There are three parts to every division problem:

The Dividend is the number that is being divided up.
The Divisor is the number of equal groups it is divided into.
The Quotient is the answer, or the amount in each group once everything is shared.
Sometimes there are leftovers that wont fit evenly in each group. We call that the Remainder.

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I teach two different ways to do division.

Here is a link that does a good job explaining Long Division.
Here is a link that does a good job explaining Partial Quotient.


Remainders

There are three different ways we show a remainder in the quotient.
As a remainder, as a fraction, and as a decimal. We usually round the decimal to the nearest hundredth, so it can be use to find a percent if we need to.
1. As a whole number and the remainder. 123 R 1

external image divide15.gif
4 ÷ 25 = 0 remainder 4
The first number of the dividend is divided by the divisor.
external image divide16.gif

The whole number result is placed at the top. Any remainders are ignored at this point.
external image divide17.gif
25 × 0 = 0
The answer from the first operation is multiplied by the divisor. The result is placed under the number divided into.
external image divide18.gif
4 – 0 = 4
Now we take away the bottom number from the top number.
external image divide19.gif

Bring down the next number of the dividend.
external image divide20.gif
43 ÷ 25 = 1 remainder 18
Divide this number by the divisor.
external image divide21.gif

The whole number result is placed at the top. Any remainders are ignored at this point.
external image divide22.gif
25 × 1 = 25
The answer from the above operation is multiplied by the divisor. The result is placed under the last number divided into.
external image divide23.gif
43 – 25 = 18
Now we take away the bottom number from the top number.
external image divide24.gif

Bring down the next number of the dividend.
external image divide25.gif
185 ÷ 25 = 7 remainder 10
Divide this number by the divisor.
external image divide26.gif

The whole number result is placed at the top. Any remainders are ignored at this point.
external image divide27.gif
25 × 7 = 175
The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into.
external image divide28.gif
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.
external image divide29.gif

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


2. As a mixed number, a whole number and a fraction combined. 123 1/3
Doing this way is easy. All you do is take the remainder and use it as the top or numerator of the fraction, and then use the divisor as the bottom or denominator of the fraction. Always check to see if you can simplify once you have put the two into a fraction. Here is how the example above would work. You have the quotient of 17 and that will never change, the remainder of 10 goes on top, and the divisor of 25 goes on the bottom, so the answer is 17 10/25. Then I need to simplify 10/25 by dividing it by 5 top and bottom, so the perfect answer for the quotient is 17 2/5.
3. As a decimal number. 123.33




external image divide15.gif
4 ÷ 25 = 0 remainder 4
The first number of the dividend is divided by the divisor.
external image divide16.gif

The whole number result is placed at the top. Any remainders are ignored at this point.
external image divide17.gif
25 × 0 = 0
The answer from the first operation is multiplied by the divisor. The result is placed under the number divided into.
external image divide18.gif
4 – 0 = 4
Now we take away the bottom number from the top number.
external image divide19.gif

Bring down the next number of the dividend.
external image divide20.gif
43 ÷ 25 = 1 remainder 18
Divide this number by the divisor.
external image divide21.gif

The whole number result is placed at the top. Any remainders are ignored at this point.
external image divide22.gif
25 × 1 = 25
The answer from the above operation is multiplied by the divisor. The result is placed under the last number divided into.
external image divide23.gif
43 – 25 = 18
Now we take away the bottom number from the top number.
external image divide24.gif

Bring down the next number of the dividend.
external image divide25.gif
185 ÷ 25 = 7 remainder 10
Divide this number by the divisor.
external image divide26.gif

The whole number result is placed at the top. Any remainders are ignored at this point.
external image divide27.gif
25 × 7 = 175
The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into.
external image divide28.gif
185 – 175 = 10
Now we take away the bottom number from the top number.
external image divide30.gif

Now we have reached the end of the whole numbers we add a decimal place and the first zero. Notice the decimal point which has appeared on the answer line and by the dividend. It does not appear anywhere else.
external image divide31.gif

Bring down the next number of the dividend.
external image divide32.gif
100 ÷ 25 = 4 remainder 0
Divide this number by the divisor.
external image divide33.gif

The whole number result is placed at the top. Any remainders are ignored at this point.
external image divide34.gif
25 × 4 = 100
The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into.
external image divide35.gif
100 – 100 = 0
Now we take away the bottom number from the top number.
external image divide36.gif

The subtraction has given zero. We stop when this happens. The answer will be17.4 As long as the subtraction gives a number above zero the long division can carry on to as many decimal places as we wish.


All three ways are just different ways to show the same number. The only difference between the three is how the leftovers are shown.