To explain better: I both agree and don't agree with @ericweinstein and @terrencehoward. I just think the language is wrong. Multiplication isn't the opposite of division. I try to explain this with a simple thought experiment: When you divide something, you are simply cutting it into parts. If you slice an apple in half and ask someone if they see half an apple or 2 halves, they'll say two halves, because one half hasn't been deleted. Division in the sense that math uses it, isn't division, it's dividing then deleting. So if you have 2 and divide it by 2, you still have 2, but in two parts 1 & 1, then you delete the other part to make just 1. So if you use the same concept, if claiming multiplication is the opposite, you'd do the same, but in reverse. You'd take the deleted part and add it back. So 1x1 would be (1 1) x 1, which is 2. So they are both right but for different reasons. From maths point of view, 1 x 1 is 1, because that's how we use it. But the error is that it's not the opposite of division, which is where the confusion steps in and gives rise to Terrence's train of thought. So really, all it is, is that they are using different language when explaining times vs division. My use of the word duplicate in the previous post probably wasn't accurate - without adding additional information. I'm not sure if anyone else see's it like this. But that's how I see it.