Here's a physical example for those who have trouble intuitively grasping why the product of two negative numbers is positive. Let's say we have a water tank.

Here's a physical example for those who have trouble intuitively grasping why the product of two negative numbers is positive. Let's say we have a water tank. We can fill it by opening a faucet on the top, or drain it by unplugging the bottom. For simplicity let's say that if we fill it we add 1 liter per minute, and if we drain it we lose 1 liter per minute (or equivalently, add -1 liter per minute). Q1: if we open the top faucet for 2 minutes, how much water do we add? 1 liter/min times 2 minutes: 2 liters. Q2: if we open the bottom faucet for 2 minutes, how much water do we add? -1 liter/minute times 2 minutes, -2 liters. What about the volume two minutes ago? That would be -2 minutes, right? So suppose the drain was open, how much more water did we have -2 minutes from now, or 2 minutes ago? -2 times -1: 2 liters more.