Article: Long division is easier to understand if you start with a large number that’s divided evenly. This will show the student the process for working though the problem without any complicating factors.  For example, 63/3=21. The 3 will go into the 6 evenly, then the 3 will go into the 3 evenly. There are no remainders on either step. Most students will begin learning long division in 3rd grade, or around the age of 8 or 9. The divisor is the number that you are dividing by, while the dividend is the number you’re dividing into. Tell your student that they will need to divide each unit in the dividend by the divisor, starting with the largest unit.  For example, you’d divide the 100s unit, then the 10s unit, and finally the 1s unit. Let’s say your problem is 54/3. Your divisor is 3, which goes into 5 just 1 time. However, you are left with a remainder of 2, which your student will need to save for the next step. Similarly, let’s say your problem is 155/4. You can’t divide 4 into 1, so you’d divide it into 15. This would give you 3, with a remainder of 3. Explain that they will need to multiply the number of times that the divisor goes into the first number by the divisor. They will subtract this product from the units in the dividend to find the remainder, which they’ll carry over to the next unit.  As you work though 54/3, you know that 3 goes into 5  just 1 time with a remainder of 2. You’d multiply 3 x 1 = 3. Subtract 3 from 5 to get 2. Leave the 2 in the 10s spot. Similarly, for 155/4, you know that 4 goes into 15 just 3 times. You’d multiply 4 x 3 = 12. Subtract 15-12= 3. Carry the 3 down in the 10s spot. Carry the next unit down, adding it to the remainder. Then, divide the divisor into this number. Write the result into your answer, and then subtract to find your remainder, if you have 1.  Working through 54/3, you will carry the 4 down, writing it next to the 2, which gives you 24. You’ll next divide 3 into 24. This gives you 8. Putting it all together, your answer is 54/3=18. Similarly, as you work through 155/4, you’d now have a 3 left in your 10s spot. Carry down the 5, to give you 35. Divide the 4 into 35, which will give you a result of 8, with 3 remaining. Explain that the number of steps you’ll take depends on how many numbers are in the dividend. For example, 155/3 will have fewer steps than 1555/3. However, the process for each unit remains the same. Once the student has divided the divisor into the 1s place, they’ve reached the end of the problem. If the divisor does not go in evenly, there will be a remainder. They’ll need to include this remainder in their answer.  Since 3 goes into 54 evenly, you don’t have a remainder. However, 55/3 would give you a remainder of 1. You would find this remainder like this: If you divide 3 into 5, you get 1, with 2 remaining. You’d then divide 3 into 25, which would give you 8, with 1 remaining. This is your remainder. Your remainder should be written as part of your answer. You can indicate that it’s a remainder by writing “R” in front of it. Alternatively, you may write out the word “Remainder" followed by the number. For example, you’d write 55/3=18 R 1 or 55/3=18 Remainder 1. Lots of practice is essential for mastering math concepts. You can create your own worksheets or download them for free online. You could provide your student with real world scenarios to help them practice long division. For example, they could practice dividing large quantities of food among party guests. Similarly, you could have them divide their birthday money into 3 categories: spend now, save for later, save for college.
What is a summary of what this article is about?
Start with numbers that divide evenly. Explain how to divide the divisor into the first number of the dividend. Show the student how to find the remainder to carry over. Divide the divisor into the next number, including any remainder. Continue working the problem until you arrive at your answer. Demonstrate how to find the remainder. Show them how to write a remainder, if there is one. Provide practice problems to help them work through the steps.