**How to do long division with remainders?**

When we are given a long division to do it will not always work out to a whole number. Sometimes there will be numbers left over. These are known as

**remainders**. Taking an example similar to that on the Long Division page it becomes more clear: 435 ÷ 25.*If you feel happy with the process on the Long Division**page you can skip the first bit.*

**For E.g.**, Answer the questioni.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 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 yeild another result.This article concentrates on solving procedure for division in this method.## Explanation with Steps

To learnlong division with remaindersyou 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.

Now, let us proceed to the main concept.

Consider solving the above example = ?

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

**1) 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.

**2) 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.

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

**4) 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 multiplcation and subtraction steps

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

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

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

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

Dividend = Divisor * Quotient + Remainder

## Practice Problems

1)Find the quotient and remainder for 85582 divided by 24 ?

Sol:Upon successful completion of above steps you will get

Quotient =3524 Remainder=6.

2)Find the quotient and remainder for 98744 divided by 24 ?

Sol:

Quotient = 4114

Remainder = 8

**External Link**

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