**CBSE Class 6 Maths Notes Chapter 2 Whole Numbers**

Whole numbers are the set natural numbers including with 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

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**The different topics covered in CBSE Class 6 Mathematics Chapter 2 are tabulated below:**

Exercise | Topics |

2.1 | Introduction |

2.2 | Whole Numbers |

2.3 | The Number Line |

2.4 | Properties of Whole Numbers |

2.5 | Patterns in Whole Numbers |

**Ex : 2.1 – **** Introduction**

**Natural numbers:**The counting numbers 1,2, 3,4, are called natural numbers.**Predecessor:**If we subtract 1 from a natural number, what we get is its predecessor. For example, the predecessor of 10 is 10 – 1 = 9.**Successor:**If we add 1 to a natural number, what we get is its successor. For example, the successor of 9 is 9 + 1 = 10.- The natural number 1 has no predecessor in natural numbers.
- There is no largest natural number
- If we add the number 0 to the collection of whole numbers. Thus, the numbers 0, 1, 2, 3,… form the collection of whole numbers, natural numbers, what we get is the collection
- We regard 0 as the predecessor of 1 in the collection of whole numbers.
- Every whole number has a successor.
- Every whole number except zero has a predecessor.
- All the natural numbers are whole numbers but all the whole numbers are not a natural number. [0 is a whole number but not a natural number]

**Ex : 2.2 – **** Whole Numbers**

- Natural numbers along with zero form the collection of whole numbers.
**0**,1,2,3,4,5… are called whole numbers.

**Ex : 2.3 – **** Number Line**

- It is the infinitely long line containing all the whole numbers.
- The line starts at zero, and any two consecutive whole numbers have the same distance between them.

**Operations on a number line**

**⇒ Addition on a number line**. For example, addition of 1 and 5 (1 + 5 = 6). First, locate 1 on the number line. Then moving 5 places to the right will give 6.

**⇒ Subtraction on a number line**. For example, subtraction of 3 from 7 (7 – 3 = 4). First, locate 7 on the number line. Then moving 3 places to the left will give 4.

**⇒ Multiplication on a number line**. For example product of 3 and 4 (3 × 4 = 12). Start from 0 and skip 3 places to the right 4 times.

**⇒ Division on a number line**. For example 6 ÷ 3 = 2. Start from 6 and subtract 3 for a number of times till 0 is reached. The number of times 3 is subtracted gives the quotient.

**Ex : 2.4 – **** Properties of Whole Numbers**

**Properties of Operators: Commutative Associative and Distributive**

**Division by zero**

Division of any whole number by 0 is **not **defined.

Mathematical operations are simplified due to certain properties that every number follows. They are:

**Commutative property**

Addition and multiplication are commutative for whole numbers. i.e whole numbers can be added or multiplied in any order.

For e.g: 2 + 3 = 5 = 3 + 3 × 4 = 12 = 4 × 3

**Associative property**

Associativity of addition and multiplication

For eg: (5 +6) + 4 = 15 = 5 + (6 + 4)

(2 × 3) × 4 = 24 =2 × (3 × 4)

**Distributive Property**

With distributivity property, 4 × (5 + 3) can be written as (4 × 5) + (4 × 3)

Here, 4 × (5 + 3) = 4 × 13 = 52

Also, (4 × 5) + (4 × 3) = 20 + 32 = 52

There exists certain numbers, when included in mathematical operations like addition and multiplication, the value of the operation remains unchanged. Such numbers are called as identities.

**Additive Identity**

Additive identity gives the same whole number when added to another whole number.

Zero is the additive identity as a + 0 = a, (a is any whole number).

**Multiplicative Identity**

Multiplicative identity gives the same whole number when multiplied by another whole number.

1 is the Multiplicative identity as a × 1 = a, (a is any whole number)

**Ex : 2.5 – **** Patterns in Whole Numbers**

- Some numbers can be arranged in elementary shapes: a line, a rectangle, a square and a triangle only made up of dots.
- Every number can be arranged as a line.
- Some numbers like 6 can be arranged as a rectangle. Note that the number of rows should be smaller than the number of columns. Also, the rectangle should have more than 1 row.
- Some numbers like 4, 9 can be arranged as a square.
- Note that every square number is also a rectangular number.
- Some numbers like 3, 6 can be arranged as a triangle.
- Note that the triangle should be right-angled and its two sides must be equal.
- The number of dots in the rows starting from the bottom row should be like 4, 3,2, 1. The top row should always have 1 dot.
- The patterns with numbers are not only interesting but also useful especially for mental calculations and help us understand the properties of numbers better.

**Numbers between square numbers**

- Between 2 successive square numbers there exists
**2n**non-square numbers. Between, n² and (n + 1)² there are non-square numbers. Here is a whole number. - For example, between 9 (3)² and 16 (4)², there are 10 , 11, 12, 13, 14, 15 which is 6 = 2 × 3 numbers.

**Adding odd numbers**

- Sum of the first n natural odd numbers gives n² which is a perfect square.
- For example : Sum of first 5 natural odd numbers ⇒ 1 + 3 + 5 + 7 + 9 = 25 = 5²

**Properties of Operators: Closure Properties**

**Closure property**

Whole numbers are closed under addition and also under multiplication.

3 | + | 1 | = | 4, a whole number |

5 | + | 3 | = | 8, a whole number |

4 | × | 4 | = | 16, a whole number |

9 | × | 2 | = | 18, a whole number |

Whole numbers are **not **closed under subtraction and division.

8 | – | 5 | = | 3, a whole number |

5 | – | 8 | = | -3, not a whole number |

12 | ÷ | 4 | = | 3, a whole number |

9 | ÷ | 2 | = | 9/2, not a whole number |

**CBSE Notes for Class 6 Maths Free Download for All Chapters**

CBSE Class 6 Maths Study Notes | CBSE Class 6 Maths Study Notes |

Knowing our Numbers Class 6 Notes Chapter 1 | Decimals Class 6 Notes Chapter 8 |

Whole Numbers Class 6 Notes Chapter 2 | Data Handling Class 6 Notes Chapter 9 |

Playing with Numbers Class 6 Notes Chapter 3 | Mensuration Class 6 Notes Chapter 10 |

Basic Geometrical Ideas Class 6 Notes Chapter 4 | Algebra Class 6 Notes Chapter 11 |

Understanding Elementary Shapes Class 6 Notes Chapter 5 | Ratio And Proportion Class 6 Notes Chapter 12 |

Integers Class 6 Notes Chapter 6 | Symmetry Class 6 Notes Chapter 13 |

Fractions Class 6 Notes Chapter 7 | Practical Geometry Class 6 Notes Chapter 14 |

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