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**NCERT solutions for class 6 maths chapter 2 Whole Numbers** provided here that are created by expert team at careers360. These solutions are developed considering the latest syllabus of CBSE. Students looking for NCERT Class 6 solution for Maths chapter 2 pdf can access the solutions for all topics in this article. The Whole Number chapter is a part of the number system unit. Referring to NCERT 6 Maths solution chapter 2 aid to clear doubts and prepare well. CBSE NCERT solutions for whole numbers class 6 are covering the solutions for the questions from every concept of NCERT. Representation and properties of whole numbers are important topics.

This Story also Contains

- NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers - Important Formula
- NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers - Important Topics
- NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers
- NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers (Intext Questions and Exercise)
- NCERT Solutions for Class 6 Subject wise
- NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers - Topics
- NCERT Solutions for Class 6 Mathematics Chapter wise
- Key Features Of NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers

Class 6 NCERT Maths solutions of chapter 2 are prepared as per questions available in NCERT Class 6 Syllabus. There are **3 exercises in this chapter containing 38 questions**. NCERT Class 6 maths solution chapter 2 contains the answer to all the 38 problems. CBSE NCERT solutions for Class 6 Maths chapter 2 Whole Numbers are answering every problem related to the whole numbers. Along with all these, you can click on the link given to get NCERT Solutions for other classes and subjects.

Whole numbers: 0, 1, 2, 3, and so on.

A factor of a number is a number that divides the other number without leaving a remainder.

A multiple of a number is a number that is exactly divisible by the given number.

The number 1 is a factor of every number and has only one factor.

Even numbers are those that are divisible by 2, while odd numbers are not divisible by 2.

Divisibility rules:

A number is divisible by 2 if its unit digit is 0, 2, 4, 6, or 8.

A number is divisible by 3 if the sum of its digits is divisible by 3.

A number is divisible by 4 if the digits in its tens and units place are divisible by 4.

A number is divisible by 5 if its unit digit is 0 or 5.

A number is divisible by 6 if it satisfies the divisibility rules for both 2 and 3.

A number is divisible by 8 if the number formed by its hundreds, tens, and units placed is divisible by 8.

A number is divisible by 9 if the sum of its digits is divisible by 9.

A number is divisible by 10 if its units place digit is 0.

A number is divisible by 11 if the difference between the sum of its digits in odd places and the sum of its digits in even places is either 0 or divisible by 11.

The LCM (Least Common Multiple) of two numbers, a and b, is the smallest positive integer that is divisible by both a and b.

The HCF (Highest Common Factor) of two numbers, a and b, is the largest positive integer that divides both a and b.

LCM(A, B) HCF(A, B) = AB

Properties of whole numbers:

Closure Property of Addition: a + b is a whole number

Closure Property of Multiplication: a × b is a whole number

Associativity of Addition:

(a + b) + c = a + (b + c)Associativity of Multiplication:

a × (b × c) = (a × b) × cDistributive Property of Multiplication over Addition:

a × (b + c) = a × b + a × cDistributive Property of Multiplication over Subtraction:

a × (b - c) = a × b - a × c.Existence of Multiplicative Identity:

a + 0 = a = 0 + aExistence of Multiplicative Identity:

a × 0 = 0 = 0 × aUnit Multiplication:

a × 1 = a = 1 × a

**Natural Numbers:** The numbers 1, 2, 3,... which we use for counting are known as natural numbers. Natural numbers represent the set of positive integers starting from 1 and extending infinitely. They are the most basic numbers used for counting and ordering objects.

**Successor and Predecessor:** If you add 1 to a natural number, we get its successor. If you subtract 1 from a natural number, you get its predecessor. Successor and predecessor are terms used to denote the number that comes after or before a given number in the natural number sequence.

**Existence of Successor and Predecessor**: Every natural number has a successor, meaning that we can always find the next number in the sequence by adding 1. Every natural number except 1 has a predecessor, which is the number that comes before it in the sequence.

Whole Numbers: If we add the number zero to the collection of natural numbers, we get the collection of whole numbers. Whole numbers include 0 along with the set of natural numbers. Thus, the numbers 0, 1, 2, 3,... form the collection of whole numbers.

**Successor and Predecessor of Whole Numbers**: Every whole number has a successor, meaning there is always a next number in the sequence. Every whole number except zero has a predecessor, which is the number that comes before it in the sequence.

**Relationship between Natural Numbers and Whole Numbers:** All natural numbers are whole numbers because they are included in the set of whole numbers. However, all whole numbers are not natural numbers since zero is a whole number but not a natural number.

**Number Line Representation: **A number line is a line marked with points at equal intervals, starting from 0 and extending in both positive and negative directions. It provides a visual representation of numbers. Natural and whole numbers can be represented on a number line, allowing for easy visualization and operations such as addition, subtraction, and multiplication.

**Operations on Number Line: **Addition on a number line corresponds to moving to the right, whereas subtraction corresponds to moving to the left. Multiplication corresponds to making jumps of equal distance starting from zero. Number lines aid in understanding and performing these operations.

**Closure Property:** Adding two whole numbers always gives a whole number. Similarly, multiplying two whole numbers always gives a whole number. This property is known as closure, which means that a particular operation performed on two whole numbers results in another whole number. However, whole numbers are not closed under subtraction and division.

**Division by Zero:** Division by zero is not defined. It is considered undefined because it leads to contradictory or nonsensical results. Dividing any number by zero is not permissible in mathematics.

Free download **NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers PDF **for CBSE Exam.

**NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers Topic: Predecessor and Successor **

**Q1 ** Write the predecessor and successor of 19; 1997; 12000; 49; 100000.

**Answer: **The predecessor and successor of:

**19:**- Predecessor : 18
- Successor : 20

**1997:**- Predecessor : 1996
- Successor : 1998

**12000**- Predecessor : 11999
- Successor : 12001

**49:**- Predecessor : 48
- Successor : 50

**100000:**- Predecessor : 99999
- Successor : 100001

**Q2 ** Is there any natural number that has no predecessor?

**Answer: ** Every natural number has a predecessor. Although, it is interesting to know that the predecessor of 1 is not a natural number.

**Q3 ** Is there any natural number which has no successor? Is there a last natural number?

**Answer: **Every natural number has a successor. There is no last natural number. There are infinite natural numbers.

**NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers Topic: Whole Numbers **

**Q1 ** Are all natural numbers also whole numbers?

** Answer: **Yes, all the natural numbers are whole numbers. But, all whole numbers are not natural numbers.

Natural numbers = 1, 2, 3, 4, ....

Whole numbers= 1, 2, 3, 4, ....

**Q2 ** Are all whole numbers also natural numbers?

**Answer: **No, all whole numbers are not natural numbers. 0 is a whole number, but it is not a natural number.

**Q3 ** Which is the greatest whole number?

**Answer: **There are infinite whole numbers. Hence, there is no greatest whole number. Every whole number you can think of has a successor, which is greater than than the number.

**NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers Exercise: 2.1 **

**Q1 ** Write the next three natural numbers after 10999.

**Answer: ** Given, 10999

The next three natural numbers are:

10999 + 1 = 11000

10999 + 2 = 11001

10999 + 3 = 11002

**Q2 ** Write the three whole numbers occurring just before 10001.

**Answer: **Given, 10001

Three whole numbers occurring just before are:

11001 - 1 = 10000

11001 - 2 = 9999

11001 - 3 = 9998

** Q3 ** Which is the smallest whole number?

** Answer: **The smallest whole number is 0. It has no whole number predecessor.

** Q4 ** How many whole numbers are there between 32 and 53?

** Answer: **Given numbers are: 32 and 53

Number of whole numbers between 32 and 53 = (53-32) - 1 = 21 - 1 = 20

There are 20 whole numbers between 32 and 53

** Q5 ** Write the successor of :

(a) 2440701 (b) 100199 (c) 1099999 (d) 2345670

** Answer: **The successor of following numbers are:

- (a) 2440701
- (b) 100199
- (c) 1099999
- (d) 2345670

** Q6 ** Write the predecessor of :

(a) 94 (b) 10000 (c) 208090 (d) 7654321

** Answer: ** The predecessor of the following numbers are:

- (a) 94
- (b) 10000
- (c) 208090
- (d) 7654321

** Answer: ** The number on the left on the number line is smaller than the number that is on the right on the number line.

- (a) 530, 503
- is on the left.

- (b) 370, 307
- is on the left.

- (c) 98765, 56789
- is on the left.

- (d) 9830415, 10023001
- is on the left.

** Answer: **

(a) Zero is the smallest natural number. - ** False. 0 is not a natural number. **

(b) 400 is the predecessor of 399. - ** False. 400 is the successor of 399. **

(c) Zero is the smallest whole number. - ** True. **

(d) 600 is the successor of 599. - ** True **

(e) All natural numbers are the whole numbers.- ** True. **

(f) All whole numbers are natural numbers.- ** False. 0 is a whole number but not a natural number. **

(g) The predecessor of a two-digit number is never a single-digit number.- ** False. The predecessor of 10 is 9. **

(h) 1 is the smallest whole number. - ** False. 0 is the smallest whole number. **

(i) The natural number 1 has no predecessor. - ** True. **

(j) The whole number 1 has no predecessor. - ** False. The whole number 1 has 0 as its predecessor. **

(k) The whole number 13 lies between 11 and 12.- ** False. The whole number 13 lies on the right side of 12 on the number line. **

(l) The whole number 0 has no predecessor.- ** True. **

(m) The successor of a two-digit number is always a two-digit number- ** False. The successor of 99 is 100. **

** NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers Topic: Properties of Whole Numbers **

** Q ** Find : 7 + 18 + 13; 16 + 12 + 4.

** Answer:** 7 + 18 + 13; 16 + 12 + 4

** NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers Exercise: 2.2 **

** Q1 ** Find the sum by suitable rearrangement:

(a) 837 + 208 + 363 (b) 1962 + 453 + 1538 + 647

** Answer:** Sum by suitable rearrangement:

- (a) 837 + 208 + 363
- (b) 1962 + 453 + 1538 + 647

** Answer: ** The product of the following by suitable rearrangement are:

- (a)
- (b)
- (c)
- (d)
- (e)
- (f)

** Answer: **

- (a)

Using Distributive law. - (b)

Using Commutative under multiplication

Using Distributive law. - (c)

Using Distributive law. - (d)

Using distributive law.

** Answer: ** The product of the folllowing using suitable properties are:

- (a)

Using distributive law. - (b)

Using distributive law. - (c)

Using Distributive law. - (d)

Using Distributive law.

** Answer: ** Amount of petrol filled on Monday =

Amount of petrol filled on Tuesday =

Total amount of petrol =

Cost of 1 litre of petrol =

Cost of of petrol =

** Answer: **Amount of milk supplied in the morning =

Amount of milk supplied in the evening =

Total amount of petrol =

Cost of 1 litre of milk =

Cost of of milk =

** Answer: **

(i) | (c) Distributivity of multiplication over addition. |

(ii) | (a) Commutativity under multiplication. |

(iii) | (b) Commutativity under addition. |

** NCERT solutions for class 6 maths chapter 2 Whole Numbers Topic: Patterns in Whole Numbers **

** Q1 ** Which numbers can be shown only as a line?

** Answer: ** can be shown only as a line. They cannot be shown as a rectangle or square or triangle.

** Q2 ** Which can be shown as squares?

** Answer: ** and can be shown as squares.

4: 2 rows and 2 columns.

9: 3 rows and 3 columns

** Q3 ** Which can be shown as rectangles?

** Answer: ** can be shown as rectangles. (Note: We are not counting squares as rectangles here)

** Q4 ** Write down the first seven numbers that can be arranged as triangles, e.g. 3, 6, ...

** Answer: ** 3, 6, 10, 15, 21, 28, 36.

** Q5 ** Some numbers can be shown by two rectangles, for example

Give at least five other such examples.

** Answer: ** We can represent a number by two rectangles. for example 12 = 3 x 4 or 2 x 6

five other such examples are :

- 24 = 12 x 2 or 24 = 6 x 4
- 18 = 9 x 2 or 18 = 3 x 6
- 15 = 15 x 1 or 15 = 3 x 5
- 30 = 10 x 3 or 30 = 5 x 6
- 40 = 10 x 4 or 40 = 5 x 8.

** NCERT solutions for class 6 maths chapter 2 Whole Numbers Exercise: 2.3 **

** Q1 ** Which of the following will not represent zero:

(a) 1 + 0 (b) 0 × 0 (c) 0/ 2 (d) (10-10)/2

** Answer: **

- (a) 1 + 0

It does not represent zero. - (b) 0 × 0

It represents zero. - (c)

It represents zero. - (d)

It represents zero.

** Answer: ** If the product of 2 whole numbers is zero, then one of them is definitely zero.

For example, 0 x 2 = 0 and 17 x 0 = 0

If the product of 2 whole numbers is zero, then both of them may be zero.

0 x 0 = 0

However, 2 x 3 = 6 (Since numbers to be multiplied are not equal to zero, the result of the product will also be non-zero.)

**Answer: ** If the product of 2 numbers is 1, then both the numbers have to equal to 1.

For example, 1 x 1 = 1

However, 1 x 6 = 6

Clearly, the product of two whole numbers will be 1 in the situation when both numbers to be multiplied are 1.

** Q4 ** Find using distributive property :

(a) 728 101 (b) 5437 1001 (c) 824 25 (d) 4275 125 (e) 504 35

** Answer: **

- (a) 728 101= 728 (100 + 1)
- = 728 100 + 728 1
- = 72800 + 728
- = 73528

- (b) 5437 1001 = 5437 (1000 + 1)
- = 5437 1000 + 5437 1
- = 5437000 + 5437
- = 5442437

- (c) 824 25 (800 + 24) 25 = (800 + 25 - 1) 25
- =800 25+25 x 25-1 25
- = 20000 + 625 - 25
- = 20000 + 600
- = 20600

- (d) 4275 125 = (4000 + 200 + 100 - 25) 125
- = 4000 125 + 200 125 + 100 125 - 25 125
- = 500000 + 25000 + 12500 - 3125
- = 534375

- (e) 504 35 = (500 + 4) 35
- = 500 x 35 +4 35
- = 17500 + 140
- = 17640

**Answer: ** 123456 8 + 6 = 987648 + 6 = 987654

1234567 8 + 7 = 9876536 + 7 = 9876543

Yes, the pattern works.

As 123456 = 111111 + 11111 + 1111 + 111 + 11 + 1,

123456 8 = (111111 + 11111 + 1111 + 111 + 11 + 1) 8

= 111111 8 + 11111 8 + 1111 8 + 111 8 + 11 8 + 1 8

= 888888 + 88888 + 8888 + 888 + 88 + 8

= 987648

And,

123456 8 + 6 = 987648 + 6 = 987648

2.1 Identities and Special Properties of Whole Numbers.

2.2 Introduction to Whole Numbers.

2.3 Patterns in Whole Numbers.

2.4 Properties of Whole Numbers.

Chapters No. | Chapters Name |

Chapter - 1 | |

Chapter - 2 | Whole Numbers |

Chapter - 3 | |

Chapter - 4 | |

Chapter - 5 | |

Chapter - 6 | |

Chapter - 7 | |

Chapter - 8 | |

Chapter - 9 | |

Chapter -10 | |

Chapter -11 | |

Chapter -12 | |

Chapter -13 | |

Chapter -14 |

**Comprehensive Coverage:** The class 6 chapter 2 provides comprehensive coverage of the topic of whole numbers, ensuring that all important concepts and subtopics are included. It covers the definition of whole numbers, their properties, representation on a number line, and operations such as addition, subtraction, and multiplication.

**Conceptual Clarity:** The chapter focuses on providing conceptual clarity to students. It explains the fundamental concepts of whole numbers in a clear and concise manner, enabling students to grasp the underlying principles and theories effectively.

**Problem-solving Approach: **The chapter adopts a problem-solving approach, offering numerous examples and practice exercises to reinforce understanding. It encourages students to apply the concepts learned to solve real-life problems and mathematical problems related to whole numbers.

**Step-by-step Solutions:** The chapter provides step-by-step solutions to exercises and examples, guiding students in the correct approach to solving problems. This systematic approach assists students in understanding the process of solving mathematical problems related to whole numbers.

**Practice Exercises: **The chapter includes a variety of practice exercises, ranging from basic to challenging, to reinforce the understanding of whole numbers. These exercises allow students to practice and apply their knowledge, enabling them to develop proficiency in working with whole numbers.

**Also Check - **

**NCERT Books and NCERT Syllabus**

*Keep Working hard and happy learning! *

1. What is a number line as per Chapter 2 of NCERT Solutions for Class 6 Maths?

According to NCERT Solutions for Class 6 Maths Chapter 2, a number line is a graphical representation of a straight and horizontal line that is graduated, and numbers are marked on it. Numbers written on the left-hand side of the number line are smaller, while numbers written on the right-hand side are greater.

2. What is the meaning of multiplicative identity in Chapter 2 of NCERT Solutions for Class 6 Maths?

As per NCERT Solutions for Class 6 Maths Chapter 2, the multiplicative identity is a number that, when multiplied by another whole number, gives the same whole number. In this context, the number 1 is the multiplicative identity, as a × 1 = a (where 'a' is any whole number). NCERT Solutions provide students with clear definitions and explanations of mathematical concepts in line with the CBSE syllabus. Several examples presented in the solutions will assist students in solving problems related to mathematical relations with ease.

3. What are the topic covered in NCERT Class 6 Maths Chapter 2

The following topics are covered in the NCERT syllabus Class 6 Maths chapter 2

- Whole Numbers
- The Number Line
- Properties Of Whole Numbers
- Patterns in Whole Numbers

4. Explain the properties of whole numbers in NCERT Solutions for Class 6 Maths Chapter 2.

The properties of whole numbers, as covered in NCERT Solutions for Class 6 Maths Chapter 2, are as follows:

- Addition and multiplication of any two whole numbers result in a whole number.
- Subtraction and division of any two whole numbers may or may not result in a whole number.

Students are provided with solved examples before each exercise-wise problem to help them understand the problem-solving methods efficiently. By practicing problems from the NCERT textbook, students can enhance their conceptual understanding, which is essential for performing well in the annual exams.

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