I have to format my pc, so I have downloaded a BTC wallet also on my tablet. Is there a way to send BTC without commission fees?
It might be possible to export the private keys from your PC wallet and import them into your tablet's wallet. The details and practicality of this would depend on which wallet software you are using at each end.
It would certainly be easier just to create an address on the tablet and send all the coins there. You may have to pay a transaction fee (most people don't call it "commission") but it's not likely to be more than a few pennies.
each account is represented by an address. which address has what amount of funds, is stored on the blockchain (the bitcoin network) for everyone to see. it's not only stored locally by your client. every client on the bitcoin network has a copy of the complete blockchain.
a transaction means sending funds from one address to another. usually after a few clients confirm the transaction, it is safe to assume that it has been processed. transactions are the only time there could be a fee.
but to be able to do a transaction (send funds). you need the private key (this is like a password), of the address sending the funds. so if you have an address and it's secret key, you own that address because you can control it.
if you delete everything from your pc (ex: by formatting), you will lose your funds because the address and secret key are stored there (it's like throwing away your login information).
you can keep using the same address(es) if you transfer this information (each address & it's private key) to the new client (on your tablet) and format your pc, then you're done. this does not involve any transaction. [this may be more complicated though as Nate suggests]
before you do anything, make a backup of (each address & it's key). some clients use more than 1 address so there may be more to backup (i suggest also printing each address and it's private key).