Column divisions are a fundamental concept of arithmetic; the method allows you to find the quotient and the rest of the operations involving at least two digits. If you learn this method, you will be able to divide numbers of any length, both integers and decimals. This is a simple process to learn and allows you to sharpen your understanding of mathematics, which will help you both in school and in everyday life.
Steps
Part 1 of 4: Divide
Step 1. Set up the equation
On a sheet of paper write the dividend (the number to be divided) on the right, under the division symbol, while on the left, outside the division symbol, write the divisor (the number that divides).
- The quotient (the solution) will be written at the top, above the dividend.
- Make sure you have plenty of free space on the paper so that you can perform various subtraction operations.
- Here is an example: if there are 6 mushrooms in a 250 g pack, how much does each mushroom weigh on average? In that case you have to divide 250 by 6. So 6 (divisor) will be written on the outside of the division symbol and 250 (dividend) on the inside.
Step 2. Divide the first digit
Working from left to right, determine how many times the divisor is in the first digit of the dividend.
According to the example you have to calculate how many times 6 is in 2. Since 6 is greater than 2, the answer is zero. If you wish, you can write a 0 right above the 2, you will delete it later. Alternatively, leave a blank space and move on to the next calculation
Step 3. Divide the first two digits
If the divisor is a number greater than the first digit of the dividend, then you need to determine how many times the divisor is in the first two digits of the dividend.
- If the answer from the previous step was 0, as in our example, then you need to consider the first two digits. You have to ask yourself how many times 6 goes into 25.
- If the divisor has more than two digits, you will need to consider far more than the first two of the dividend, coming up to the third or even the fourth to calculate how many times the divisor is in the dividend.
- Work in terms of integers. If you use a calculator, you will find that 6 goes into 25 4, 167 times. In column divisions you must always consider the integer value, in this case 4.
Step 4. Enter this first digit in the quotient
Write it over the dividend. If the result is more than one integer, write them all down.
- In column divisions it is very important that the figures always remain well aligned. Work calmly and be precise, otherwise you will make a mistake that will drag you to the final result which will be wrong.
- In the case of the example, write 4 above the 5 digit of the dividend, since you are calculating how many times 6 is in 25.
Part 2 of 4: Multiply
Step 1. Multiply the divisor
At this point you need to multiply the divisor by the figure you wrote above the dividend. For the example of the bag of mushrooms, this is the first digit of the quotient.
Step 2. Make a note of the product
Write the result of the multiplication from the previous step under the dividend.
In our example, 6 x 4 = 24. After writing 4 above the dividend, write 24 below the 25, always keeping the numbers well lined up
Step 3. Draw a line
You have to put it under the product of your multiplication, in our example it is 24.
Part 3 of 4: Subtract and Lower a Digit
Step 1. Subtract the product
You need to calculate the difference between the first two digits of the dividend and the product you calculated earlier.
- In our example, subtract 24 from 25 and you get 1.
- Do not consider the entire dividend in the subtraction, but only the figures you considered in the first and second sections of this article. In the example of the bag of mushrooms you need to consider only 25 and not 250.
Step 2. Lower the next digit
Write the next digit of the dividend next to the result of the subtraction.
Always following our example, since 6 does not fit in 1, you have to lower a figure from the dividend. In this case you consider the 0 from 250 and bring it back down, close to 1, getting 10, a value in which the 6 fits
Step 3. Repeat the process all over again
Divide the new number by the divisor and write the result at the top near the first digit of the quotient.
- Determine how many times 6 goes into 10. Solution (1) must be printed at the top, above the dividend. Then multiply 6 x 1 and subtract the product from 10. You get 4.
- If the dividend has more than three digits, then keep lowering the next digit until you have used all of them. If we had considered a 2506 gram bag of mushrooms, at this point you would have had to lower the 6 and write it next to the 4.
Part 4 of 4: Finding the Remainder or Decimal Digits
Step 1. Write down the rest
Depending on the problem where the division fits, you could end the operations by writing the quotient as an internal number and then the remainder without proceeding further.
- In the example, our remainder is 4 since 6 does not fit into 4 and there are no other digits to lower.
- Put the remainder after the quotient by writing an "r" first. In our example the solution would be expressed as "41 r4."
- You could stop here if the value you need to find doesn't make any sense in decimal places, for example if you were to calculate how many cars you need to transport a certain number of people. In such a case it is not useful to think in terms of "tenths of a car" or "tenths of a person".
- If you need to calculate the decimal places, proceed with the next steps.
Step 2. Add the decimal point
If you have to find the precise solution, instead of an integer quotient and the rest, you have to go beyond integers. When you reach the point where the remainder is less than the divisor, put a comma after the last digit of the quotient and dividend.
In our example, since 250 is an integer, each digit that follows after the decimal point will be zero resulting in a write like 250,000
Step 3. Continue repeating the above procedure
You now have other digits to lower (they are all 0's). Lower one and continue as before by determining how many times the divisor is in the new number.
In the example, determine how many times 6 goes into 40. Add the result you get (6) next to the quotient, above the dividend and after the decimal point. Now multiply 6 x 6 and subtract the result from 40. You will get a 4 again
Step 4. Stop and round
In some cases, you will find that solving the division even for decimal values, the digits repeat continuously. This is the time to stop and round the result (up if the value is greater than or equal to 5 and down if it is even to 4 or lower).
- In our example, we will continue to find 4 from subtracting 40-36 forever by adding an infinite number of 6 into the quotient as the nth decimal place. Instead of continuing, stop and round. Since 6 is greater than 5, you can round up and your final quotient will be 41.67.
- Alternatively, you can indicate the decimal that repeats itself indefinitely by placing a small horizontal dash above the digit. In our example you can draw the dash above the 6 of 41, 6.
Step 5. Add the unit of measurement to the result
If the problem considers values that express measurable quantities (kilograms, meters, liters, degrees and so on) you must also add the unit of measurement to the solution.
- If you wrote a zero as the first digit of the quotient, now is the time to delete it.
- To answer the problem in the example, if you want to know how much each mushroom in our 250g pack weighs on average, you will need to indicate 41.67g.
Advice
- If you have time, it would be best to do the calculations first on a piece of paper and then check them with a calculator or computer. Remember that sometimes machines give you wrong answers for various reasons. If there is an error, then check a third time using logarithms. Doing mental calculations and not always relying on machines is also useful for understanding mathematical concepts and improving your skills in this subject.
- Look for practical examples in everyday life. This will help you to memorize the methodology, because you will be able to use it in daily actions.
- Start with simple calculations. This helps you practice and you can develop all the skills you need to move on to more complex calculations.
