What are Whole Numbers? Definition and Examples

Whole numbers form the foundation of basic mathematical calculations. From counting objects to measuring quantities and distance, whole numbers are useful in everyday life. 

It is a collection of all the numbers starting from zero and going to infinity. No fractions or decimals; these are just simple positive numbers. This article discusses the important properties of whole numbers in detail.  

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Definition of Whole Numbers

Whole numbers are numbers that start from zero and go on to infinity (0, 1, 2, 3, 4, ...). They do not include any fractions, decimals, or negative numbers. In simple words, whole numbers are the counting numbers plus zero. These numbers are used to count complete objects or things, but not parts or pieces. For example, 5 is a whole number, but 2.5 and -3 are not whole numbers.

Whole Numbers Definition and Examples

The definition of whole numbers states that it is a set of all positive, countable numbers, along with the number zero. Fractions, decimals, or negative numbers are not whole numbers. Therefore, we can say that whole numbers consist of 0, 1, 2, 3, 4, 5… and so on.

For example, 8, 33, 276, and 1045 are all whole numbers.

Numbers like 22/7, 1.73, -14, 0.54, etc. are not whole numbers.

The set of whole numbers is represented by the symbol W. Therefore, we can write W = {0, 1, 2, 3, 4, 5, 6 …}

Whole Numbers on a Number Line

According to the whole number definition and examples, we can easily represent them on a number line that starts from zero and increases by 1 at an equal distance from left to right along the line.

The arrow indicates that whole numbers continue to infinity. 

Read More - Composite Numbers: Definition, List, Properties, and Examples

What are Whole Numbers?

Whole numbers definition is that the numbers we use for counting and start from zero: 0, 1, 2, 3, 4, and so on. They do not have any fractions, decimals, or negative signs—so numbers like 2.5 or -3 are not whole numbers. The set of whole numbers goes on endlessly and only includes positive numbers and zero. Think of whole numbers as the most basic numbers you use every day for things like counting objects or steps.

Find the Mean of the First Five Whole Numbers

The first five whole numbers are 0, 1, 2, 3, and 4. To find their mean, we first add them: 0 + 1 + 2 + 3 + 4 = 10. Next, we count how many numbers there are; in this case, it’s 5. Now, we divide the total sum (10) by the number of numbers (5): 10 ÷ 5 = 2. So, the mean of the first five whole numbers is 2. This is the average value when you add them and share equally.

What are Whole Numbers and Natural Numbers?

As per the definition of whole numbers, they include all positive numbers plus zero. Natural numbers are also all positive numbers, but they don’t include zero. In other words, natural numbers are a subset of whole numbers. 

Let’s look at the primary differences between whole numbers and natural numbers as mentioned in the table below.

Whole Numbers Definition and Examples

Whole numbers are the numbers we use for counting and measuring everyday things, like 0, 1, 2, 3, 4, 5, and so on. They do not include fractions, decimals, or negative numbers—just simple positive numbers and zero. For example, 0, 8, 15, and 237 are all whole numbers, but numbers like 2.5, -7, or 3/4 are not. Whole numbers are easy to spot because they have no decimal or fractional part, and zero is considered the smallest whole number.

Properties of Whole Numbers

After getting an idea of what whole numbers are, it is necessary to understand the properties of whole numbers, which help in performing mathematical calculations conveniently and accurately. The four main properties of whole numbers are as follows:

• Closure Property

• Commutative Property

• Associative Property

• Distributive Property

We will explain these properties in detail with the whole numbers and examples.

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Closure Property of Whole Numbers

According to this property, when we add or multiply two whole numbers, we always get a whole number as the sum or product, respectively. We can never get a negative, fraction, or decimal number by adding or multiplying two whole numbers.

For example, let’s take two whole numbers, 7 and 12.

By adding, we get 7 + 12 = 19. Here, 19 is a whole number.

Again, by multiplying we get 7 x 12 =84. Here, 84 is a whole number.

Read More - What Is BODMAS Rule? | Solved Examples

Commutative Property of Whole Numbers

According to this property, when two whole numbers are added or multiplied, the addition or multiplication can be done in any order, and the sum or product will always be the same.

If a and b are two whole numbers, a + b = b + a and a x b = b x a.

For example, for two whole numbers, 15 and 23, we get:

15 +23 = 38 and 23 + 15 =38

The sum is the same in both cases, although the order changes.

Similarly, for two whole numbers, 10 and 18, we get

10 x 18 = 180 and 18 x 10 =180

The product is identical in both cases, even if the order changes.

Associative Property of Whole Numbers

According to this property, in case of addition or multiplication of three whole numbers, they can be grouped in any order, and the result will be the same.

It means, if p, q, and r are three whole numbers, then we can say, p + (q + r) = (p + q) = r

For example, let’s add three whole numbers: 6, 7, and 8.

Option 1: 6 + (7 + 8) = 6 + 15 = 21

Option 2: (6 + 7) + 8 = 13 + 8 =21

So, regardless of the grouping, the sum remains the same.

Again, for example, multiply three whole numbers: 2, 3, and 4.

Option 1: (2 x 3) x 4 = 6 x 4 = 24

Option 2: 2 x (3 x 4) = 2 x 12 = 24

So, no matter how the numbers are arranged, the product will always be the same. 

Distributive Property of Whole Numbers

This property of whole numbers states that the multiplication of a whole number is distributed over the sum of the other two whole numbers.

It means that if x, y, and z are three whole numbers, then the sum of y and z multiplied by x gives the same result when y and z are multiplied by the same number x and then added.

In other words, x (y + z) = x.y + x.z

Let’s take an example.

There are three whole numbers: 3, 5, and 9.

Now, we calculate 3 x (5 + 9) = 3 x 14 = 42

Again, 3 x 5 + 3 x 9 = 15 +27 = 42

Therefore, we can say: 3 x (5 + 9) = 3 x 5 + 3 x 9

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Additive Identity for Whole Numbers

When zero is added to a whole number, the value of the number remains unchanged.

It means, for any whole number m,

m + 0 = m and 0 + m = m

For example, for a whole number 75, we get 75 + 0 = 0 + 75 = 75.

Multiplicative Identity of Whole Numbers

When we multiply a whole number by 1, the product is the same as the original whole number.

It means, for any whole number k, we get k x 1 = k

For example, for the whole number 28, we get 28 x 1 =28.

Read More - Ratio: Meaning, Formulas, How to Solve, Types, Examples

Multiplication of Whole Numbers by Zero

When multiplied by zero, any whole number gives zero as a result.

It means, for any whole number p, we get p x 0 = 0

For example, for a whole number 36, we get 36 x 0 = 0.

Solved Examples on Whole Numbers

1. Find the mean of the first five whole numbers.

Solution:The first five whole numbers are 0, 1, 2, 3, 4.

The mean of the first five whole numbers =

Sum of the first five whole numbers/Total numbers

= (0 + 1 + 2 + 3 + 4)/5

= 10/5

= 2

Ans. The mean of the first five whole numbers is 2.

2. Using the distributive property of whole numbers, solve the following:

12 (7 + 10)

Solution: 12 (7 + 10)

= 12 x 7 + 12 x 10

= 84 + 120

= 204

3. Identify the whole numbers in the given numbers:

-2, 0, 1/5, 7, 2.63, 18

The whole numbers contain 0, 1, 2, 3, 4, …, and so on. It doesn’t include any negative numbers, decimals, or fractions.

So, the whole numbers in the given set are 0, 7, and 18.

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