Content

• To step
• Part 1 of 4: Sharing
• Part 2 of 4: Multiplication
• Part 3 of 4: Subtraction and bringing down a number
• Part 4 of 4: Finding the remainder or the decimal
• Tips

Long division is a regular part of arithmetic and a method for solving a division and finding the remainder, usually used for larger numbers.Learning the basic steps of long division allows you to divide numbers of arbitrary length, both integers and decimal places. This is easy to learn, and this skill helps you understand math, which is a great help in school and for the rest of your life.

To step

Part 1 of 4: Sharing

1. Write down the sum. Write the dividend (the number being divided) on the right, below the division symbol, and the divisor (the number being divided) on the left, outside the division symbol.
   • The quotient (the answer) is ultimately at the top, directly above the dividend.
   • Leave enough space under the dividend for the subtraction.
   • An example: You have 6 mushrooms in a box of 250 grams, how much does each mushroom weigh on average? We divide 250 by 6. The 6 goes to the outside and the 250 on the inside.
2. Divide the first digit. By now working from left to right you determine how often the divisor goes into the first digit of the dividend.
   • In the example you want to determine how often 6 goes into 2. Since 6 is greater than 2, the answer is 0. If you want, you can place a 0 directly above the 2 as a locator, and delete it later. You can leave the space open and move on to the next step.
3. Divide the next 2 numbers. If the divisor is greater than the first digit of the dividend, try to do it with the first 2 digits of the dividend.
   • If the previous answer was 0, as in the example, expand the number by 1 digit. In this case, you are going to determine how often 6 goes into 25.
   • If the divisor has more than 2 digits, it may be necessary to use not 2 but 3 digits of the dividend for the first division.
   • Work with integers. If you are using a calculator, you will see the division 25/6 = 4167. In long division, you always round down to the nearest whole number, so the answer in this case is equal to 4.
4. Write down the first digit of the quotient. Place the number of times the divisor goes in the first digit (or digits) of the dividend above the appropriate digits.
   • It is important in long division to ensure that the numbers are aligned correctly. Work accurately, otherwise you will make mistakes.
   • In this example, you would place the 4 above the 5, because we divide 25 by 6.

Part 2 of 4: Multiplication

1. Multiply the divisor. Multiply the divisor by the number you just wrote above the dividend. In the example, this is the first digit of the quotient.
2. Write down the product. Place the result of the multiplication from step 1 under the dividend.
   • In the example 6 * 4 = 24. After you have included a 4 in the quotient, write the number 24 under 25, neatly aligned.
3. Draw a line. Place a line below the product of your multiplication (24) from the example.

Part 3 of 4: Subtraction and bringing down a number

1. Subtract the product. Subtract the number you wrote below the dividend from the numbers above it. Write the result below the line you just drew.
   • In the example, we subtract 24 from 25 to yield 1.
   • Don't subtract this number from the full dividend, but only from the number you used in step 1 and step 2. So don't subtract 24 from 250, but from 25.
2. Bring down the next digit. Write down the next digit of the dividend after the result of the subtraction.
   • Because the 6 of the example does not fit in 1, you will have to add the next digit. In this case, take the zero out of 250 and place it next to the 1, making it equal to 10, where 6 will fit.
3. Repeat the whole procedure. Divide the new number by the divisor, and write the result above the dividend as the next digit in your quotient.
   • In the example you determine the number of times that 6 goes into 10. Write that number (1) to the quotient, above the dividend. Then multiply 6 by 1 and subtract the result from 10. If correct, this will give you 4.
   • If the dividend has more than 3 digits, keep repeating this procedure until you've gotten them all. For example, if we started with 2506 grams of mushrooms, we would have pulled down the 6 and placed it next to the 4.

Part 4 of 4: Finding the remainder or the decimal

1. Write down the remainder of the division. Depending on the purpose of the division, you may be looking for an integer plus a remainder.
   • In this example, the remainder is 4, because 4 is not divisible by 6 and there are no digits left.
   • Write the rest of the quotient with an "r" in front of it. In the example, you can write the answer as "41 r4."
   • You can stop now if it is not possible to express the answer in smaller parts. For example, suppose you want to calculate how many cars are needed to transport a certain number of people. It doesn't really make much sense to think in terms of a half or quarter car.
   • If you plan to calculate a decimal, you can skip this step.
2. Add a decimal point. If you plan to give the answer in decimal places instead of with a remainder, place a comma where you would otherwise stop the calculation. Do this for both the dividend and the quotient.
   • In the example, because 250 is an integer, any number after the decimal point equals 0, which ultimately adds up to 250,000.
3. Keep going. Now you have more digits that you can move down (all zeros). Bring down a zero and continue as in the previous step, which determines how many times the divisor fits into the new number.
   • In the example, you calculate 40 divided by 6. Add that number (6) to the quotient above the dividend and after the comma / decimal point. Then multiply 6 by 6 and subtract the result from 40. You should now come back to 4.
4. Stop and finish. In some cases, you will find that when you start solving the decimal, digits or groups of numbers keep repeating. That is a sign that you can stop and finish the answer.
   • In the example, you could go on indefinitely and come up with 6 in the answer over and over again. You round this to 41.67, because 6 is greater than 5 and is therefore rounded up.
   • Alternatively, you can indicate a repeating decimal with a short horizontal line through the repeating decimal. In the example, this would look like 41.6, with a dash through 6.
5. Place the unit after the answer (if any). If you are working with units, such as grams, degrees or liters, you can place these after the answer after all calculations have been completed.
   • If you have now noted a locator, you should now also remove it.
   • In the example where you were asked for the weight of 1 mushroom in a box of 250 grams, you will have to give the answer in grams. Thus, the final answer: 41.67 grams.

Tips

• If you have enough time, it is a good idea to do your calculations on paper first and then with a calculator or computer. Keep in mind that machines don't always give the right answer, for a variety of reasons. If an error has occurred, check again using logarithms. Calculating division by hand instead of a machine is better for your arithmetic skills and understanding.
• One way to remember the steps of a long division is: "De Vos At Brood." D stands for division, V for multiplication, A for subtraction, and B for bring down.
• Find real-life examples. This will help you learn this method as you will see how to use it.
• Start with simple calculations. This gives you the confidence and the necessary skills to be able to do more difficult tasks.