NCERT Maths Class 6 Chapter 2 pdf: Students will be able to understand the core parts of Class 6 chapter 2 Maths Whole Numbers by using SpeEdLabs’s CBSE Class 6 Maths Revision Notes. This will help them prepare for the exam well. The Class 6 Maths Chapter 2 Revision notes will also help them to understand how sums are calculated from an examination perspective. The Whole Numbers Class 6 notes PDF can be downloaded for a better understanding and practice of the concepts in this chapter.
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Whole Numbers Class 6 Chapter 2 Maths Notes
In this lesson, we have studied the natural numbers from 1 to 10. A whole number is a set of natural numbers including zero. 0 is the smallest whole number. Whole numbers are 0, 1, 2, 3 … All natural numbers are whole numbers, but all whole numbers are not natural numbers.
CBSE Class 6 Chapter 2 Maths: Overview
The concepts of Class 6th Math Whole Numbers form the foundation for higher classes’ Maths concepts. Therefore, you should be aware of the concepts you will learn in this chapter.
Here are some of the important topics covered in Class 6 Maths Chapter 2:
- Introduction to Predecessor and successor
- Whole Numbers
- The Number Line
- Addition on the number line
- Subtraction on the number line
- Multiplication on the number line
- Properties of Whole Numbers
- Closure property
- Commutativity of addition and multiplication
- Associativity of addition and multiplication
- Distributivity of multiplication over addition
- Patterns in Whole Numbers
- Patterns Observation
Notes of CBSE Class 6 Whole Numbers
- Counting numbers are called natural numbers.
- 1, 2,3,4,5………. are natural numbers
- Predecessor: A number that is obtained by subtracting 1 from a given number is called the predecessor of the given number
- Successor: A Number which is obtained by adding 1 from a given number is called the successor of the given number.
Whole Numbers
- On adding the predecessor of 1, i.e., 0 in the queue of natural numbers, we get the whole number.
- 0, 1, 2,3,4,5……. are whole numbers.
- All whole numbers are natural numbers but all natural numbers are not whole numbers.
The Number Line
A number line is a picture of a graduated straight and horizontal line in which numbers are written. A number written on the left-hand side of the number line is lesser and number written on the right-hand side of the number line is greater. Let’s us look into some solved example problems.
Find 12 × 35 using distributivity.
12 × 35 = 12 × (30 + 5)
= 12 × 30 +12 × 5
= 360 + 60 = 420.
Calculate – (2 + 3) + 4 =? = 5+ 4 = 9.
Adding on the Number Line
- Suppose a+b is to be found from the number line. Then mark a unit on the number line and move the b units towards the right of a.
For example: The addition of 2 and 3
- Move 3 units towards the right of 2, we will get 5
Subtracting on the Number Line:
- Suppose a−b is to be found from the number line then mark a on the number line then move b unit towards the left of a
For example: The subtraction of 5 and 3
- Move 3 units towards the left of 5, we will get 2
Properties of the Whole Number
- Closure Property
- The whole numbers are closed under addition means the sum of two whole numbers is always a whole number.
For example: 5 and 8 are whole numbers and their sum 13 is also a whole number.
- The whole numbers are also closed under multiplication, which means the multiplication of two whole numbers is always a whole number.
For example: 5 and 8 are whole numbers and their multiplication 40 is also a whole number.
- Commutative Property
- Whole numbers are commutative under addition. It means that they can be added in any order and the result will be the same.
For example: 4+2=6 and 2+4=6.
- Whole numbers are also commutative under multiplication. It means that they can be multiplied in any order and the result will be the same.
For example: 5×3=15 and 3×5=15.
- Associative Property
- Whole numbers are associative under addition means rearranging the whole number in parenthesis and then adding will not affect the answer.
For example:
(12+5)+6
=17+6
=23
And
12+ (5+6)
=12+11
=23
- Whole numbers are associative under multiplication means rearranging the whole number in parenthesis and then multiplying will not affect the answer.
For example:
(2×5)×3
=10×3
=30
And
2× (5×3)
=2×15
=30
- Distributivity of Multiplication Over Addition
- When a whole number is multiplied by the sum of the whole number then the distributive property of multiplication over addition is used.
For example:
8× (5+2)
= (8×5) + (8×2)
=40+16
=56
- Additive Identity
- If adding 0 to any whole number gives the whole number itself, then 0 is the additive identity.
For example: 9+0=9
- Multiplicative Identity
- If multiplying 1 to any whole number gives the whole number itself, then 1 is the multiplicative identity.
For example: 6×1=6
Main Takeaways from Class 6 Chapter 2 Whole Numbers
- The numbers 1, 2, 3 … which we use for counting are known as Natural Numbers. If you add 1 to a natural number, we get its Successor.
- When 1 is subtracted from a natural number, then you get its Predecessor.
- Every natural number has a Successor.
- All whole numbers cannot be natural numbers, but all natural numbers are always whole numbers.
- The whole numbers can be represented on a number line. A number of operations like division, multiplication, addition, and subtraction can be performed on whole numbers on the number line.
- Addition corresponds to moving to the right of the number line, whereas subtraction corresponds to moving to the left. Multiplication matches to making jumps of equal intervals on the number line starting from zero.
- When two whole numbers are added, you will always get a whole number. Similarly, if two whole numbers are multiplied, you always get a whole number. Hence, we can say that the whole numbers are closed under addition and also under multiplication. However, whole numbers are not closed under division and under subtraction because when you subtract or divide two whole numbers, you do not get a whole number as a final product.
- Division by zero is not defined.
- Zero plays as the identity solution for the addition of whole numbers. The whole number 1 is identified for the multiplication of any number of whole numbers.
- You can add two whole numbers in any given order; you will get the same result at the end. You can multiply two whole numbers in any order; you will get the same result at the end. We can say that the addition and multiplication properties of whole numbers are commutative.
- Multiplication is the distributive property of whole numbers.
- Commutativity, associativity, and distributivity properties of whole numbers help to simplify calculations and can be used without being aware of them.
- Patterns with numbers are not only interesting but are useful especially for verbal calculations and help us to understand the properties of numbers better.
Why Choose SpeEdLabs for Class 6 Maths Notes?
By providing experienced and skilled tutors, SpeEdLabs increases students’ online engagement. To help students grasp the concepts of whole numbers, revision notes on whole numbers are provided. Furthermore, students are provided with subjective and objective tests, regular homework, and assignments in Class 6 Maths that enable them to progress academically. By analysing the results of the tests, parents can determine how their children are progressing.
Also Read –
- Knowing our Numbers: Class 6 Chapter 1 Maths Notes
- Food: Where does it come from? Class 6 Notes
- Components of Food: Class 6 Chapter 2 Science Notes
- Fibre to Fabric: Class 6 Chapter 3 Science Notes
- Sorting Materials into Groups Class 6 Chapter 4 Science Notes
- Separation of Substances: Class 6 Chapter 5 Science Notes
- Changes Around Us: Class 6 Chapter 6 Science Notes
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