Division of Numbers: Know All The Important Properties- Embibe
• Written By trisha
• Written By trisha

# Division of Numbers

The division is basically the distribution of numbers into small groups or parts. It is one of the four fundamental operations in mathematics that signifies equal sharing amongst all the components. The division of numbers is the exact opposite of the multiplication of numbers.

For example, suppose you and your three siblings are given 40 chocolates to share for. So, what number of chocolates will each one get? That comes when 40/4= 10 chocolates each.

## Division Method

The division symbol is in the shape of an obelus as a horizontal line with a dot above and below the line, ÷. It was first used as the sign for the division by the Swiss mathematician Johann Rahn in his book Teutsche Algebra in 1659.1659. In this article, we will discuss everything about the division operation, different methods, and division algorithm along with solved examples.

### Terms Used in Division of Numbers

Following are some of the common terms which are used for the division of numbers:

Dividend: The dividend is the number that is being divided in the division process.
Divisor: The number by which the dividend is being divided is called the divisor.
Quotient: The quotient is defined as a result obtained in the division process.
Remainder: The remainder is the portion of the dividend that is left over after division.

Example: If you want to divide the numbers 30÷5= 6, in this 30 is the dividend, the number 5 is the divisor, and the result you get is 30÷5=6, so, the number 6 is the quotient and 0 as the remainder.

### Properties of Division

Following are some of the properties of division that students must know:

#### Closure property:

For any two whole numbers a and b, a ÷ b is not always a whole number. Hence closure property is not applicable to division.
For example- 61 and 5 are whole numbers but 61 ÷ 5 is not a whole number.

#### Commutative property:

For any two whole numbers a and b, a ÷ b ≠ b ÷ a. This means the division of the whole numbers is not commutative.
For example- 20 ÷ 4 ≠ 4 ÷ 20

#### Associative property:

For any 3 whole numbers a, b and c,(a ÷ b)  ÷ c ≠ a ÷ (b ÷ c)
For example, consider (80 ÷ 10) ÷ 2 = 8 ÷ 2 = 4
80 ÷ (10 ÷2) = 80 ÷ 5 = 16 and (80 ÷ 10) ÷ 2 ≠80 ÷ (10 ÷2). Hence division does not follow the associative property.

#### Division by 1

For any whole number a, a ÷ 1 = a, this means any whole number divided by 1 gives the quotient as the number itself.
For example, 15 ÷ 1 = 15;

#### Division of 0 by Any Whole Number

For any whole number, a ≠ 0, 0 ÷ a = 0, this shows zero divided by any whole number (other than zero) gives the quotient as zero.
For example, 0 ÷ 1 = 0 and, 0 ÷ 25 = 0;

Question: Is (9 ÷ 3) the same as (3 ÷ 9)? Justify it by taking a few more combinations of whole numbers.
Solution: (9 ÷ 3) = 3 but  (3 ÷ 9) = 1/3  ≠ 3. Therefore (9 ÷ 3) is not same as (9 ÷ 6).

Few examples,
(12 ÷ 4) = 3 but  (4 ÷ 12) = 1/3 ≠ 3. Therefore (12 ÷ 4) is not same as (4 ÷ 12).
(25 ÷ 5) = 5 but  (5 ÷ 25) = 1/5  ≠ 5. Therefore (25 ÷ 5) is not same as (5 ÷ 25).

METHODS OF DIVISION

### Questions on Division of Numbers

Here are some questions on the division of numbers that students can practice:

1. 6 children share 18 chocolates. How many does each child get?
2. Ron distributes 24 bananas equally among 4 monkeys. How many bananas does each monkey get?
3. There are 18 apples. Jon arranges them in 2 plates. How many apples are there in each plate?
4. Tom puts. 50 eggs equally in 5 boxes. How many eggs are there in each box?
5. Jenny has 100 stickers. She wants to distribute these equally among 10 children. How many stickers does each child get?
6. There are 500 students in a school containing 25 sections. If in each section there are equal number of students, find their number in each section.
7. The cost of 15 cycles is $54,205. Find the cost of each cycle? 8. The cost of 30 ceiling fans is$43,050. How much does each fan cost?
9. A school has collected $14,000 from 24 students for the Prime Minister’s relief fund. How much has each student paid? 10. 25 students of class X collected$275 for an orphanage. If each student contributed an equal amount for the cause, how much amount of money was contributed by each student?

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