Don't worry Greg. I understand why you are confused. It is because you know your maths and this stupid piece of algebra took you to space and back for no reason.
So how can you have 45 as the common denominator for 4 and 5? It doesn't make sense does it. It can be 20, 40 or 60 but not 45. Correct! you cannot have 45 as the common denominator for 4 and 5.
1 on 4 times 8 on 5 is 8 on 20. 8 on 20 can be simplified to 2 over 5. Got it?
Now some silly bugger for some unknown reason happened to multiple 2 over 5 by 9. That gave you 18 on 45. Confusing isn't it? It is no worse than 6 / 15 I guess.
:D