Multi-digit division (remainders)
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.