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My current crankset has teeth of 28/38/48 if I buy a crankset with 22/32/44 will this work? Also my bike is 7 speed so could I buy one that works with 9 speed or will that not work?
 

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yes,but your chain maybe too long and your front derailer will need to be adjusted.Maybe even replaced.
I'm no expert,so here is my explanation of the gears.
The rear gears(freewheel/cassette) can have 1 to 10 gears on it.this multiplied by the crank gears(chain rings) equals the speed of your bike.ex.3 rings in front 7 in back is a 21 speed. 2 in front 5 in back is a ten speed.
You should really check out Sheldon Brown's articles I've learned a lot.
http://sheldonbrown.com/articles.html
 

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There won't be any problem using a modern 9s crankset with your 7s cassette. As Hilltop said you'll have to shorten the chain and reposition or replace the front derailluer.

There may also be chainline problems if using the new crankset wth an old bottom bracket.
 
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