you can clearly see from the formula the above are not equal, as using ticks we basically add them to the calculation and change the result without deducting them/ dividing by them anywhere else.
Any ideas? Where am I going wrong?