Multiplying 4-digit by 1-digit (regrouping)

Let's multiply 9 times 8,085. That should be a pretty fun little calculation to do. So like always, let's just rewrite this. So I'm going to write the 8,085. I'm going to write the 9 right below it and write our little multiplication symbol. And now, we're ready to compute. So first we can tackle 9 times 5. Well, we know that 9 times 5 is 45. We can write the 5 in the ones place and carry the 5 to the tens place. So 9 times 5 is 45. Now we're ready to move on to 9 times 8. And we're going to calculate 9 times 8 and then add the 4 that we just carried. So 9 times 8 is 72, plus the 4 is 76. So we'll write the 6 right here the tens place and carry the 7. Now we are ready to calculate, and I'm looking for a suitable color. 9 times 0 100's plus-- and this is a 7 in the hundreds place, so that's actually 700. Or if we're just kind of going with the computation, 9 times 0 plus 7. Well, 9 times 0 is 0, plus 7 is 7. And then, finally, we have-- and once again, I'm looking for a suitable color-- 9 times 8. This is the last thing we have to compute. We already know that 9 times 8 is 72. And we just write the 72 right down here, and we're done. 8,085 times 9 is 72,765. Let's do one more example just to make sure that this is really clear in your brain, at least the process for doing this. And I also want you to think about why this works. So let's try 7 times 5,396. And I encourage you to pause it and try it on your own as well. I'm going to rewrite it-- 5,396 times 7. First, we'll think about what 7 times 6 is. We know that's 42. We'll put the 2 in the ones place. 4 we will carry. Then we need to concern ourselves with 7 times 9. But then, we have to calculate that and then add the 4. 7 times 9 is 63, plus 4 is 67. So we put the 7 down here and carry the 6. Then we have to worry about 7 times 3 plus this 6 that we had just finished carrying. 7 times 3 is 21, plus 6 is 27. So we'll write the 7 here in the hundreds place and carry the 2. And then, finally, we have 7 times 5, which is 35. But we have to add the 2. 35 plus 2 is 37. So 5,396 times 7 is 37,772.