Multiplying 2-digit by 2-digit: 23x44

Compute 23 times 44. And maybe the hardest part of this problem, or maybe the first hard part, is to recognize that that dot even means multiplication. This could have also been written as 23 times 44, or they could have written it as 23 in parentheses times 44, so you just put the two parentheses next to each other. That also implies multiplication. So now that we know we're multiplying, let's actually do the problem. So we're going to multiply 23-- I'll write it bigger. We're going to multiply 23 by 44. I'll write the traditional multiplication sign there, just so that we know we're multiplying. When you write it vertically like this, you very seldom put a dot there. So let's do some multiplication. Let's start off multiplying this 4 in the ones place times 23. So you have 3 times 4 is 12. We can write 2 in the ones place, but then we want to carry the 1, or we want to regroup that 1 in the tens place. So it's 12, so you put the 1 over here. And now you have 4 times 2 is 8 plus 1 is 9. So you can think about it as 4, this 4 right here, times 23 is 92. That's what we just solved for. Now, we want to figure out what this 4 times 23 is. Now what we do here is, when you just do it mechanically, when you just learn the process, you stick a 0 here. But the whole reason why you're putting a 0 here is because you're now dealing with a 4 in the tens place. If you had another-- I don't know, a 3 or a 4 or whatever digit, and you're dealing with the hundreds place, you'd put more zeroes here, because we're going to find out 4 times 23 is 92. We just figured that out. If we just multiplied this 4 times 23 again, we would get 92 again. But this 4 is actually a 40, so it actually should be 920, and that's why we're putting that 0. Now you're going to see it in a second. So we have-- so let me put this in a different color. So this 4 now we're multiplying. 4 times 3 is 12. Let's put the 2 right here. It should be in the tens place because this is really a 40 times the 3. Just think about it, or you could just think of the process. It's the next space that's free. 4 times 3 is 12. Carry the 1. This blue 1 is from last time. You ignore it now. You don't want to make that mess it up. That's when we multiplied this 4. So now we have 4 times 2 is 8 plus 1 is 9. So what we figured out so far is 4 times 23 is 92, and this green 4 times 23 is 920, and that's because this green 4 actually represents 40. It's in the tens place. So when you multiply 44 times 23, it's going to be 4 times 23, which is 92, plus 40 times 23, which is 920. I just want to make sure we understand what we're doing here. And so we can take their sum now. Let's add them up. 2 plus 0 is 2. 9 plus 2 is 11. Carry the 1. 1 plus 9 is 10. Put a comma here, just so it's easy to read, every third digit. So 23 times 44 is 1,012.