Division

= 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. = 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


 * [[image:http://www.mathsisfun.com/images/divide15.gif height="60"]] || 4 ÷ 25 = 0 remainder 4 || The first number of the dividend is divided by the divisor. ||
 * [[image:http://www.mathsisfun.com/images/divide16.gif height="60"]] ||  || The whole number result is placed at the top. Any remainders are ignored at this point. ||
 * [[image:http://www.mathsisfun.com/images/divide17.gif height="100"]] || 25 × 0 = 0 || The answer from the first operation is multiplied by the divisor. The result is placed under the number divided into. ||
 * [[image:http://www.mathsisfun.com/images/divide18.gif height="100"]] || 4 – 0 = 4 || Now we **take away** the bottom number from the top number. ||
 * [[image:http://www.mathsisfun.com/images/divide19.gif height="100"]] ||  || Bring down the next number of the dividend. ||
 * [[image:http://www.mathsisfun.com/images/divide20.gif height="100"]] || 43 ÷ 25 = 1 remainder 18 || Divide this number by the divisor. ||
 * [[image:http://www.mathsisfun.com/images/divide21.gif height="100"]] ||  || The whole number result is placed at the top. Any remainders are ignored at this point. ||
 * [[image:http://www.mathsisfun.com/images/divide22.gif height="150"]] || 25 × 1 = 25 || The answer from the above operation is multiplied by the divisor. The result is placed under the last number divided into. ||
 * [[image:http://www.mathsisfun.com/images/divide23.gif height="150"]] || 43 – 25 = 18 || Now we **take away** the bottom number from the top number. ||
 * [[image:http://www.mathsisfun.com/images/divide24.gif height="150"]] ||  || Bring down the next number of the dividend. ||
 * [[image:http://www.mathsisfun.com/images/divide25.gif height="150"]] || 185 ÷ 25 = 7 remainder 10 || Divide this number by the divisor. ||
 * [[image:http://www.mathsisfun.com/images/divide26.gif height="150"]] ||  || The whole number result is placed at the top. Any remainders are ignored at this point. ||
 * [[image:http://www.mathsisfun.com/images/divide27.gif height="150"]] || 25 × 7 = 175 || The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into. ||
 * [[image:http://www.mathsisfun.com/images/divide28.gif height="175"]] || 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. ||
 * [[image:http://www.mathsisfun.com/images/divide29.gif height="175"]] ||  || With a long division with remainders the answer is expressed as **17 remainder 10**as 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


 * [[image:http://www.mathsisfun.com/images/divide15.gif height="60"]] || 4 ÷ 25 = 0 remainder 4 || The first number of the dividend is divided by the divisor. ||
 * [[image:http://www.mathsisfun.com/images/divide16.gif height="60"]] ||  || The whole number result is placed at the top. Any remainders are ignored at this point. ||
 * [[image:http://www.mathsisfun.com/images/divide17.gif height="100"]] || 25 × 0 = 0 || The answer from the first operation is multiplied by the divisor. The result is placed under the number divided into. ||
 * [[image:http://www.mathsisfun.com/images/divide18.gif height="100"]] || 4 – 0 = 4 || Now we **take away** the bottom number from the top number. ||
 * [[image:http://www.mathsisfun.com/images/divide19.gif height="100"]] ||  || Bring down the next number of the dividend. ||
 * [[image:http://www.mathsisfun.com/images/divide20.gif height="100"]] || 43 ÷ 25 = 1 remainder 18 || Divide this number by the divisor. ||
 * [[image:http://www.mathsisfun.com/images/divide21.gif height="100"]] ||  || The whole number result is placed at the top. Any remainders are ignored at this point. ||
 * [[image:http://www.mathsisfun.com/images/divide22.gif height="150"]] || 25 × 1 = 25 || The answer from the above operation is multiplied by the divisor. The result is placed under the last number divided into. ||
 * [[image:http://www.mathsisfun.com/images/divide23.gif height="150"]] || 43 – 25 = 18 || Now we **take away** the bottom number from the top number. ||
 * [[image:http://www.mathsisfun.com/images/divide24.gif height="150"]] ||  || Bring down the next number of the dividend. ||
 * [[image:http://www.mathsisfun.com/images/divide25.gif height="150"]] || 185 ÷ 25 = 7 remainder 10 || Divide this number by the divisor. ||
 * [[image:http://www.mathsisfun.com/images/divide26.gif height="150"]] ||  || The whole number result is placed at the top. Any remainders are ignored at this point. ||
 * [[image:http://www.mathsisfun.com/images/divide27.gif height="150"]] || 25 × 7 = 175 || The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into. ||
 * [[image:http://www.mathsisfun.com/images/divide28.gif height="175"]] || 185 – 175 = 10 || Now we **take away** the bottom number from the top number. ||
 * [[image:http://www.mathsisfun.com/images/divide30.gif height="175"]] ||  || 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. ||
 * [[image:http://www.mathsisfun.com/images/divide31.gif height="175"]] ||  || Bring down the next number of the dividend. ||
 * [[image:http://www.mathsisfun.com/images/divide32.gif height="175"]] || 100 ÷ 25 = 4 remainder 0 || Divide this number by the divisor. ||
 * [[image:http://www.mathsisfun.com/images/divide33.gif height="175"]] ||  || The whole number result is placed at the top. Any remainders are ignored at this point. ||
 * [[image:http://www.mathsisfun.com/images/divide34.gif height="200"]] || 25 × 4 = 100 || The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into. ||
 * [[image:http://www.mathsisfun.com/images/divide35.gif height="200"]] || 100 – 100 = 0 || Now we **take away** the bottom number from the top number. ||
 * [[image:http://www.mathsisfun.com/images/divide36.gif height="200"]] ||  || The subtraction has given zero. We stop when this happens. The answer will be**17.4** 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.