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**Properties of Whole Numbers – Explanation, Solved Examples and FAQs**

## What is a Whole Number In Maths?

A whole number is a number that can be divided evenly by two integers, with no remainder. For example, the whole numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.

### Properties of Whole Numbers with Examples

The properties of whole numbers are as follows:

1. Whole numbers are positive integers.

2. Whole numbers are counting numbers.

3. Whole numbers are rational numbers.

4. The order of whole numbers is the natural number order.

5. The addition of two whole numbers is the sum of their individual parts.

6. The multiplication of two whole numbers is the product of their individual parts.

7. The square of a whole number is the result of multiplying the number by itself.

8. The natural number 1 is the identity element for addition.

9. The natural number 1 is the identity element for multiplication.

10. There is an inverse element for every whole number in the set of whole numbers.

### Properties of Addition

The sum of two numbers is called their addition. The following are some of the properties of addition:

1. Commutative Property: This property states that the order of the numbers does not affect the sum. That is, the sum of two numbers is the same regardless of the order in which the numbers are added. For example, 5 + 3 = 3 + 5.

2. Associative Property: This property states that the grouping of numbers does not affect the sum. That is, the sum of three numbers is the same regardless of how the numbers are grouped. For example, (5 + 3) + 4 = 5 + (3 + 4).

3. Identity Property: This property states that the sum of zero and any number is the number itself. That is, 0 + x = x for any number x.

4. Inverse Property: This property states that the sum of a number and its inverse is the number itself. That is, x + (-x) = x for any number x.

#### Properties of Subtraction

The properties of subtraction are as follows:

Commutative: For any two numbers a and b, a – b is the same as b – a.

Associative: For any three numbers a, b, and c, (a – b) – c is the same as a – (b – c).

Identity: For any number a, a – 0 is the same as a.

Inverse: For any number a, there exists a number b such that a – b = 0.

#### Properties of Multiplication

The product of two whole numbers is always greater than or equal to the sum of the two numbers.

The product of two negative numbers is always less than the sum of the two numbers.

The product of two positive numbers is always greater than the product of the two numbers if the signs are different. If the signs of the two numbers are the same, the product is the same as the product of the two numbers.

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##### Properties of Division

A division operation always produces a number that is less than the number that is divided by.

A division operation always produces a number that is a whole number.

A division operation always produces a number that is greater than 0.