7 times a day for a 9 week old pup is not too bad. 9 week old pups tend to urinate a lot. Usually they urinate after they eat and drink, after they wake up, before they go to sleep, after playing even if it was just for 5 minutes. So urinating that much is not that unusual. They really don't have control over their bladder much either at this age. He may have never been an inside dog and many pups raised outside tend to eliminate where they are whenever they feel the urge.
Now it is possible he has a urinary tract infection causing excessive urination. In that case I would expect him to drink more as well as urinate more. A dog needs a cup of water for each 8 pounds of body weight each day and pups need a little more, so if he is drinking more than 1.5 cups of water per 8 pounds of body weight, then I might suspect a urinary tract infection.
Dogs need to be taught how to hold their bladder. Crate training helps teach them as if they don't learn to hold it, then end up laying in wet urine which they don't like. It takes them until they are older to control the bladder for longer and longer periods of time and most aren't totally house trained until they are 5-6 months of age. Let me give you a site on crate training.
This is how I house train all my dogs. In addition, put a bell or other noise maker on the door low enough for the dog to reach. Each time you take the dog out, ring the bell. The dog will associate ringing the bell with going out and one day ring the bell to signal to you that he needs to go out.
If he is drinking more than normal and you really think he is urinating excessively, go ahead and have your vet take a look at him. He is likely going to need either deworming or a vaccination pretty soon if he doesn't already need one. It is always a good idea to have your vet take a look when you get a puppy anyway. Often contracts received with a new pup are voided if the pup is not examined by a vet within a certain period of time.
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