What is Long division?

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Take a dozen Bananas and arrange them into rows containing 4 bananas each. How many rows were made? 4 + 4 + 4 = 12 means 3 rows you made. Here you divided 12 bananas into 3 rows by placing 4 in each row. This is called division. Division means dividing something into equal parts. But if you have a bigger number like 1221 and you have to divide it by a smaller number like 11, how will you do that? Let me help you. The bigger numbers can be divided successfully by a smaller number using the long division method. We shall discuss this long division method in detail now.

Parts of Division:

Before proceeding with long division, it is important to learn the basics of division. As you know division is dividing something into parts. For example: 25  3. By performing division, we get 25 = (3  8) + 1. where 25 is the dividend, 3 is the divisor, 8 is the quotient, and 1 is the remainder.

Hence the parts of division are into:

  1. Dividend: Number which is to be divided.
  2. Divisor: Number which divides the dividend.
  3. Quotient: Number resulted from the division of a number from another.
  4. Remainder: The number which is left after performing division. It cannot be further divided.

The parts of division and long division are one and the same.

Steps Involved in Long Division

Performing division necessitates the creation of a tableau. A right parenthesis ) or vertical bar | separates the divisor from the dividend, and a vinculum separates the dividend from the quotient (an overbar). Now, to further grasp the process, let’s go over the long division procedures listed below.

  • Divide the first digit of the dividend using a divisor. If it is smaller than the divisor, then put zero on top as a quotient. If the number is bigger or equal to the divisor, then divide it by the divisor and write the answer on top as the quotient.
  • Example: 1021 Here 10 < 11. Hence quotients will be written as zero.

1221  11 Here 12 > 11. Hence after dividing, the quotient obtained is 1.

  • Multiply the quotient with the divisor then write the value below the first digit/First 2 digits of the dividend.
  • Subtract to get the remainder.
  • Then bring down the next number of the dividend and repeat the steps.
  • Repeat these steps until all the numbers in the dividend are taken down and you get a non-divisible remainder.

Solved Examples

Let me explain these steps using some examples.

Example 1: 535  15

Solution: Since we are dividing from a 2-digit number, Divide the first 2 digits from the left first. i.e. 53/15. 15 3 = 45. Here 3 is the quotient.

Now you subtract 45 from 53. So, 53 – 45 = 8. 8 is the remainder.

Now bring down the next number of the dividend next to the remainder. i.e. 5. Hence the number formed is 85.

Divide 85 by 15. 15  5 = 75. Here 5 is the quotient.

Subtract 75 by 85. Hence the remainder is 10.

Since the remainder is less than the divisor, we cannot divide it.

Hence, we end it here.

So, the remainder = 10 and quotient = 35.

Example 2: 354  4

Solution: 3 cannot be divided by 4 hence quotient is 0.

Multiply quotient with 0. So, 4  0 = 0

Subtract from 3. 3 – 0 = 3 remainder.

Bring down the next number from the dividend. Hence the number formed is 35.

35  4, 4 8 = 32. 8 is the quotient.

Subtract 32 from 35 = 35 – 32 = 3 remainder.

Bring down the next number from the dividend. Hence the number formed is 34.

34  4, 4 8 = 32. 8 is the quotient.

Subtract 32 from 34 = 34 – 32 = 2 remainder.

Hence the final quotient obtained by dividing 354 by 4 is 88 and the remainder is 2.

This is how you perform long division. I learned in detail about long division and some other math concepts using Cuemath. It is the best platform to improve your mathematical knowledge. To learn math concepts online, visit their website, book a free trial class and enroll in their math classes.








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