# NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers (Ex 2.3) Exercise 2.3

## NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers (Ex 2.3) Exercise 2.3

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Highly proficient mentors of Extramarks have crafted the NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3.  These NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3 are excellent study materials for students because they will help them review key concepts like whole numbers, natural numbers, predecessor and successor relationships, and many more.The number line, applying mathematical operations to it, and the characteristics of whole numbers will all be covered in NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3.

The answers to all the problems in the NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3 are thorough and exact. Each and every answer is laid out step-by-step. These inquiries will put a student’s capacity for logic and reasoning to the test. The NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3 have all been thoroughly examined and further explained. The following is a list of the exercises that are part of the NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3:

• NCERT solutions Class 6 Maths Chapter 2 Ex 2.1
• NCERT solutions Class 6 Maths Chapter 2 Ex 2.2
• NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3

A thorough study guide is available in the form of NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3 based on Whole Numbers for students who are striving to perform well in examinations. The numerous characteristics of whole numbers, including their closure, commutativity, associativity, and distributivity, are covered in these NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3. For students, Maths is made simple and easy by these features of the NCERT solutions. On the Extramarks website and mobile application, there are links available to access the NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3.

### Access Other Exercises of Class 6 Maths Chapter 2

 Chapter 2 – Whole Numbers Exercises Exercise 2.1 8 Question & Solutions Exercise 2.2 7 Questions & Solutions

## NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers (Ex 2.3) Exercise 2.3

Students will learn about various properties, including the commutative property of addition and subtraction, the closure property, the associative property of addition and multiplication, and many more, in NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3. These properties will help students understand whole numbers. The analysis of NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3 centred on Whole Numbers is provided below, divided in accordance with the topics covered in each exercise.

• Class 6 Maths Chapter 2 Ex 2.1 – 8 Questions
• Class 6 Maths Chapter 2 Ex 2.2 – 7 Questions
• Class 6 Maths Chapter 2 Ex 2.3 – 5 Question

Number lines, the characteristics of whole numbers, and patterns in whole numbers are a few of the significant topics addressed in NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3. Relevant examples are used to discuss each of the qualities. Additionally, each of these qualities’ proofs will be clearly described for the benefit of the students.

The NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3 consist of a total of 20 questions related to the theme of Whole Numbers, 15 of which are divided into sums that are easy to medium-level difficulties. The remaining 5 problems are complicated and call for creative problem-solving at the same time. The NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3 are comprehensive and detailed.

### Access NCERT Solutions for Class 6 Maths Chapter 2 – Whole Numbers

There are numerous mathematical formulas in the NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3, and there are some key ideas that will be covered in this section, including the properties of whole numbers and performing mathematical operations on a number line. Students will analyse the nature of numbers with the aid of these characteristics. These ideas in the NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3 can be covered by students one at a time:

• Any order can be used when adding or multiplying two whole numbers. It is asserted that addition and multiplication are commutative for whole numbers.
• On the number line, moving to the right represents addition, and moving to the left represents subtraction. Making equal-distance hops from a zero starting point is what multiplication entails.
• A whole number is always the result of adding two whole numbers. A whole number can also be produced by multiplying two whole numbers.

### Class 6 Maths Exercise 2.3

The solutions to the questions in NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3 are focused on the subject of Whole Number Patterns. It is well known that using dots, full numbers can be organised into simple geometric designs. To help students understand how the questions should be answered, mentors of Extramarks have prepared NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3. By working through these NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3, students can improve and practise their responses in accordance with the examination point of view.

### Maths Chapter 2 Whole Numbers

Students are given all of the crucial information on whole numbers in these NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3. Students would not get confused while studying. This is due to the fact that all of the NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3 are written in straightforward language to enable students to understand exactly how to handle complex problems. With plenty of exercises and examples, students can truly obtain the best answers without needing to go through any other reference materials or manuals.

### Representation of Whole Numbers on a Number Line

The courses created by qualified teachers are available on the Extramarks website and mobile application and allow for the proper understanding of the Number Line. This greatly aids in providing the ideal solution so that the students can develop the best concept for how to approach the problem. In other words, it becomes simple for the students to understand the ideal concept for the Number Line. Students can use the NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3 to improve their academic performance.

### Order of Numbers

All positive integers from 0 to infinity are included in the group of numbers known as whole numbers. The number line has these numbers. They are all real numbers as a result. All whole numbers are real numbers, however not all real numbers are whole numbers, it can be argued. As a result, the set of natural numbers plus zero can be used to define whole numbers. The category of whole numbers and the negative of natural numbers is known as integers. Thus, integers can be either positive or negative, including 0. Natural numbers, whole numbers, integers, and fractions all fall under the category of real numbers. The NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3 explain this theme in detail.

### Addition on the Number Line

Students can perform the addition operation on small numbers visually with the aid of addition on a number line. An illustration of numbers on a straight line where the value of the numbers rises as one moves from left to right is called a number line. On a number line, several arithmetic operations can be carried out, including addition, subtraction, multiplication, and division. The NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3 provide detailed explanations of this topic.

### Subtraction on the Number Line

Smaller numbers can be easily subtracted when doing so on a number line. Students must move towards the left side of a number line while subtracting numbers from it. Students must always start with the minuend and work their way to the left based on the subtrahend number provided.The number from which a subtraction is made is called the “minuend,” and the number from which a removal is made is called the “subtrahend.” With the assistance of NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3, students can fully comprehend these ideas.Multiplication on the Number Line

The phrase “multiplication on a number line” describes the use of a number line to apply the multiplication operation to a given set of numbers. A number line is a graphic representation of numbers on a horizontal, endless line that extends on both sides, with the numbers spaced at equal intervals. The addition, subtraction, division, and multiplication operations can be carried out using a number line. On a number line, the numbers get larger as one moves to the right; they get smaller as one gets to the left. The NCERT Solutions Class 6 Maths Chapter 2 Exercise 2.3 include descriptive explanations of this topic.

### Properties of Whole Numbers

In this Class 6 Maths Chapter 2 Exercise 2.3, Extramarks has made an effort to give the students all the knowledge they need to understand the characteristics of whole numbers. It is much simpler for students to understand the ideal approach to take when solving various challenges. As a result, it greatly aids students in fully grasping the subject without any issues.

### Patterns in Whole Numbers

With the aid of quality reference materials offered by Extramarks, students can learn all the patterns in whole numbers. It, therefore, encourages the growth of mathematical interest when the instructions are followed exactly. NCERT Class 6 Maths solutions ensure that students never face any difficulties.

### The Role of Zero

All positive counting numbers, including zero, are included in the set of whole numbers.

0 is a whole number as well. Between the positive and negative numbers on the number line, zero is used as a placeholder in this instance. Since zero has no value and can be neither positive nor negative, it solely serves as a placeholder.

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Q.1

$\begin{array}{l}\mathrm{Which}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{will}\mathrm{not}\mathrm{represent}\mathrm{zero}:\\ \left(\mathrm{a}\right)1+0\left(\mathrm{b}\right)0×0\left(\mathrm{c}\right)\text{\hspace{0.17em}\hspace{0.17em}}\frac{0}{2}\text{}\left(\mathrm{d}\right)\frac{10–10}{2}\end{array}$

Ans.

Option (a) will not represent zero.

Q.2 If the product of two whole numbers is zero, can we say that one or both of them will be zero? Justify through examples.

Ans.

Yes, product of two whole numbers is zero if one or both of them will be zero.
Example: 0 × 2 = 0
0 × 0 = 0

Q.3 If the product of two whole numbers is 1, can we say that one or both of them will be 1? Justify through examples.

Ans.

Product of two whole numbers will be 1 if and only if both of them will be 1. For example: 1 × 1 = 1.

Q.4 Find using distributive property:
(a) 728 × 101 (b) 5437 × 1001
(c) 824 × 25 (d) 4275 × 125
(e) 504 × 35

Ans.

(a) 728 × 101 = 728 × (100 + 1)
= 728 × 100 + 728 × 1
= 72800 + 728
= 73,528

(b) 5437 × 1001 = 5437 × (1000 + 1)
= 5437 × 1000 + 5437 × 1
= 5437000 + 5437
= 54,42,437

(c) 824 × 25 = 824 × (20 + 5)
= 824 × 20 + 824 × 5
= 16480 + 4120
= 20,600

(d) 4275 × 125 = 4275 × (100 + 20 + 5)
= 4275 × 100 + 4275 × 20 + 4275 × 5
= 427500 + 85500 + 21375
= 5,34,375

(e) 504 × 35 = 35 × (500 + 4)
= 35 × 500 + 35 × 4
= 17500 + 140
= 17,640

Q.5 Study the pattern:
1 × 8 + 1 = 9 1234 × 8 + 4 = 9876
12 × 8 + 2 = 98 12345 × 8 + 5 = 98765
123 × 8 + 3 = 987
Write the next two steps. Can you say how the pattern works?

Ans.

The next two steps are:
123456 × 8 + 6 = 987654
1234567 × 8 + 7 = 9876543
The working pattern is as given below:
1 × 8 + 1 = 9
12 × 8 + 2 = (11 + 1) × 8 + 2
= 11 × 8 + 1 × 8 + 2
= 88 + 9 + 1
= 88 + first term + 1
= 98
123 × 8 + 3 = (111 + 11 + 1) × 8 + 3
= 111 × 8 + 11 × 8 + 1 × 8 + 3
= 888 + 88 + 8 + 2 + 1
= 888 + second term + 1
= 987
1234 × 8 + 4 = (1111 + 111 + 11 + 1) × 8 + 4
= 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8 + 4
= 8888 + 888 + 88 + 8 + 3 + 1
= 8888 + third term + 1
= 9876
12345 × 8 + 5 = (11111 + 1111 + 111 + 11 + 1) × 8 + 5
= 11111 × 8 +1111 × 8 + 111 × 8 +11 × 8
+ 1 × 8 + 4 + 1
= 88888 + 8888 + 888 + 88 + 8 + 4 + 1
= 88888 + fourth term + 1
= 98765
In this way we can follow this pattern to find next terms.