As part of basic arithmetic, long division is a way to solve and find answers to long division problems of numbers that consist of at least two digits. Learning the basic steps of long division division will help you to divide any number, be it integers or decimals. This process is easy to learn and the ability to do long division will help you hone your math understanding that will be useful both at school and in other parts of your life.
Step
Method 1 of 4: Divide
Step 1. Prepare the equation
On a piece of paper, write the number that is divided on the right side, below the divisor symbol and the number that divides on the left side of the divisor symbol.
- You will write the answer above the number you are dividing.
- Leave enough space under the equation to perform several subtraction operations.
- Here's an example: If there are six mushrooms in a 250 gram package, what is the average weight of each mushroom? In this problem, we have to divide 250 by 6. The number 6 is written outside and 250 is written inside the divisor symbol.
Step 2. Divide the first number
Working from left to right, determine how many times the divisor can be multiplied by the first digit of the number divided without exceeding it.
In our example, you will determine how many times 6 equals 2. Since 6 is greater than 2, the answer is zero. If you want, write the number 0 above the number 2 as a sign, and delete it later. Alternatively, you can leave it blank and move on to the next step
Step 3. Divide the first two numbers
If the divisor is greater than the first digit of the number being divided, determine how many times the divisor is multiplied so that it approaches the first two digits of the number being divided without exceeding it.
- If your answer to the first step is 0, as in the example, use the number next to the first number. In this example, it means how many times 6 equals 25.
- If your divisor has more than two digits, then you need to use the number next to it again, for example the third or even fourth digit of the number you divided to get the answer.
- Work out the whole number. If you use a calculator, you will find that the number of times 6 equals 25 is 4,167. In long division, you will always even up to the nearest whole number, so in this case, the answer is 4.
Step 4. Enter the first digit of your answer
Place the number obtained as the first number above the divisor symbol.
- The important thing with long division is to make sure that the columns are in the right order. Work carefully or you may make mistakes so that your final answer is wrong.
- In the example, you have to put the number 4 above the number 5, because we are entering 6 times to 25.
Method 2 of 4: Multiplying
Step 1. Multiply the divisor
The divisor must be multiplied by the number you just wrote above the divisible number. In our example, this number is the first number of the answer.
Step 2. Record the results
Enter your product in step 1 under the number you divided.
In the example, 6 times 4 is 24. After you have written 4 in your answer, write 24 under the number 25, again, being careful that the writing is parallel
Step 3. Draw the lines
A line must be placed under your product, for example under the number 24.
Method 3 of 4: Subtracting and Subtracting Numbers
Step 1. Subtract the result
Subtract the number you just wrote below the number divided by the divisor number directly above it. Write the result under the line you have made.
- In our example, we will subtract 24 from 25, so the result is 1.
- Do not subtract from the whole number the number that is divided, only subtract from the number you used in Parts One and Two. In the example, you should only subtract 24 from 25.
Step 2. Lower the next number
Write the number that is divided next next to the result of your subtraction operation.
In the example, since 6 cannot be multiplied by a certain number to become 1 without exceeding it, then you need to decrease the other number. In this case, you're going to take the 0 from 250 and put it behind the 1 to make it 10, so that 6 can be multiplied by 10
Step 3. Repeat this process in its entirety
Divide the new number by the divisor and write the result above the divided number as the next number in your answer.
- In the example, determine how many times 6 can be 10. Write the number (1) in the answer above the number that is divided. Then multiply 6 by 1 and subtract the result from 10. You should now have 4 as the remainder.
- If the number being divided has more than three digits, repeat this process again until all of them are used up. For example, if we make a problem with 2506 grams of mushrooms, then we can lower the number 6 next to the number 4.
Method 4 of 4: Finding Decimals Or Remains
Step 1. Record the rest
Depending on how you use this division, you may need to solve it with an integer answer, with a remainder, which indicates how much is left after you finish the division.
- In the example, the remainder is 4, because 6 cannot be multiplied by 4, and there are no further numbers to derive.
- Put the remainder after the answer with an "r" in front of it. In the example, the answer could be expressed as "41 r4."
- You can stop here if you're trying to calculate something that doesn't make sense to be expressed as a fraction, for example, if you're trying to determine how many cars it takes to move a certain number of people. In a question like this, it is useless to state the answer in the form of fractions of cars or fractions of people.
- If you plan to calculate decimal numbers, then you can skip this step.
Step 2. Provide a decimal point
If you plan to calculate the correct answer and not write down the remainder, then you need to continue dividing beyond the whole number. When you reach a point where the remaining number is less than the divisor, then add a decimal point to the answer and divide the number.
In the example, since 250 is an integer, each number after the decimal point is 0, making it 250,000
Step 3. Keep repeating
Now you have more numbers to derive (all zeros). Decrease the number 0 and continue as before, re-determining the number of times the divisor can be the new number.
In the example, determine how many times 6 can be 40. Add the number (6) to the answer above the number divided, after the decimal point. Then multiply 6 by 6 and subtract the result from 40. You'll get another 4
Step 4. Stop and round
In some problems, you will find that the result of the decimal number of division will repeat and repeat again and again. At this point, it's time to stop and round your answer up (if the repeating number is 5 or more) or round down (if the number is 4 or less).
- In the example, you could keep getting the remainder of 4 out of 40 minus 36 over and over, and adding 6 to your answer over and over. Instead of continuing to do this, stop and round off the answer. Since 6 is greater than (or equal to) 5, you can round it to 41.67.
- Alternatively, you can mark repeated numbers by placing a small horizontal line above the number. In the example, your answer would be 41.6, with a line above the number 6.
Step 5. Add units back into your answer
If you work on a problem with certain units such as grams, gallons or degrees, then after you finish counting, you need to add units back behind your answer.
- If you write zero as the initial number of the answer, then you must delete it first.
- In this example, because you were asked what the average weight of each mushroom is in a 250 gram bag containing 6 mushrooms, you need to give the answer in grams. Thus, your final answer is 41.67 grams.
Tips
- If you have more time, do the calculations on paper first, then check the answers with a calculator or computer. Keep in mind that machines often get answers wrong for various reasons. If there is an error, you can check it again with the logarithm. Counting long divisions by hand is better for your math skills and conceptual understanding than counting by machine.
- The way to remember the steps in this long line calculation is: "Divide, multiply, subtract and derive numbers."
- Look for practice questions from your daily life. This will help the learning process because you can see its use in everyday life.
- Start by using simple calculations. This will give you confidence and increase the skills needed to work on more difficult questions.
