Just a simple skills question

[Invader]

If I take 3 levels of bard (1-3) and 3 levels of barbarian (4-6) how many total ranks can I put into knowledge arcana or perform? Is it 9 (6 for bard and 3 for barbarian) or 7.5 (6 for bard and 1.5 for barbarian) or am I figuring things out totally wrong both ways?

 

[Dandu]

Your skill points are capped at 9 ranks, but if you purchase ranks as a barbarian, it will cost 2 skill points for 1 rank.

 

[Invader]

That's what I thought but for some reason I was reading it in the PHB as I was only allowed to take half a rank per level of barbarian.

Thank You