Whole Numbers

Whole numbers are the numbers we use to count things. They start with 0 and go on to 1, 2, 3, and so on. Whole numbers are also called natural numbers.

Whole numbers are used in many different ways. We use them to count how many people are in a room, how many apples are in a basket, and how many days are in a week. We also use whole numbers to measure things, such as how long a piece of string is or how heavy a box is.

Whole numbers are important because they help us to understand the world around us. They allow us to compare different things and to make sense of the world around us.

Here are some examples of whole numbers:

• 0
• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10

Whole Numbers Definition

Whole Numbers Definition

Whole numbers are the numbers we use to count things. They are the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and so on.

Examples of Whole Numbers

Here are some examples of whole numbers:

• 0: The number of apples in an empty bowl
• 1: The number of people in a room with one person
• 2: The number of eyes on a human face
• 3: The number of legs on a stool
• 4: The number of wheels on a car
• 5: The number of fingers on one hand
• 6: The number of sides on a cube
• 7: The number of days in a week
• 8: The number of notes in an octave
• 9: The number of months in a school year
• 10: The number of commandments

Whole Numbers Properties

Whole numbers are the natural numbers 0, 1, 2, 3, …, and so on. They are also known as counting numbers. Whole numbers have several important properties that make them useful in mathematics.

1. Closure under addition and multiplication

This means that when you add or multiply two whole numbers, the result is always a whole number. For example, 3 + 4 = 7 and 5 × 2 = 10.

2. Commutativity of addition and multiplication

This means that the order in which you add or multiply two whole numbers does not matter. For example, 3 + 4 = 4 + 3 and 5 × 2 = 2 × 5.

3. Associativity of addition and multiplication

This means that the way you group three or more whole numbers when adding or multiplying them does not matter. For example, (3 + 4) + 5 = 3 + (4 + 5) and (5 × 2) × 3 = 5 × (2 × 3).

4. Identity elements for addition and multiplication

The identity element for addition is 0, and the identity element for multiplication is 1. This means that when you add 0 to any whole number, the result is that whole number, and when you multiply 1 by any whole number, the result is that whole number. For example, 3 + 0 = 3 and 5 × 1 = 5.

5. Distributive property of multiplication over addition

This means that when you multiply a whole number by a sum of two or more whole numbers, the result is the same as if you multiplied the whole number by each of the addends separately and then added the products. For example, 3 × (4 + 5) = (3 × 4) + (3 × 5).

These are just a few of the important properties of whole numbers. These properties make whole numbers a useful tool for counting, measuring, and performing other mathematical operations.

Difference Between Whole Numbers and Natural Numbers

Whole Numbers

• Whole numbers are the numbers we use to count things. They start with 0 and go on to 1, 2, 3, and so on.
• Whole numbers can be positive or negative. Positive whole numbers are the numbers we use to count things we have, while negative whole numbers are the numbers we use to count things we owe or are missing.
• Whole numbers are also called integers.

Natural Numbers

• Natural numbers are the numbers we use to count things that can only be counted in whole units. They start with 1 and go on to 2, 3, 4, and so on.
• Natural numbers are always positive. There is no such thing as a negative natural number.
• Natural numbers are a subset of whole numbers. All natural numbers are whole numbers, but not all whole numbers are natural numbers.

Examples

• The numbers 0, 1, 2, 3, 4, and 5 are all whole numbers.
• The numbers -1, -2, -3, -4, and -5 are all negative whole numbers.
• The numbers 1, 2, 3, 4, and 5 are all natural numbers.
• The number 0 is not a natural number because it is not positive.

Solved Examples

Solved examples are a powerful tool for learning and understanding new concepts. They provide a step-by-step demonstration of how to solve a problem, making it easier to grasp the underlying principles and apply them to similar situations. Here are a few examples of solved examples:

1. Mathematics:

• Example: Solve the equation 2x + 5 = 15.

Solution:

• Subtract 5 from both sides: 2x + 5 - 5 = 15 - 5
• Simplify: 2x = 10
• Divide both sides by 2: 2x/2 = 10/2
• Simplify: x = 5

Frequently Asked Questions on Whole Numbers

What are whole numbers?

Whole Numbers

Whole numbers are the numbers we use to count things. They are the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and so on.

Examples of Whole Numbers

Here are some examples of whole numbers:

• The number of apples in a basket: 5
• The number of people in a room: 10
• The length of a piece of string: 12 inches
• The weight of a person: 150 pounds
• The amount of money in a wallet: $20

Can whole numbers be negative?

Whole numbers, by definition, are non-negative integers. This means that they cannot be negative. The set of whole numbers includes the numbers 0, 1, 2, 3, and so on.

Here are some examples of whole numbers:

• 0
• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10

What are the properties of whole numbers?

Properties of Whole Numbers

Whole numbers are the numbers 0, 1, 2, 3, …, and so on. They are also known as the natural numbers. Whole numbers have several important properties, including:

• Closure under addition and multiplication. This means that when two whole numbers are added or multiplied, the result is always a whole number. For example, 3 + 4 = 7 and 3 × 4 = 12.
• Commutativity of addition and multiplication. This means that the order in which two whole numbers are added or multiplied does not matter. For example, 3 + 4 = 4 + 3 and 3 × 4 = 4 × 3.
• Associativity of addition and multiplication. This means that the way in which three or more whole numbers are grouped together for addition or multiplication does not matter. For example, (3 + 4) + 5 = 3 + (4 + 5) and (3 × 4) × 5 = 3 × (4 × 5).
• Identity elements for addition and multiplication. The identity element for addition is 0, and the identity element for multiplication is 1. This means that when any whole number is added to 0, the result is the same whole number, and when any whole number is multiplied by 1, the result is the same whole number. For example, 3 + 0 = 3 and 3 × 1 = 3.
• Inverse elements for addition and multiplication. Every whole number has an inverse element for addition, which is the number that, when added to the whole number, results in 0. The inverse element for addition of a whole number n is -n. For example, the inverse element for addition of 3 is -3, because 3 + (-3) = 0. Every whole number except 0 has an inverse element for multiplication, which is the number that, when multiplied by the whole number, results in 1. The inverse element for multiplication of a whole number n is 1/n. For example, the inverse element for multiplication of 3 is 1/3, because 3 × 1/3 = 1.

These properties of whole numbers are essential for understanding the basic operations of arithmetic. They are also used in more advanced mathematics, such as algebra and calculus.

Examples of the Properties of Whole Numbers

The following are some examples of the properties of whole numbers:

• Closure under addition and multiplication: 3 + 4 = 7 and 3 × 4 = 12.
• Commutativity of addition and multiplication: 3 + 4 = 4 + 3 and 3 × 4 = 4 × 3.
• Associativity of addition and multiplication: (3 + 4) + 5 = 3 + (4 + 5) and (3 × 4) × 5 = 3 × (4 × 5).
• Identity elements for addition and multiplication: 3 + 0 = 3 and 3 × 1 = 3.
• Inverse elements for addition and multiplication: 3 + (-3) = 0 and 3 × 1/3 = 1.

These properties of whole numbers are essential for understanding the basic operations of arithmetic. They are also used in more advanced mathematics, such as algebra and calculus.

Is 10 a whole number?

Is 10 a Whole Number?

Yes, 10 is a whole number.

Definition of a Whole Number

A whole number is a number that represents a whole quantity, without any fractional parts. Whole numbers are the numbers 0, 1, 2, 3, and so on.

Which numbers are not whole numbers?

Numbers that are not whole numbers are called non-whole numbers. They include:

Here are some examples of non-whole numbers:

• The square root of 2 is an irrational number. This means that it cannot be expressed as a fraction of two integers. It is approximately equal to 1.414213562373095.
• Pi is a transcendental number. This means that it is not algebraic, meaning it cannot be expressed as the root of a polynomial equation with integer coefficients. It is approximately equal to 3.141592653589793.
• The number e is a transcendental number. This means that it is not algebraic, meaning it cannot be expressed as the root of a polynomial equation with integer coefficients. It is approximately equal to 2.718281828459045.

Are all whole numbers real numbers?

Yes, all whole numbers are real numbers. The set of real numbers includes all rational numbers (numbers that can be expressed as a fraction of two integers) and all irrational numbers (numbers that cannot be expressed as a fraction of two integers). Whole numbers are a subset of the rational numbers, so they are also real numbers.

Are all natural numbers, whole numbers?

Yes, all natural numbers are whole numbers.

Natural numbers are the numbers we use to count things. They start with 1 and go on to 2, 3, 4, and so on.

Whole numbers are the numbers that include 0 and all the natural numbers. So, the whole numbers are 0, 1, 2, 3, 4, and so on.

Examples:

• 1, 2, 3, 4, 5 are all natural numbers.
• 0, 1, 2, 3, 4, 5 are all whole numbers.

Are natural numbers and counting numbers the same?

Natural numbers are the numbers we use to count things. They start with 1 and go on to 2, 3, 4, and so on. Counting numbers are also the numbers we use to count things, but they start with 0 and go on to 1, 2, 3, 4, and so on.

So, are natural numbers and counting numbers the same? The answer is yes, but there is a slight difference between the two. Natural numbers do not include 0, while counting numbers do.

Conclusion:

Natural numbers and counting numbers are the same, but there is a slight difference between the two. Natural numbers do not include 0, while counting numbers do.