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## Arithmetic

### Course: Arithmetic > Unit 8

Lesson 3: Division with place value# Division using place value

CCSS.Math:

Sal uses an understanding of place value to divide 5600÷8 and 846÷2.

## Want to join the conversation?

- How Sal could divide before multiply. According to PEMDAS multiplying come first?(30 votes)
- PEMDAS, Parenthases, exponents, multiplication, division, addition, subtraction.

This order is correct, but you sometimes also see BEDMAS, brackets, exponents... and so on. This is because +- can be done in either order, the same is also true for */(4 votes)

- This is off topic but can you divide by 0?(18 votes)
- This is a very good question, and the answer is important to understand.

Division by 0 is not a well-defined operation. There are two situations to consider when dividing by 0. If you take calculus later on, you will need to be able to tell the difference between these two situations.

Situation 1: If we divide 0 by 0, then this is the same as asking what number times 0 is 0. Any number times 0 is 0, so 0/0 can have any value. So 0/0 is called**indeterminate**.

Situation 2: Let x be any nonzero number (a number other than 0). If we divide x by 0, this is the same as asking what number times 0 is x. No number times 0 can be the nonzero number x, so x/0 cannot have a value. So x/0 is called**undefined**. Also x/0 can be thought of as positively or negatively infinite, because if we divide the nonzero number x by a number that is very near 0, the answer would be very far from 0.

(Note well: dividing a number by 0 is generally not the same as dividing 0 by a number. Zero divided by any nonzero number is just 0.)(21 votes)

- me doing math...😶😐😕😑 🤕(brain damage) Vs. me not doing math....🙂😀😄😁😁😁😁😁😁😁😁😁😁😁🐕🐕🐕🐕🐕🐕🐕🐕(12 votes)
- so if its missing numbers in divison ? divided by 2=8 we can do 8 times 2 that is 16 and 16 is the missing number can it be true.(9 votes)
- why was divisoin made?(7 votes)
- to split anything equally so everyone's happy :)(2 votes)

- I do not understand this(6 votes)
- what don't you understand about this video?(3 votes)

- This might be off topic, but when do we learn algebra?(5 votes)
- I have seen variables and algebraic expressions introduced as early as 6th grade.(4 votes)

- what if you still don't get the video and the problem it is asking and there is no one there to help you and you cant go look for someone to help you?(7 votes)
- do you guys have fraction refreshers and algebra(7 votes)
- Talks about Long Division before even bringing up what it is? Why not introduce it first?(5 votes)
- You won't understand how to do it if you tried to do it first, the Estimation, Area Models and these Division place value questions are there to help prepare your brain and create the right connections it needs to understand by breaking up the numbers, every Concept you do Addition, Subtraction, Multiplication, Division... always require you to see it quite differently so it's worth going through this so you can understand what to do when you get to doing it using Carrying/Regrouping, which is when you'll see it all coming together nicely :)

Each Unit always starts off with this Estimation, Area Model stuff or whatever other stuff it has to get you to break up the numbers first and also encourages you to check your work, THEN the other bit is to start learning to do it as Carrying/Regrouping, with Division however because there's also Remainders involved you've got a bit more preparation to do but it's worth it in the end.(4 votes)

## Video transcript

- [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.