Whole numbers is a collection of all the basic counting numbers and 0. In mathematics, counting numbers are called natural numbers. So, we can define the whole number as a collection of all natural numbers and 0. Whole numbers also include all positive integers along with zero.
Whole numbers include natural numbers that begin from 1 onwards.
The symbol to represent whole numbers is the alphabet ‘W’ in capital letters.
W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,…}
Thus, the whole numbers list includes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ….
Properties of Whole Numbers:
The basic operation of addition, subtraction, multiplication, and division give rise to four main properties of whole numbers:
(i) Closure Property:
The sum and product of two whole numbers is always a whole number and is closed under addition and multiplication.
Consider two whole numbers, 5 and 8.
5 + 8 = 13; a whole number
5 × 8 = 40; a whole number
(ii) Commutative Property:
The sum and product of whole numbers are the same even if the order of the numbers are interchanged.
Consider two whole numbers, 2 and 7.
2 + 7 = 7 + 2 = 9
2 × 7 = 7 × 2 = 14
The commutativity property holds true for addition and multiplication.
(iii) Associative Property:
How the whole numbers are grouped during addition or multiplication does not change the sum or product.
Consider three whole numbers, 2, 3, and 4.
2 + (3 + 4) = 2 + 7 = 9
(2 + 3) + 4 = 5 + 4 = 9
Thus, 2 + (3 + 4) = (2 + 3) + 4
2 × (3 × 4) = 2 × 12 = 24
(2 × 3) × 4 = 6 × 4 = 24
Thus, 2 × (3 × 4) = (2 × 3) × 4
(iv) Distributive Property:
The multiplication of a whole number is distributed over the total or difference of the whole numbers. Applying the distributive property makes the equation easier to solve.
Consider three whole numbers, 9, 11, and 6.
9 × (11 + 6) = 9 × 17 = 153
(9 × 11) + (9 × 6) = 99 + 54 = 153
Thus, 9 × (11 + 6) = (9 × 11) + (9 × 6)
