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# Whole Numbers Basics

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 Sub Topics Whole number is one of the classification of number systems. Whole numbers are numbers without fractions, percentages or decimals. Zero is neither a fraction nor a decimal, so zero is a whole number. A whole number is denoted by W. Whole numbers can be finite or infinite. Finite defines the numbers in the set are countable and infinite means the numbers in the set are uncountable. They include only the rounded value. The term whole number is one you’ll find often in mathematics. Whole numbers can never be negative. Whole numbers stop decreasing at Zero.

## Difference Between Whole Numbers and Natural Numbers

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The following differences between whole numbers and natural numbers are given below:
• A whole number is a positive integer including zero. The set of natural numbers is the set of positive integers beginning at one.
• Natural numbers are whole numbers, however whole numbers are not natural because zero is not a natural number. Infinite number of zeroes can be attached at the end to whole numbers.
• Smallest whole number is 0 greatest
• Smallest natural number is 1greatest

The difference between natural and whole numbers is where they start. A whole number is any positive number including a zero. A natural number is a positive integers number which starts at one.

## Operations on Whole Numbers

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There are some basic operations performed by whole numbers. They are:

Whole number addition
When two whole numbers are added we get a Whole Number. Therefore, whole numbers are closed under addition.
Examples : 4 + 5 = 9, 1 + 2 = 3, 9 + 7 = 16

Whole number Subtraction
When two whole numbers are subtracted we get a whole number. In some cases, subtraction of whole number does not always give a whole number. Therefore, whole numbers are not closed under subtraction.
e.g. 9 - 2 = 7, 8 - 11 = - 3
From the above, in some problems we can notice that the the difference of whole numbers is not a whole number, the result obtained is an integer.

Whole number Multiplication
When two whole numbers are multiplied we get a whole number. Therefore, whole numbers are closed under multiplication
Examples : 7 * 3 = 21, 5 * 4 = 20, 6 * 6 = 36, 7 * 6 = 42

Whole Number Division
Dividing a whole number by another does not always give a whole number. Whole numbers are not closed under division.

Examples : $\frac{12}{6}$ = 2, $\frac{5}{15}$ = 0.33, $\frac{36}{128}$ = 0.2812

From the above, we see that in some problems the result obtained is a fraction. We can say that division of two whole numbers is not always a whole number.

## Properties of Whole Numbers

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Important properties of whole numbers are explained below.

Closure property

Addition of two whole numbers will always be a whole number.
Examples : 56 + 13 = 69, 2 + 8 = 10, 35 + 10 = 45

Commutative property

If a and b are two whole numbers, then
a + b = b + a

Examples : 5 + 6 = 6 + 5, 2 + 9 = 9 + 2, 89 + 96 = 96 + 89

Associative property

Consider a, b and c to be whole numbers then,
a + ( b + c) = (a + b) + c

Examples : 4 + (5 + 10) = (4 + 5) + 10 = 19, 5 + ( 2 + 3 ) = (5 + 2) + 3 = 10

Additive Property

If we add Zero with any whole result would be same whole number
Suppose a is a whole number, then
a + 0 = 0 + a = a

Examples: 1 + 0 = 0 + 1 = 1, 63 + 0 = 0 + 63 = 63

Multiplicative Property

If we multiply 1 with any whole number result would be number itself.
Suppose a is a whole number, then
a * 1 = 1 * a = a

Distributive Property

Let a, b and c be three whole numbers then,
a * ( b + c) = (a * b) + (a * c)

Examples : 2 * (6 + 3) = ( 2 * 6) + (2 * 3) = 18, 5 * ( 6 + 3 ) = (5 * 6) + (5 * 3 ) = 45