Different ways to represent division and recording remainders

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Division

Dividing a number, amount or quantity involves splitting it into equal parts. We use division many times in our daily lives such as when we share sweets, when we divide a pizza or when we halve the quantity of ingredients required for a cooking recipe.

The division calculation

In a division calculation, the number being divided is called the dividend. The number which is being 'divided by' is called the divisor and the answer is called the quotient. Any leftover amount after the division process has occurred is called a remainder.

The division symbol
There are several signs or symbols that are used to indicate the division process:

a) dividend divisor (25 4)

b)

c) as a fraction bar

Remainders

Remainders can be recorded as fractions or decimals.

Possible answers: 6 r 3 (6 remainder 3) or 6 or 6.75

Grouping and sharing

Division involves either sharing or grouping.

Sharing: If 35 sweets are shared evenly between 7 children at a party, how many sweets will each child receive?

Grouping: How many groups of 6 eggs will be required to fill 14 egg cartons with each carton holding a dozen eggs?

The sharing process is done individually but, in the grouping example, an amount for each 'group' is already given and the challenge is to find out how many groups will be required.

See animation

Long Division Processes

Let's see how it is done with:
738 ÷ 8

 To start we divide 7 by 8 and realise it is not possible, so we can place a 0 and move to look at the next possible set of numbers which is 73. We realise that we cannot directly divide 73 by 8. Therefore, the closest number we can choose is 72. So, 72 ÷ 8 = 9 Doing this however, leaves a remainder of 1. The 1 is then combined with the 8 that is brought down to make 18. As above, it is not possible to divide 18 directly by 8. The closest number would be 16. So, 16 ÷ 8 = 2 Doing this however, leaves a remainder of 2. At this point, the answer we have derived is 92 r 2.

However, we are able to carry on the division process, but in doing so, we would be able to derive an answer in the decimal form. This is possible by simply adding on zeros. For example,

738 = 738.0000000....

Using this principle, we can carry on the process as below:

 We first add decimal points after 92 and 738 as shown. We then add a 0 after 738 which is brought down to make 20.   As above, it is not possible to divide 20 directly by 8. The closest number would be 16. So, 16 ÷ 8 = 2 Doing this however, leaves a remainder of 4. We add another 0 which we have brought down to make 40. We know 40 is directly divisible by 8, so, 40 ÷ 8 = 5 Therefore, at the end of this division process, we derive the answer: 92.25

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Question 1/5

1. In the division process what is a remainder?

 The number that is being used to divide another number The answer to a division sum Any leftover amount after the division process The number that is being divided

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