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Long Division with Remainders

In the starting levels of learning mathematics you might have studied about basic Arithmetic operations such as Addition, subtraction, multiplication and division. Coming into Division concept, Its very easy to divide a small number with another small number.

For Example: Answer the question `9/3` i.e. 9 divided by 3?

You will say immediately the answer is 3. Because 9 goes 3 times by 3. i.e., 3 × 3 = 9. Its simple. Right?

Now Answer this `23576/13` i.e 23576 divided by 13?

Thus when the division comes to big numbers, you may feel difficult to solve. There is a simple method available to solve these complex divisions known as long Division with Remainders. By learning this simple method you can go for solving any big divisions easily. It involves continuous division of result obtained in one step with divisor to yield another result. This article concentrates on solving procedure for division in this method.

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How to do Long Division with Remainders

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To learn how to do long division with remainders you must be knowing the following terminologies.

  • Dividend: It is the number which is going to get divided by another number.
  • Divisor: It is the number which is going to divide the Dividend.
  • Quotient: It is the number obtained after division.
  • Remainder: It is the number left over after division.

See the following figure to get clear idea.

Simple Division

Now, let us proceed to the main concept.

Consider solving the above example `23576/13` = ? , we need to Find the quotient and remainder.

Long division with remainders includes 4 simple steps which need to be repeated till we get the result. They are

  • Decision step: In this step we take only first digit of dividend and check whether the selected digit is greater than the divisor, if yes - that is it is greater than the divisor then proceed to step 2. Else take 2nd digit also and check the same. Continue this till you find the selected number of digits are greater than the divisor. This is the first step.

For the current problem, first digit of dividend is 2.Here 2<13, so check along with 2nd digit. i.e., with 23. Now 23>13. So in this problem we take 1st and 2 digits together in first step.

Long Division

  • Multiplication Step : Now check how many times the selected digits goes by the divisor, and multiply the divisor as many number of times and put the result just below the selected digit/digits.

How do you do Long Division with Remainders

  • Subtraction Step : Now subtract the written number from the selected digit/digits and put it below this as a result.

Long Division Remainder

  • Bringing Down Step: Now check the step 1with the subtraction result and our divisor. If it(subtraction result) is less than the divisor, then bring the next digit down and do the same multiplication and subtraction steps

Long Division Remainders

Now repeat the same steps above taking 105 obtained with the divisor. See the following figures showing the consequent steps in the solving process.

Long Division with Remainder

As 1<13 bring down 7, Now 17>13. So proceed further.

How to do Long Division with Remainders

as 4<13, bring down 6 and proceed as did above.

Long Division with Remainders

Now you are left with no digits in dividend after 6. So stop now. This result is Know as Remainder( =7 here). And all the multiplication factors above together as Quotient( = 1813 here).

This way we can proceed for solving any complex division.

We have a relation among Divisor, Dividend, Quotient and Remainder. It is

Dividend = Divisor x Quotient + Remainder

Long Division with Remainders Practice Problems

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Below you could see long division with remainders practice problems

Practice Problems

Question 1: Find the quotient and remainder for 85582 divided by 24 ?
Question 2: Find the quotient and remainder for 98744 divided by 24 ?
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