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Performing Long Division with Large Numbers: Steps and Examples

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  • 0:02 Long Division
  • 1:02 The Procedure
  • 1:34 Example 1
  • 4:48 Example 2
  • 7:54 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will be able to divide larger numbers. You'll learn an easy to follow procedure that you can use to divide any two numbers.

Long Division

Division is the equal sharing of something into groups. So, for smaller numbers, we can apply this definition to figure out our answers. For example, if we wanted to divide 8 by 4, we could picture having 8 candy bars and then sharing them equally among a group of 4 friends. We could start by handing each friend one candy. We would keep this going as long as we can hand out an equal number of candy bars to each person.

After doing this, we see that 8 divided by 4 is 2 because each person would end up with 2 candy bars. But, what if we wanted to divide larger numbers such as 96 by 3? What would we do then? It wouldn't be particularly useful for us to picture 96 candy bars being distributed to 3 people. That would take quite a bit of time and a lot of candy bars! What we can do is follow a procedure called long division, a special procedure to divide larger numbers.

The Procedure

How does this procedure work? Let me give you a quick overview before we go into some examples. To put it simply, what we do is take our number that we want to divide and break it up into little pieces, and we divide these little pieces by our divisor, the number we are dividing by. This makes our job of dividing larger numbers easier. Because we can easily divide smaller numbers, this process allows us to break down our larger division into manageable pieces. So, now let's see some examples of how it is done.

Example 1

Why don't we try to divide 96 by 3 right now? To set up our problem for long division, we will first write our divisor, the number we are dividing by. Yes, our numbers are switched for long division - our 3 comes first. Then we have our long division symbol covering our dividend, the number that we want to divide. We end up writing our answer on top of our long division symbol.

The long division symbol
long division

So, now that we have our problem all set up, what we do now is to try to divide the first digit of our dividend by our divisor. The first digit we have is 9. So, we will try to divide 9 by 3. We want to see how many 3's we can take out of our 9. These are small numbers and we can easily do this. 9 divided by 3 is 3. So, we write this part of our answer on top of our 9.

Beginning long division
long division

Now, what we want to do is we multiply the number we just wrote down on top by our divisor, our 3. What is 3 * 3? It is 9. We write this 9 underneath our 9. We draw a line underneath to show that we are going to be performing an operation here. What we do now is we subtract this 9 from the number directly on top of it. So, we write a minus sign in front of our second 9. 9 - 9 is 0. Yes, we are ignoring all the digits to our right; we are only concerned about the digits we are currently on and the digits to our left. We write this 0 underneath the line we just drew.

Since we have more digits to work with in our dividend, we check to see if we can divide our result here by our divisor. Does 3 go into 0? No, it doesn't. So, that means we need to pull down our next digit in our dividend to work with. Our next digit is 6. So, we pull that down and write it next to our 0. Now we ask ourselves the same question. Does 3 go into 6? Yes, it does! How many times? 3 goes into 6 two times. So, 6 divided by 3 is 2. We write this 2 on the very top next to our 3.

Next, we multiply our 2 by our divisor. We multiply 3 by 2. We get 6; write this number underneath our 6. We draw a line underneath this and put a minus sign out front. We are now repeating the steps we took with our first digit. We subtract: 6 - 6 is 0. Are there more numbers to pull down? No. Is my last line a 0? Yes. That means we are done with dividing. Our answer is 32.

Finishing the problem
long division

Notice how we treat each digit like we did the last digit. Once we are done with one digit, we move ourselves over to the right one place and we repeat what we did before. This is the process of long division. Yes, there is quite a bit of repetition. But it is an easy to follow procedure that works with all numbers. To help us divide our smaller numbers, we can always go back to thinking about sharing candy bars or whatever else you want to think about.

Example 2

Let's look at another number. How about dividing 123 by 12? We set up our problem by writing the 12 first, followed by our long division symbol covering 123. Good. Next, we look at our first digit of our dividend, the 1. Can I divide 1 by 12? No. So, I can write 0 on top of my 1 in the answer part. That means I need to look at the next digit of the dividend, the 2.

So, I'm now looking at 12. Can I divide 12 by 12? Yes, I can. It is 1. So, I write this 1 on my answer line next to the 0. I now multiply this 1 with my divisor, my 12. 1 multiplied by 12 is 12. I write this 12 underneath the 12 I already have. I draw a line underneath and add a minus sign. What is 12 - 12? It's 0.

Okay, so far, so good. Does 12 go into 0? No. So, that means I need to pull down my next digit. So, I pull down my 3. Now the number I am looking at is 3. Can I divide 3 by 12? No, so I write a 0 on my answer line next to my 1. Now, because my last line is not 0 even though I've reached the end of my dividend, I need to pull down another digit. But wait, I have no more digits to pull down. What do I do?

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