Multi-digit division (remainders)
Let's divide 7,182 by 42. And what's different here is we're now dividing by a two-digit number, not a one-digit number, but the same idea holds. So we say, hey, how many times does 42 go into 7? Well, it doesn't really go into 7 at all, so let's add one more place value. How many times does 42 go into 71? Well, it goes into 71 one time. Just a reminder, whoever's doing the process where you say, hey, 42 goes into 71 one time. But what we're really saying, 42 goes into 7,100 100 times because we're putting this one in the hundreds place. But let's put that on the side for a little bit and focus on the process. So 1 times 42 is 42, and now we subtract. Now, you might be able to do 71 minus 42 in your head, knowing, hey, 72 minus 42 would be 30. So 71 minus 42 would be 29, but we could also do it by regrouping. To regroup, you want to subtract a 2 from a 1. You can't really do that in any traditional way. So let's take a 10 from the 70, so that it becomes a 60, and give that 10 to the ones place, and then that becomes an 11. And so 11 minus 2 is 9, and 6 minus 4 is 2. So you get 29. And we can bring down the next place value. Bring down an 8. And now, this is where the art happens when we're dividing by a multi-digit number right over here. We have to estimate how many times does 42 go into 298. And sometimes it might involve a little bit of trial and error. So you really just kind of have to eyeball it. If you make a mistake, try again. The way you know you make a mistake is, if say it goes into it 9 times, and you do 9 times 42 and you get a number larger than 298, then you overestimated. If you say it goes into it three times, you do 3 times 42, you get some number here. When you subtract, you get something larger than 42, then you also made a mistake, and you have to adjust upwards. Well, let's see if we can eyeball it. So this is roughly 40. This is roughly 300. 40 goes into 300 the same times as 4 goes into the 30, so it's going to be roughly 7. Let's see if that's right. 7 times 2 is 14. 7 times 1 is 28, plus 1 is 29. So I got pretty close. My remainder here-- notice 294 is less than 298. So I'm cool there. And my remainder is less than 42, so I'm cool as well. So now let's add another place value. Let's bring this 2 down. And here we're just asking ourselves, how many times does 42 go into 42? Well, 42 goes into 42 exactly one time. 1 times 42 is 42, and we have no remainder. So this one luckily divided exactly. 42 goes into 7,182 exactly 171 times.