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### Course: Arithmetic>Unit 14

Lesson 4: Multi-digit division

# Dividing by 2-digits: 9815÷65

In this math lesson, we learn the process of dividing large numbers, specifically 9,815 divided by 65. The technique involves estimation, multiplication, and subtraction to find the quotient. By following these steps, we discover that the result is 151. Created by Sal Khan.

## Want to join the conversation?

• At , can't you just round 331 to 340 since you rounded 65 up to 70?
(66 votes)
• You technically could to try to get the approximate answer, but you'd want to round down to 330 since it's closer. However, this strategy will not get you the correct answer, just an approximation/estimate, that will help you find and check your answer.
(52 votes)
• you said 2-2 is 1 it is 0
(14 votes)
• go easy on him, he made like almost all the math ka videos without going mad.
(32 votes)
• Is there any easier way to work division? or is this the only way?
(20 votes)
• Actually, there are several ways to do division, I usually use multiplication to help me.
(15 votes)
• what would happend if your mom had two bananas then drop 7 how many do she have?
(6 votes)
• This is not a practical example that you provided, but the mathematical answer would be -5 bananas.
(15 votes)
• Ha i still did not understand
(8 votes)
• that is not good i fill so bad for u right ow that is so sad for u not to get it
(3 votes)
• i don't understand how he is so confident that he is right. And how IS he always right. its a mystery...
(4 votes)
• Everyone makes mistakes. Even Sal Khan makes mistakes... There are videos that have correction boxes posted on them. As you get more practice, you make less mistakes. So, just keep practicing and learning.
(8 votes)
• My process 9815/65 = z
changed to 9000/60 first number above division sign 1 , 9000 - 6000 = 3000
next number 5, 3000 - 3000 = 0
so you know the number it's start with 15
now the art
60 x 150 = 9750
60 x 151 = 9815
9815/65 = 151
Simple Quick and Effective
Wish I could show it the way it looks on my paper much cleaner looking than the above.
(7 votes)
• What I want to know is how you get the numbers at the top of the divisor? When you carry, where does the numbers that you carry come from?
(4 votes)
• How can it be an art if there is the correct answer is set in stone, and there is ABSOLUTELY NO CREATIVITY POSSIBLE in math?
(0 votes)
• There is creativity in math, though your teachers might not yet have shown you this.

One type of creativity is finding multiple ways of solving problems, which by the way is an excellent way of checking answers. Example: if we want to find 600 divided by 25, we could do it the usual long division method, OR we could recognize that because 25 x 4 = 100, 600 divided by 25 is just 6 x 4 = 24 (a good math trick!).

Another type of creativity, at high levels of math, is to find a clever way of solving more difficult math problems. This is often useful for problems in math competitions.

Still another type of creativity, at the highest levels of math, is discovering new theories. For example, the British mathematician John Conway discovered a deep connection between mathematics and games (combinatorial game theory) and invented a number system called the surreal numbers! He invented a game called Red-Blue Hackenbush, which is a good model for the surreal numbers!

Still another type of creativity is the connection between math and art. If you look up the Mandelbrot set, then even though the math might be beyond your level of understanding, you can still see and appreciate the beauty of mathematics!

Still another type of creativity is creating math problems, which is the type of work that I do for my job. Creativity is often needed to find different ways of testing a math skill.

Have a blessed, wonderful day!
(17 votes)
• why not add a comma to its place
(3 votes)
• If it's easier for you, then of course you can add a comma when you're doing your math problems. However, it's quicker to do it without a comma and plus you should learn both ways.
(6 votes)

## Video transcript

Let's divide 9,815 by 65, or figure out how many times the 65 go into 9,815. And I encourage you to pause this video and try this on your own. So let me just rewrite this as 9,815 divided by 65. And we write it this way because it's easier to manipulate the numbers, kind of doing the standard process here. And as we'll see, whenever we divide by a number that has more than one digit, there's a little bit of an art to it. And hopefully you'll get an appreciation for that art over the course of this video. So first we could think about well, how many times does 65 go into 9? Well it doesn't go into 9 at all so we can move one digit to the right. How many times does it go into 98 without going over it? Well 65 times 1 is 65 so that doesn't go over it. And 65 times 2, well that would be 130 so that would go over 98. So it only goes one time. We multiply 1 times 65, which is 65. And then we could subtract to see how much we have left over. So 8 minus 5 is 3 and 9 minus 6 is 3. And now we can bring down the next digit, this 1 here. And now this is where the art is going to come into play because we need to figure out how many times does 65 go into 331 without going over it. And you might just try to look at these numbers, try to approximate them a little bit. You might say, well, maybe 65, let me round this thing up. Maybe this is close to 70. And let's see, this is close to 300. So maybe we say, well, 70 would go into 300. So maybe we think about how many times does 70 go into 300? And we say without going over it, it doesn't go exactly into 300. Well you could say, well how many times does 7 go into 30? Well we know 7 goes into 30 four times. 4 times 7 is 28. So maybe try a 4 right over here because then this will be 280, 4 times 70 is 280. You're still going to have a little bit left over, but what you have left over is going to be less than 70. It's going to be 20. So you say, well, if this is roughly 70 and if this is roughly 300, then maybe it's going to be the same thing. So let's try that out. Let's see if it goes four times. So 4 times 5 is 20, carry the 2. 4 times 6 is 24 plus 2 is 26. And now let's see how much we had left over. So when we subtract, we are left with-- I'll do this in a new color-- 1 minus 0 is 1. We have a 3 here and a 6 here so we're going to have to do a little regrouping. Let's take 100 from the hundreds place. It becomes 200. Give those 10 tens, that 100, to the tens place. So now we have 13 tens. 13 minus 6 is 7 and then 2 minus 2 is 1. So did this work out? Well no, our remainder, after we said it went in four times, we actually had 71 left over. 71, this right over here, is larger than 65. You don't want a situation where what you have left over is larger than what you're trying to divide into the number. You could have gone into it one more time because you had so much left over. So this 4 was actually too low. We should have probably approximated this as 60, and 60 goes into 300, if we were to estimate, we'd say, well that might be closer to five times. So this is where the art of this comes into play. So it was very reasonable to do what I just did, but it just turned out to not be the right way to think about it. I could just say, well the 4 wasn't enough. I had too much left over. Let me try 5 now. 5 times 5 is 25, carry the 2. 5 times 6 is 30, plus 2 is 32. There you go. We got much closer to 331 without going over. Now we can subtract. And once again, we could do a little regrouping. Take a 10 from the tens place. This becomes two tens. This becomes an 11. 11 minus 5 is 6, 2 minus 2 is 0, 3 minus 3 is 0. So we only have 6 left over, which is obviously less than 65. So we're all good. And if we put a 6 here, we would have gone over 331. And so that wouldn't have been cool either. But anyway, let's bring down the next digit. Let's bring down the 5. So how many times does 65 go into 65? Well, it goes one time. 1 times 65,-- OK. Ignore this, that's from a previous step-- 1 times 65 is 65. And then you subtract, and we have no remainder. So we see that 65 goes into 9,815 exactly 150-- let me just that in that same blue color, I don't want to do all these arbitrary colors-- 151 times.