How to Do Long Division | A Step-by-Step Review

Welcome to Math with Mr. J. In this video, I'm going to go through a review of long division. And we have three sections here that we're going to go through. We'll start with dividing by one-digit numbers. Then we'll move on to dividing by two-digit numbers. And after that, we will take a look at division problems with a zero in the quotient. So, a zero in the answer. Once we are done with those three sections, I'll give you some practice problems that you can try on your own. Let's jump into number one where we have 632 / 4. Now, the first thing that we need to do is set this problem up. 632 is the number being divided. That's what we call the dividend. It goes under the division bar. So 632 is the number being divided and we are dividing 632 by 4. Four is what we call the divisor. It's the number we are dividing by. Four goes on the outside of the division bar. And now we are set up and ready to go through our steps. Divide, multiply, subtract, bring down, repeat. So we start with divide. We need to do six / 4. So how many whole groups of four in six? How many fours in six? Well, one. So we put 1 above the six here. And now we multiply. So we do 1 * 4. 1* 4 gives us 4. Now we subtract. 6 - 4 gives us 2. After we subtract, we bring down the next digit. So we bring down this three. After we bring down, we repeat. So we start our process over again and we go back to divide. So now we have 23 / 4. How many groups of four in 23? How many fours in 23? Well, five. That gets us to 20. So, we put our five up here above the three. And now that we divided, we multiply. We have 5 * 4. That gives us 20. After we multiply, we subtract. So, we have 23 - 20. That gives us three. After we subtract, we bring down. So we bring down that next digit two. And now we repeat. So we go back to divide. We have 32 now. So 32 / 4. How many groups of four in 32? How many fours in 32? Well, 8. That gets us to 32 exactly. So let's put our eight above the two there. And now after we divide we multiply. So we have 8 * 4 which is 32. After we multiply we subtract and we have 32 - 32 which gives us zero. So our answer is 158. We know we are done because we went all the way over to the ones place in our dividend, the number under the division bar. And we don't have anything else to bring down. And since we have a zero down here, we do not have a remainder. We don't have anything left over after dividing. So this worked out perfectly. 632 / 4 = 158. Let's move on to number two where we have 5,178 / 7. Let's set this up. 5,178 is our dividend. It's the number being divided. So, it goes under the division bar and we are dividing by seven. So, seven goes on the outside of the division bar. That's our divisor. And now that we're set up, we go through our steps. We start with divide. So, we have 5 / 7. So how many whole groups of seven in five? Well, we can't do that. So what we need to do, we need to look at this five and this one and think of this as 51. So we do 51 / 7. How many whole groups of 7 in 51? How many sevens in 51? Well, seven. That gets us to 49. Now here, be careful. The seven needs to go above 51. So above the one, not the five. Since we used that one and thought of this as 51. Now we multiply. 7 * 7 is 49. After we multiply, we subtract. 51 - 49 gives us 2. After we subtract, we bring down. So we bring down our next digit which is seven. And after bringing that seven down we repeat. So we go back to divide. We have 27 / 7. How many groups of seven in 27? Well three. That gets us to 21. So we write our three here above the seven. And then we multiply. 3 * 7 is 21. After we multiply, we subtract. So we have 27 minus 21. That gives us six. After we subtract, we bring down. So our next digit is an 8. So bring that eight down. And now we have 68. And we repeat. So we go back to divide. We have 68 / 7. How many groups of seven in 68? Well, 9. That gets us to 63. So we write our nine up top above the eight. Then we multiply. So we have 9 * 7, which is 63. After we multiply, we subtract. 68 - 63 gives us 5. Now we went all the way over to the furthest place to the right, the ones place. And we don't have anything else to bring down here. So that five is our remainder. It's what's left after dividing. So our answer here is 739 remainder 5. So 5,178 / 7 gives us 739 remainder 5. So there's how to divide by a one-digit number. Let's move on to dividing by a two-digit number. Here's our section on dividing by two-digit numbers. Let's jump into number one where we have 723 / 30. 723 is our dividend. It goes under the division bar. It's the number we are dividing. And then 30 is our divisor. It goes on the outside. It's the number we are dividing by. And now we are set up. So we go through the division process and we're going to go through the same exact steps we use when we divide by a onedigit number. So nothing is changing here. We divide, multiply, subtract, bring down, repeat. So let's start with divide. Here we have 7 / 30. How many whole groups of 30 in seven? How many 30s in seven? Well, we can't do that. So we need to use the two and think of this as 72. So we have 72 / 30. How many whole groups of 30 in 72? How many 30s in 72? Well, two groups of 30 gets us to 60. 2 * 30 is 60. And then three groups of 30. 3 * 30 gets us to 90. So three is going to be too much. It's going to be two. So, we put our two above the 72, above the two there, not above the seven. Since we did 72 / 30, now we multiply. So, we do 2 * 30, that's 60. Subtract 72 - 60 gives us 12. After we subtract, we bring down. So, we bring down that next digit there, the three. And we have 123. And now we repeat. So we go back to divide. We have 123 divided by 30. So how many groups of 30 in 123? How many 30s in 123? Well, thinking through this, three groups of 30 gets us to 90. 3 * 30 is 90. Four groups of 30 gets us to 120. 4 * 30 is 120. So, it's going to be four here. And then, just to check, five groups of 30. 5 * 30 is 150. So, that's too much. It's going to be 4, which again gets us to 120. So, we put the 4 up here above the three. Then, we multiply. 4 * 30 gives us 120. we subtract 123 minus 120 gives us 3. So we went all the way over to the ones place in our dividend that number under the division bar. So we don't have anything else to bring down. So we are done here. Our answer is 24 and then this three down here is our remainder. So our final answer here 24 remainder 3. Let's move on to number two where we have 4,682 / 64. We'll start by setting this up. So we have 46 82 / 64. Now we need to start with divide. So we have 4 / 64 which we don't have any whole groups of 64 and 4. So we need to use the six and do 46 / 64. And we don't have any whole groups of 64 in 46 either. So we need to use the 8 and do 468 / 64. So we need to figure out how many whole groups of 64 how many 64s are in 468. And off the top of my head, I don't know. So, we're going to need to estimate and check. Now, we can use what we know in order to inform this estimation in order to give us a starting point. Now, 64 * 10 we know is 640. Now, to go off of that, 468 is less than 640. So, let's scale back a little from 10 and we'll try 8. We'll do 64 * 8 and see how close we get to 468. And then we will go from there. So, 64 * 8. 8 * 4 is 32 and then 8 * 6 is 48 + 3 is 51. So, we get 512. So, eight groups of 64 is too much. Let's scale that back and try seven. So, we'll do 64 * 7. 7 * 4 is 28. 7 * 6 is 42 + 2 is 44. So, we get 448. It's going to be seven here. So we have seven whole groups of 64 in 468. So we put our seven above the 8. And we put it above the 8 since we did 468 / 64. Now we multiply. 7 * 64 is 48. Now we subtract. 468 - 448 gives us well 8 - 8 is 0. 6 - 4 is 2 and then 4 - 4 is zero. So we end up with 20. And after we subtract we bring down. So we bring down that next digit which is a two. And now we have 202. And we repeat. So we go back to divide. We have 202 / 64. So, how many groups of 64 in 202? Well, we know that 64 * 7 is 448. 202 is less than that. So, we need something less than 7 here. And we can also think, well, 64 is close to 60. 60 * 1 is 60. 60 * 2 is 120. 60 * 3 is 180. And then 60 * 4 is 240. So let's try 64 * 3 and see how close we get. So 64 * 3. 3 * 4 is 12 and then 3 * 6 is 18 + 1 is 19. So we get 192 which is pretty close to 202. And that's going to be what we need here. 64 * 4 is going to be over 202. So, we're as close as we can get here. So, we put our three up here above the two. Then, we multiply. 3 * 64 is 192. And now we subtract. So, we have 202us 192. Now, I do want to mention if we run into a subtraction problem that we can't solve mentally, we can always work through it within the problem. So, just to show what that looks like, let's do that here. We have 2 - 2, which is 0. Then, we have 0 - 9, which we need to borrow. So, we have 10 - 9, which gives us 1. And then 1 - 1 is 0. So 202 minus 192 is 10. Now we went all the way over to the ones place in our dividend. So we don't have anything else to bring down. We are done. So our answer here is 73. And then this 10 down here is our remainder. So our final answer 73 remainder 10. So, there's how to divide by a two-digit number. Now, let's move on to division problems with a zero in the quotient. So, here's our section on division problems with a zero in the quotient, a zero in the answer. This is a type of problem where some common mistakes are made. So, we're going to go through a couple of examples here to show us what to look out for. Let's jump into number one where we have 927 / 3. The first thing that we need to do is set this problem up. 927 is our dividend and then three is the divisor. And now we are ready to go through our division steps starting with divide. So we have 9 / 3. How many whole groups of three in nine? How many threes in nine? Well, three. And that hits 9 exactly. So we write our three up top here. And now we multiply. 3 * 3 is 9. After we multiply, we subtract. 9 - 9 is zero. After we subtract, we bring down. So we bring down that next digit, which is a two. And now after we bring down that next digit, we repeat. So we go back to divide. and we have two divided by three. So, how many whole groups of three in two? How many threes in two? Well, none. We can't do that. Now, this is a common place where people get stuck or make a mistake since we don't have any whole groups of three in two. We don't have any threes in two. So, what we do, we put a zero up top above the two. So, we're just going through our normal division steps. We just happen to have a zero in our answer. And now we multiply. 0 * 3 is zero. Subtract 2 - 0 is 2. Bring down. So, bring down the 7. And now we have 27. And we repeat. So, we go back to divide. And we have 27 / 3. So, how many groups of three in 27? Well, nine. And that hits 27 exactly. So, we write our 9 up here and then multiply. 9 * 3 is 27. Subtract 27 - 27 is 0. And we are done. Our answer is 309. And we know we are done because we went all the way over to the ones place within our dividend. So that number under the division bar and we don't have anything else to bring down. And then this zero at the bottom tells us we do not have a remainder here. So this worked out perfectly. Our final answer 39. Let's move on to number two where we have 1,285 / 8. We'll start by setting this up. So 1,285 divided by 8. Let's start with divide. We have 1 / 8. How many whole groups of eight in one? How many eights in one? Well, we can't do that. So we are going to use that two and think of this as 12. So we have 12 / 8. How many groups of eight in 12? Well, one. So, we need to put the one above the two. And that's very important. It needs to go above the two, not the one since we used that 2 and thought of this as 12. Now, we multiply. 1 * 8 is 8. Subtract 12 - 8 gives us 4. Then, we bring down and we have 48. Now, we repeat. So, we go back to divide. We have 48 / 8. How many groups of eight in 48? Well, six. That gets us to 48 exactly. So, we write our 6 and then multiply. 6 * 8 is 48. Subtract. 48 - 48 is 0. After we subtract, we bring down this five. And now we repeat. So we go back to divide. We have five / 8. So how many whole groups of eight in five? How many eights in five? Well, none. We don't have any whole groups of eight in five. We need a zero right here. Don't leave this as 16. 16 is a lot different than 160. We need that zero in the ones place. Now we multiply. 0 * 8 is 0. subtract 5 - 0 is 5. Now, we went all the way over to the ones place within our dividend, the number under the division bar, and we don't have anything else to bring down. So, that five is our remainder. So, our answer here is 160 remainder five. So, now that we've gone through some examples together, let's move on to some practice problems that you can try on your own. So, have paper and a pencil ready. So, here are your practice problems. I'll give you 8 minutes and then we will go over the answers. Feel free to press pause if you need more time or jump ahead to the answers whenever you are ready. And just a quick hint here, numbers one and three do not have remainders. Numbers two and four do have remainders. Go ahead and start. Hey, hey, hey. Hey honey. Everybody. Hey. Hey oh. Okay, so that was eight minutes. Let's go over the answers. So here are our answers for number one. 768 / 6 equ= 128. For number two, 1,851 / 9 gives us 205, remainder 6. Moving on to number three, 910 / 14 equals 65. And then lastly, moving on to number four, 5,517 / 37 gives us 149 remainder 4. If you need more time to check your work, feel free to pause the video now. So, there you have it. There's how to divide. There's how to go through the long division process. I hope that helped. Thanks so much for watching. Until next time, peace.