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Find the rod attached to a ball that floats on the top of the water and controls the intake of water from the pipes into the tank. This is the floating arm. If you lift up on the arm and the water stops, then your problem is that the water in the tank isn't coming up high enough to turn off and the pipes are getting the message that more water needs to come in, so the toilet runs constantly, or often. A running toilet can cost a fortune in wasted water. While it may seem like a minor inconvenience, a running toilet is a serious and usually easily fixable problem. Sometimes, the floating arm will be bent so the ball will rub or catch on the side of the tank or the tank ball arm. Flush the toilet and see if the arm catches on anything. If it does, just bend the arm gently so it floats freely and can rise to the level it needs to. Sometimes, water will get trapped in the ball, weighing it down and keeping the water from rising as it should. If this happens, dump the water out and replace the ball by screwing it back on. If the ball is cracked or otherwise damaged and allows water in freely, replace it with a new one. If lifting up on the arm doesn't halt the running water and adjusting the floating arm doesn't seem to help, the problem is probably with the flapper assembly, which creates the seal at the bottom of the tank leading to the bowl and connects to the toilet handle by a rod.  Shut off the water and flush the toilet to empty the tank of water. Examine the flapper for signs of wear or corrosion. If you find build-up from the water or other gunk, scour it off with a kitchen pad or a pocketknife and see if you can get the flapper to create a good seal. Also check the opening for the same corrosion issues and clean it. If water still gets through the opening, examine the wire rod that connects to the toilet handle and make sure it's aligned and allowing the flapper to fall freely and plug the hole. Like the floating rod, you should be able to bend it back into place relatively gently, or replace it with a new one. Some are connected with a chain that can become tangled or loose and may need replaced as well. If none of this seems to stop the toilet from running, you'll probably need to replace the ballcock assembly.
Remove the top of the tank and lift up the floating arm. Check the floating arm for misalignment. If it doesn't seem to be caught on anything, unscrew the ball from the arm by twisting it counter-clockwise. Check the flapper seal.