Introduction

Whole numbers are a set of numbers that include all natural numbers and zero. They are used in counting, measuring, and ordering and form the foundation of arithmetic.

1. What are Whole Numbers?

Whole Numbers: {0, 1, 2, 3, 4, 5, 6, ...}

• Start from 0
• No end – infinite set

Natural Numbers vs Whole Numbers

Property	Natural Numbers	Whole Numbers
Starts from	1	0
Includes 0?	No	Yes

2. Representation on Number Line

Whole numbers can be shown on a number line starting from 0 and moving to the right.

3. Properties of Whole Numbers

Closure Property

• Addition and multiplication: Closed
• Subtraction and division: Not closed

Commutative Property

• a + b = b + a
• a × b = b × a

Associative Property

• (a + b) + c = a + (b + c)
• (a × b) × c = a × (b × c)

Distributive Property

a × (b + c) = a × b + a × c

Identity Elements

• Additive Identity: 0 → a + 0 = a
• Multiplicative Identity: 1 → a × 1 = a

4. Patterns in Whole Numbers

• Square numbers: 1, 4, 9, 16...
• Triangular numbers: 1, 3, 6, 10...

5. Number Line Applications

• Successor: Number after (e.g., successor of 7 is 8)
• Predecessor: Number before (e.g., predecessor of 6 is 5)
• No predecessor for 0

6. Addition, Subtraction, and Multiplication

Addition:

Move right on number line. Example: 4 + 3 = 7

Subtraction:

Move left on number line. Example: 7 - 2 = 5

Multiplication:

Repeated addition. 3 × 4 = 3 + 3 + 3 + 3 = 12

7. Division of Whole Numbers

• 4 ÷ 2 = 2 (Defined)
• 5 ÷ 0 = Not defined
• a ÷ 1 = a

8. Common Misconceptions

• 0 has a predecessor – Incorrect
• Division by 0 is allowed – Incorrect
• Subtraction is commutative – Incorrect

9. Real-Life Applications

• Counting money, people, objects
• Assigning serial numbers
• Measuring quantities in whole units

10. Practice Questions

1. Write the first ten whole numbers.
2. Use a number line to show: 3 + 5
3. Verify: 4 × (2 + 3) = 4 × 2 + 4 × 3
4. Is subtraction commutative for whole numbers?
5. What is the predecessor of 1?

11. Key Points

• Whole numbers: {0, 1, 2, 3, ...}
• 0 is the smallest whole number
• No largest whole number
• Addition and multiplication are commutative and associative
• Distributive law helps in simplifying multiplication

12. Concept Map

         Whole Numbers
         /     |      \
 Properties  Number Line  Operations
   |           |            |
Associative  Successor   Addition
Commutative  Predecessor Subtraction
Distributive             Multiplication
    

Conclusion

Whole numbers form the building blocks of arithmetic. Their properties, patterns, and operations are essential for solving problems and understanding advanced mathematical concepts.