Division with place value
- [Voiceover] Let's say you want to figure out what 5,600 divided by 8 is. Now, you might be tempted to do some type of long division 8 into 5,600, and you could do it this way, and you using paper. What I want to show you is that you could maybe do this in your head, or maybe even just use less paper to do it. The key realization here is like look if you got these two zeros here, this is really the same thing as 56 times 100 divided 8. 56 times 100 is 5,600. You got the two zeros here, you got the two zeros here. Let me make it very clear. Two zeros here, you got the two zeros here. In fact, sometimes people will call this number 56 hundred, 56 hundreds. So, 5,600 is the same thing as 56 times 100. When you write it this way, then you might say hey instead of doing 56 times 100 divided by 8, I can switch the order. This is going to be the same thing. This is going to be the same thing as 56 divided by 8 times 100. Why'd I do this? Well, it's pretty straight forward if you remember your multiplication tables what 56 divided by 8 is. 8 times 7 is 56. This right over here is going to be 7. Then, you're just left with figuring out what 7 times 100 is. 7 times 100. Well, that's going to be 700s. 700s is just 700. 700 and you're done. Let's do more of these, where we might be tempted to do some type of long division, but if we really think about ways to break up the numbers, we might be able to do it with less paper or possibly even in our heads. Let's say that you had the number 800. Let me do this in a different color. Let's say you had the number 800 and 46. 846 and you want to divide that by 2. Well, the realization here, or what you might think about is let's break this number up. Let's break up this 846. 846 is the same thing ... this is going to be ... actually, let me do it this way. 846 is the same thing as this is the same thing as 800 plus 40 plus 6 and so 846 is the same things as 800 plus 40 plus 6. We can just divide that by 2. We can just divide that by 2. Divided by 2. Notice, I didn't do anything too fancy here. This is just the same thing as this over here. I just broke it up. You have 800s, four 10s which is 40, and 6, and you can divide that by 2. Well, how does that help us? Well, now we can divide each of these separately by 2. one way to think about it is we can distribute the division by 2. Where, you might be familiar using the distributive property in multiplication, but you could also do it with division. This thing right over here is going to be the same thing. This is going to be equal to 800 divided by 2. 800 divided by 2 plus 40 divided by 2. plus 40 divided by 2. I'm going to add parenthesis in a second to make it a little bit clearer. Plus 6 divided by 2. Plus 6 divided by 2. Once again, you have 800 divided by 2. That's that right over there. Plus 40 divided by 2. 40 divided by 2. Plus 6 divided by 2. Plus 6 divided by 2. We distributed the division by 2. Well, 800 divided by 2, you should do in your head. This is 800, divided that by 2, and you're going to get 4 hundreds. 4 tens divided by 2 is going to be 2 tens or 20. 800s divided by 2 is 4 hundreds. 4 tens divided by 2 is 2 tens. Then, 6 divided by 2 is 3. You are left with 400 plus 20 plus 3, which of course is equal to 400 and 23. I used a lot of my screen here to work this out for you. You really digest what's going on here, but once you get good at it, you could say okay look 8 divided by 2, 800s divided by 2 is 400s. Actually I could do it right over here. 8 hundreds divided by 2 is 400s. 4 tens divided by 2 is 2 tens. 6 ones divided by 2 is 3 ones. You could say hey look if I just divided each of these numbers by 2 I get 423. This is what you are really doing, you are separating it out by place value. You are dividing each of those places the hundreds, the tens, and the ones by 2. Then, you got 423. By the way, that's exactly what you would do if you actually did it through long division. You are actually dividing 2 into each of the places. Let's do one more just to really make sure that we are fully enjoying this. Let's say that I have 963 and I want to divide that by 9. Well, over here, you might make the realization well I can see parts of this that I know how to divide by 9. I could say this is the same thing as 900, and I'm breaking out the 900, because I know how to divide 900 divided by 9. That's 900. I know that 63 is a multiple of 9. Why don't I break out 63 separately. I don't even have to break out the tens and the ones separately. I could say this is the same thing as 900 plus 63 and all of that divided by 9. Well, this is going to be the same thing as 900 divided by 9. Let me do that in the brown color. 900 divided by 9 plus 63 divided by 9. I just distributed the division by 9. Let me put some parenthesis around this. What is this going to be equal to? Well, 900 divided by 9 is 100. This is going to be 100, and 63 divided by 9 is 7. This is going to be 100 plus 7, or 100 and 7. Once again, I wrote it all out like this. Once you get some practice, you'll say hey look 9 goes into 900 a hundred times. 9 goes into 63 seven times. So, 9 goes into 963 one hundred and 7 times. Hopefully you found that fun. This is useful stuff. One of the most important things you're going to have to find is that all the time you're going to find these numbers while you're doing, you know, your finances, or you're trying to calculate the check at a restaurant. You're going to find it really valuable to be able to do this type of division. With some practice, even without paper.