Jun 30, 2010

How to do long division with remainders?

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.
 
4 ÷ 25 = 0 remainder 4 The first number of the dividend is divided by the divisor.

The whole number result is placed at the top. Any remainders are ignored at this point.
25 × 0 = 0 The answer from the first operation is multiplied by the divisor. The result is placed under the number divided into.
4 – 0 = 4 Now we take away the bottom number from the top number.

Bring down the next number of the dividend.
43 ÷ 25 = 1 remainder 18 Divide this number by the divisor.

The whole number result is placed at the top. Any remainders are ignored at this point.
25 × 1 = 25 The answer from the above operation is multiplied by the divisor. The result is placed under the last number divided into.
43 – 25 = 18 Now we take away the bottom number from the top number.

Bring down the next number of the dividend.
185 ÷ 25 = 7 remainder 10 Divide this number by the divisor.

The whole number result is placed at the top. Any remainders are ignored at this point.
25 × 7 = 175 The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into.
185 – 175 = 10 Now we take away the bottom number from the top number.


There is still 10 left over but no more numbers to bring down.

With a long division with remainders the answer is expressed as 17 remainder 10 as shown in the diagram


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 learn  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.

   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.
 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.

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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Mathimagination Series: Book A, beginning multiplication and division; Book B, operations with whole numbers; Book C, number theory, sets and number bases; Book D, fractions; Book E, decimals and percentDecimals and Percentages With Pre- And Post-Tests: Place Value, Addition, Subtraction, Multiplication, Division
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