CBSE Class 6 Mathematics Whole Numbers Chapter Notes

CBSE Class 6 Whole Numbers Chapter Concepts. Learning the important concepts is very important for every student to get better marks in examinations. The concepts should be clear which will help in faster learning. The attached concepts made as per NCERT and CBSE pattern will help the student to understand the chapter and score better marks in the examinations.

Whole Numbers
The numbers used for counting are called natural numbers. The number that comes immediately before another number in counting is called its predecessor. The number that comes immediately after another number in counting is called its successor. To find the successor of any given natural number, just add 1 to the given number. The value of nothing is represented by the number zero. Example: 3 – 3 = 0.

Natural numbers together with the number zero are called whole numbers. When comparing two whole numbers, the number that lies to the right on the number line is greater. When comparing two whole numbers, the smaller number lies to the left on the number line

Properties of Whole Numbers

1. Closure Property
i) If two whole numbers are added, then the result is again a whole number. Which implies whole numbers are closed with respect to addition.
ii) If two whole numbers are multiplied, then the result is again a whole number. Which implies whole numbers are closed with respect to multiplication.

2. Associative Property
If a, b, c are whole numbers, then
i) a + (b + c) = (a + b) + c
i) ii) a × (b × c) = (a × b) × c
While adding whole numbers, we can group the numbers in any order. This is called the associative property of addition. While multiplying whole numbers, we can group them in any order. This property is called associative property of multiplication.

3. Identity
i) If a is a whole number, a + 0 = 0 + a = a A whole number added to 0 remains unchanged. Thus, 0 is called the additive identity in whole numbers.
ii) If a is a whole number, a × 1 = 1 × a = a
A whole number multiplied to 1 remains unchanged. Thus, 1 is called the multiplicative identity in whole numbers.

4. Commutative Property
If a, b, c are whole numbers, then
i) a + b = b + a ii) a × b = b × a The addition of two whole numbers is the same, no matter in which order they are added. This is called the commutative property of addition.
Similarly, the product of two whole numbers is the same, no matter in which order they are multiplied. This is called the commutative property of multiplication.

5. Distributive Property of Multiplication over Addition
The sum of the products of a whole number with two other whole numbers is equal to the product of the whole number with the sum of the two other whole numbers. This is called the distributive property of multiplication over addition. i.e., If a, b, c are whole numbers, then a × (b + c) = a × b + a × c.

Note

i) Whole numbers are not closed under subtraction and division.

ii) Subtraction and division are not commutative in whole numbers.

iii) No inverse exists for whole numbers.

iii) Associative property does not hold for subtraction and division of whole numbers.