Sal divides numbers like 2400/30 by factoring out 10s, 100s, and 1000s.
- [Instructor] We're going to do in this video is get some practice doing division with numbers that are multiples of 10, 100, 1,000, things like that. So let's say we wanted to compute what 2,400 divided by 30 is. Pause this video, and see if you can calculate it using whatever strategy makes sense to you. Alright, so let's think about this together, and I'm gonna show you how my brain likes to handle this. We'll do this out on my little digital blackboard, but eventually you'll be able to do things like this in your head. So 2,400 or 2,400 divided by 30, that is the same thing as 2,400 over 30. So this is just another way of saying 2,400 divided by 30. Now the reason why I wrote it this way is because you can now write each of these, the numerator and the denominator as the product of some number and either 10 or 100 or 1,000. So 2,400, that's the same thing as 24 times 100, and I knew that. I was like, okay, I've got these two zeros at the end, so you could view this literally as 24 hundreds, and then 30 you can view as, we got one zero here, so it's three tens. The three is in the tens place. So three times 10. Now what's valuable about thinking of it this way is you can separately divide the 24 by the three and then the 100 by the 10, so this is the same thing as, lemme do this this way, as that times that. And so we have 24 divided by three times 100 divided by 10. Now 24 divided by three, you might already know that is going to be eight. Three times eight is 24. So this is going to be equal to eight, and what's 100 divided by 10? Well, 100 divided by 10 is just going to be 10, so our quotient, I guess you could say, is going to be eight times 10, or it's going to be equal to 80, and we're done. And you might notice something interesting here. So if I take my 24 and divide it by my three, I'm gonna get this eight, and then if I take two zeros and if I take away another zero, I'm gonna be left with one zero right over here. So you get 80, but why did that thing with the zeros work? Because you're really just taking 2,400 hundreds divided by three tens. So 100 divided by 10, well, you're gonna lose a zero. That's gonna be equal to 10, which has only one zero. Let's do another example just to hit the point home, and try to do this next example the way we just did it, maybe in your head or maybe on a piece of paper. So let's say we wanted to calculate 3,500, which you could also think of as 3,500, and we wanna divide that by, lemme write the division symbol a little bit nicer than that. We wanna divide that by 700. Pause this video and see if you can compute that. So as we just did, we could view this as 3,500 over 700. 3,500 we can view as 35 times 100 over, this is going to be over. Lemme get the right color here, over seven times 100. Now the one hundreds cancel out, and we're just left with 35 over seven. Now what's 35 divided by seven? Well, that is going to be equal to five, and notice, you could just say 35 divided by seven is five, and if you're saying, "How many zeros do I have left over?" Well, I have two zeros here, but since I'm dividing by something with two zeros, those two zeros are going to be canceled out. I don't want you to just memorize that. The reason why that happens is because those two zeros here represent hundreds, 35 hundreds. These two zeros represent hundreds, so if you divide 100 by hundreds, they're all gonna cancel out. So you had two zeros before, but you're dividing by something with the two zeros, so you don't have any zeros after the five here. Lemme do one more example just to really hit that point home, but I want you to appreciate that it's not just some magical trick. It just makes sense out of things that you might already know. So if someone, and I'm gonna give a crazy one, let's say we had 42 million divided by, let's say, 60,000. What is that going to be? Pause the video and see if you can think about it on your own. Well, using the notions that we just talked about, you could say, "Alright, 42 divided by six "is going to be seven." And then if I, let's see, over here I have six zeros, so we're talking about millions, and I'm gonna divide by four zeros right over here, which is 10 thousands. So if you had six zeros, or if you have millions with six zeros and you divide by 10 thousands with four zeros, six minus four is gonna be two, so your answer's gonna have two zeros in it. So this is going to be equal to 700. Now once again, not a magical trick, the way that we got this is that this is equal to 42 times a million. We got our six zeros right over there divided by six 10 thousands, six times 10,000. So our 42 divided by six, that's where we get the seven from, and now one way to think about it, if we divide the numerator and the denominator by 10, we lose a zero. Then we do it again. We lose zeros. We do it again. We lose zeros. We do it again. We lose zeros, and so this thing just all becomes one, or another way to think about it, if we divide the numerator and the denominator by 10,000, this becomes one. This thing loses four zeros, and you're left with, 42 divided by six is seven hundreds, because we have a one now in the denominator, 100 divided by one, so 700.