How do you do long division?

Question

How do you do long division?

Answer 1

like this:           _12____

                     6/  72

                        - 6

                       ----------

                           12

                         - 12

                       ----------

                              0 <-------Remainder

Answer 2

Please try the site below.

Have fun.

Answer 3

Just take your time

3/393

3 divided into 3 is 1

1 times 3 equals 3

subtract 3 from 3 equals zero

3 divided into 9 is 3

3 times 3 equals 9

subtract 3 from 0

and keep going

Answer 4

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 8 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

Long Division

This is what is called an "algorithmic process". Below is the process written out in full. You will often see other versions. These are generally just a shortened version of the process below.

Lets see how it is done with 425 ÷ 25

There are two definitions we must make first.

the number to be divided into is known as the dividend (425 from above)

The number which divides the other number is known as the divisor (25 from above)

(Note: for a simple introduction read Long Division - Why and How)

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.

42 ÷ 25 = 1 remainder 17 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.

42 – 25 = 17 Now we take away the bottom number from the top number.

   Bring down the next number of the dividend.

175 ÷ 25 = 7 remainder 0 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.

175 – 175 = 0 Now we take away the bottom number from the top number.

    There are no more numbers to bring down. The answer must be 17

Long Division - Why and How

Long Division troubled me when I was at School - it was just plain confusing !

Until I realised it was just some way to get an answer. Not the only way, but one that works well if followed well. In other words, just follow the steps and *magic* it works!

So, what is it trying to solve? Answer: Difficult division problems !

Division vs Long Division

We don't need it for 42 ÷ 6 Which is 7 of course. Because 6 x 7 = 42 (look up your times tables if you don't believe me!)

But what is 462 ÷ 6 ? Hmmm, not so easy.

We could try guessing ... Is it 100? ... 100 x 6 = 600. No too big.

Is it 50? ... 50 x 6 = 300. Too small ... somewhere in between

Is it 75? ... 75 x 6 = 450. Close! Nearly 462. Let us try creeping up

Is it 76? ... 76 x 6 = 456. No, not yet ...

Is it 77? ... 77 x 6 = 462. BINGO!

But what if the problem is even more difficult, say 7,698 ÷ 6 ? That is going to take a LONG time to guess, so along comes Long Division to help us ...

http://www.mathsisfun.com/long_division....