One of the basic arithmetic problems is long division. It is a method of calculating the remainder and quotient of the numbers of at least two digits. When you learn the basic steps of long division, it will become easy for you to divide numbers of any length, and the number can either be integers or decimals. It is very easy to learn, and you can do it when you know the basics of mathematics that you will be taught in your school.
How to Do Long Division?
Dividing is The First Step
Set up the sum on paper – On a piece of paper, you must write the number being divided under the division symbol on the right. Then write the divisor or the number dividing outside the symbol to the left.
The quotient will come on the top of the symbol above the dividend. Below the dividend, you must leave blank spaces for the long division process. Consider the example:
250 / 6
Do the first digit division – You need to start from left to right and check for the divisor to be manipulated on the first digit without doing it. For instance, you can check how many times 6 goes into 2. As 6 is greater than 2, it will not go, and the answer is 0. So, write 0 at the quotient place, which you can erase later.
Go for the first two digits – Since the first digit is smaller than the divisor, you also need to consider the next digit; thus, you have two digits to check the divisor. Now, you have 25 as a dividend and must check how many times 6 goes into it. You will discover it to be 4.167 times; thus, write it down after rounding off the number to 4. So, the answer is 04 on the quotient place now.
Multiplication is The Next Step
Multiplying the divisor – After entering the number at the quotient, you need to multiply it with the divisor and enter them down to the first two-digit dividend.
Record the product and draw a line – Since you have 04 as a quotient and thus, 04 * 6 is 24, so enter 24 down to the dividend’s first two digits 25. Now, record the product value to the dividend and draw a line below 24.
Subtraction Comes as The Next Step
Product Subtraction – Soon after entering the product value down to the dividend, you must draw a line to do subtraction. For instance, you subtract 24 from 25 and write the result 1 below the line. Ensure you subtract the whole dividend from that product value to avoid subtracting 24 from 250.
Write down the next digit – Now, it’s time for you to bring down the next digit of the divided to the right of the subtracted value. In the example, it was 1 that is left next to the two digits. So, you will have 10 below the line.
Repeat The Above Process Again
Now, you will have a new number to carry out division using the divisor 6. So, how to divide here? Yes, you must continue the above steps and write the quotient at the top.
In the example, you will have 10 as a dividend and need to find out how many times 6 goes into it. It will be just 1; thus, write the 1 as a quotient, and now you will have 041 at your quotient place. Again multiply the quotient 1 and the divisor 6 and write the product value down, which is 6.
After writing the product value 6, you need to subtract, and the result is 4. Since there is no number in the dividend to bring down next to 4, you need another method.
Remainders & Decimals
Record the remainder – After the calculation, you need to record the remainder you got at the end. In this example, you have 4 as a remainder; thus, you must express them as “41 r4”. This expression means that the long division provides the result with
Quotient value – 41
Remainder value – 4
Some people will stop soon after getting the remainder value. But sometimes, you must continue the long division through the decimal method.
Adding the decimal point – To continue the long division, you must add a decimal point next to the quotient 41. This decimal point means adding ‘0’ next to the remainder. So, you can add a zero next to the remainder using this decimal point.
So, you will get 40 as a remainder now and repeat the same procedure again.
Repeat the same process – Soon after adding ‘0’ next to the remainder of 4, you will get 40. Now the dividend is bigger than the divisor, and thus, check how many times 6 comes in 40. The nearby number will be 6 and enter it next to the decimal point at the quotient place.
Now carry out the product between the divisor and entered quotient, which is 6 * 6 and the answer is 36. So enter them down to 40 and carry out the subtraction, which is 4. Once you add a decimal point in the quotient, you can add ‘0’ next to the subtracted value again. But you don’t have to add a decimal point again in the quotient. So, you will get 40 again and carry out the same procedure, so you will have a quotient to be 041.666….
Stop and round the quotient – In some cases, the division process will continue after adding the decimal point. In such a situation, you need to stop and round it off.
For values greater than or equal to 5 in the third digit of the decimal point, you need to round the second digit next to the decimal point adding 1 to it. So here, it is going on 41.6666… so you can round it off to 41.67
For values lesser than 5, you can write them down as it is. For example, if you have 41.64444… you can round it off to 41.64
So here the answer for 250/6 is 41.67
Conclusion
The above article gives you a step-by-step procedure to easily carry out the long division. Thus, using the above procedure, it is easy to handle even decimal points in the long division.
Also read: Guide to Convert Degree to Radian
