Most new chains arn't cir-clip (bicycle Master link style), and if ur purchasing new sprockets mide aswell do the chain also, other then that also need a chain breaker to remove links off a new chain, most bike shop mechanics will install a chain on the side for 10$ if u take ur bike down they're in the back of a truck.
Usually they are changed in pairs to kep the wear from destroying the other sprocket due primarily to the chain stretching over a period of time...if you are looking for more power just change the front one it's easy...and only go one smaller in tooth. If you are going for more top-end or better gas mileage then you would have to seee is ther is enough room to go one larger on the front. You can make the chain adjustment without making changes to the chain if you only change out the front sprocket. If you really need to replace the rear then change out the front as well, and get a new chain...keeping the old ones as well. 3 teeth more (larger rear sprocket) will increase the power, and slightly lower your fuel economy...depending on how you drive and where you are driving///riding. as well as changing the front down one tooth, smaller, will have the same effect. Both at the same time and you have a rocket launcher...and have to be very careful when shifting especially in the upper RPM's.
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