Class 6 Chapter 2: Whole Numbers

# Class 6 Chapter 2: Whole Numbers

Important Concepts and Formulas

1.      Numbers such as 1, 2, 3, 4, 5, 6, … are called natural numbers. The smallest natural number is 1 and the greatest natural number does not exist.

2.      The natural numbers along with ‘0’ form the collection of whole numbers. ‘0’ is the smallest whole number. The greatest whole number does not exist.

3.      Properties of addition of whole numbers:
·        Closure Property: (a + b) or (b + c) or (a + c) is a whole number. For example, 5 + 8 = 13
·        Commutative Property: a + b = b + a For example, 4 + 3 = 7 = 3 + 4
·        Associative Property: (a + b) + c = a + (b + c) For example, 2 + (3 + 7) = (2 + 3) + 7 = 12
·        Additive Identity: a + 0 = a = 0 + a ‘0’ is called the additive identity for whole numbers. For example, 6 + 0 = 6 = 0 +6

4.      Properties of subtraction of whole numbers:
·        a – b is not always a whole number. For example, 5 – 8 = -3. Subtraction is not closed for whole numbers.
·        Subtraction is not commutative. a – b ≠ b – a. For example, 3 – 2 ≠ 2 – 3
·        Subtraction is not associative for whole numbers. For example, (5 – 4) – 3 ≠ 5 – (4 – 3)
·        a – 0 = a. For example, 5 – 0 = 5. This is known as the property of 0 for subtraction of whole numbers.

5.      Properties of multiplication of whole numbers:
·        Closure Property: a × b or b × c is a whole number. For example, 5 × 7 = 35
·        Commutative Property of Multiplication: a × b = b × a For example, 5 × 8 = 8 × 5
·        Identity Property of Multiplication: a × 1 = a
·        Zero Property of Multiplication: a × 0 = 0
·        Associative Property of Multiplication: (a × b) × c = a × (b × c) For example, (2 × 3) × 7 = 2 × (3 × 7)
·        Distributive Property of Multiplication: a × (b + c) = a × b + a × c For example, 9 × (3 + 2) = 9 × 3 + 9 × 2

6.      Properties of division of whole numbers:
·        a ÷ b is not always a whole number. For example, 13 ÷ 2 = decimal number. Division is not closed for whole numbers
·        Division is not commutative for whole numbers. a ÷ b ≠ b ÷ a. For example, 10 ÷ 5 ≠ 5 ÷ 10
·        Division is not associative for whole numbers. For example, (10 ÷ 5) ÷ 2 ≠ 10 ÷ (5 ÷ 2)
·        Identity Property of Division: a ÷ 1 = a
·        Zero Property of Division: 0 ÷ a = 0, where a ≠ 0

7.      Patterns in numbers are useful for verbal calculations.
·        Number of dots such as 6, 8, 12, etc., can be arranged as a rectangle.
·        Number of dots such as 4, 9, 16, 25, etc., are called square numbers.
·        Number of dots such as 3, 6, 10, etc., can be arranged as a triangle.