Courses

Courses for Kids

Free study material

Store

Talk to our experts

1800-120-456-456

RS Aggarwal Solutions Class 6 Chapter-3 Whole Numbers (Ex 3D) Exercise 3.4

RS Aggarwal Solutions

RS Aggarwal Solutions Class 6 Chapter-3 Whole Numbers (Ex 3D) Exercise 3.4

RS Aggarwal Solutions Class 6 Chapter-3 Whole Numbers (Ex 3D) Exercise 3.4 - Free PDF

Free PDF download of RS Aggarwal Solutions Class 6 Chapter-3 Whole Numbers (Ex 3D) Exercise 3.4 solved by Expert Mathematics Teachers on Vedantu. All Exercise 3.4 Questions with Solutions for Class 6 Maths RS Aggarwal to help you to revise complete syllabus and score more marks. Register for online coaching for IIT JEE (Mains & Advanced) and other Engineering entrance Exams.

Every NCERT Solution is provided to make the study simple and interesting on Vedantu. Subjects like Science, Maths, English,Hindi will become easy to study if you have access to NCERT Solution for Class 6 Science , Maths solutions and solutions of other subject.

RS Aggarwal Solutions Class 6 Chapter-3 Whole Numbers (Ex 3D) Exercise 3.4

‘Whole Number’ is Chapter 3 of Class 6 Mathematics. In this Chapter, students will learn that the Whole Numbers are the part of the Number System which includes all the positive Integers, starting from 0 to infinity. It can also be said that, all the Whole Numbers are real numbers, but not all the real numbers are Whole Numbers. Thus, according to RS Aggarwal solutions, Whole Numbers can be defined as a set of natural numbers including 0. Whole Numbers are represented by W, whereas, natural numbers and Integers are represented by N and Z respectively. In simple words, all the natural numbers are Whole Numbers. All counting numbers are Whole Numbers. All the positive Integers including 0 are Whole Numbers. Also, all Whole Numbers are real numbers. Integers are the negative of natural numbers and the set of Whole Numbers. So, Integers include both positive and negative numbers including 0. Real numbers are a group of all these types of numbers, i.e. Natural numbers, Whole Numbers, Integers and fractions.The full set of natural numbers along with ‘0’ are called Whole Numbers. The Examples are: 0, 11, 251, 3700, 99999, 881100, etc.

There are many properties of Whole Numbers which are based on Mathematical operations such as addition, subtraction, division and multiplication that are defined in RS Aggarwal Chapter 3 Exercise 3.4 solutions. If we add or multiply two Whole Numbers the result will be a Whole Number itself. On the other hand, if we subtract two Whole Numbers, the result may not be a Whole Number, i.e. it can also be an Integer. Also, upon the division of two Whole Numbers the result can be a fraction sometimes.

Properties of Whole Numbers.

The properties of Whole Numbers along with their proofs and properties are given below:

Closure Property

According to the Closure Property of Whole Numbers they can be closed under addition and multiplication, which means, if x and y are two Whole Numbers then x(y) or x + y will also be a Whole Number.

Example:

3 and 8 are Whole Numbers.

3 + 8 = 11 (a Whole Number)

3 × 8 = 24 ( a Whole Number)

This proves that the Whole Numbers are closed under addition and multiplication.

Commutative Property of Addition and Multiplication

According to the Commutative property of Addition and Multiplication, the sum and product of two Whole Numbers will be the same even if the order in which they are added or multiplied is changed, i.e., if x and y are two Whole Numbers, then x + y = y + x and x . y = y . x

Proof:

Let us take two Whole Numbers 5 and 7.

9 + 3 = 12

3 + 9 = 12

Thus, 3 + 9 = 9 +3 .

Also,

5 × 7 = 35

7 × 5 = 35

Thus, 5 × 7 = 7 × 5

So the Whole Numbers are commutative under addition and multiplication.

Additive identity

According to the Additive Identity when a Whole Number is added to 0, its value remains unchanged, i.e., if x is a Whole Number then x + 0 = 0 + x = x

Proof:

Consider two Whole Numbers 0 and 12.

0 + 12 = 12

12 + 0 = 12

Here, 0 + 12 = 12 + 0

Therefore, 0 is called the additive identity of Whole Numbers.

Multiplicative identity

According to the Multiplicative Identity, when a Whole Number is multiplied by 1, its value remains unchanged, i.e., if x is a type of Whole Number then x.1 = x = 1.x

Proof:

Consider two Whole Numbers 1 and 7.

1 × 7 = 7

7 × 1 = 7

Here, 1 × 7 = 7 = 7 × 1

Therefore, 1 is the multiplicative identity of Whole Numbers.

Associative Property

According to the Associative Property, when Whole Numbers are added or multiplied as a set, they can be grouped in any order, and the result will be the same, For Example, if x, y and z are Whole Numbers then x + (y + z) = (x + y) + z and x. (y.z)=(x.y).z

Proof:

Let us take three Whole Numbers 2, 3, and 5.

2 + (3 + 5) = 2 + 8 = 10

(2 + 3) + 5 = 5 + 5 = 10

Thus, 2 + (3 + 5) = (2 + 3) + 5

2 × (3 × 5) = 2 × 15 = 30

(2 × 3) × 5 = 6 × 5 = 30

Here, 2 × (3 × 5) = (2 × 3) × 5

Hence, the Whole Numbers are associative under addition and multiplication.

Distributive Property

According to the Distributive Property, If x, y and z are three Whole Numbers, the distributive property of multiplication over addition is x. (y + z) = (x.y) + (x.z), and like this, the distributive property of multiplication over subtraction is x. (y – z) = (x.y) – (x.z)

Proof:

Let us consider three Whole Numbers 9, 10 and 6.

9 × (10 + 6) = 9 × 16 = 144

(9 × 10) + (9 × 6) = 90 + 54 = 144

Here, 9 × (10 + 6) = (9 × 10) + (9 × 6)

Also,

9 × (10 – 6) = 9 × 4 = 36

(9 × 10) – (9 × 6) = 90 – 54 = 36

So, 9 × (10 – 6) = (9 × 10) – (9 × 6)

Hence, the distributive property of Whole Numbers is verified.

Multiplication by zero

If an when a Whole Number is multiplied to 0, the result is always 0, i.e., x.0 = 0.x = 0

Example:

0 × 5 = 0

5 × 0 = 0

Here, 0 × 5 = 5 × 0 = 0

Thus, any Whole Number when multiplied by 0, gives 0.

Division by zero

Division of a Whole Number by o is not defined, i.e., if x is a type of Whole Number then x/0 is not defined.

All the solutions for questions of Exercise 3.4 related to above properties are explained and described in detail in RS Aggarwal Class 6. Students can directly refer to RS Aggarwal for the solutions related to properties questions from Exercise 3.4.

FAQs on RS Aggarwal Solutions Class 6 Chapter-3 Whole Numbers (Ex 3D) Exercise 3.4

1. Where can I find useful study resources for Class 6 Maths Chapter 3 Whole Numbers?

You can find everything you need on the Vedantu app or website. These resources are created by professionals in the field and the content is accurate and reliable. Students can find revision notes, important questions, question papers, and a whole lot more! These study materials are completely free and there is no cost involved. All students have to do is sign in and then you will be able to download what you want in PDF format. You can take advantage of these free resources that will surely help you ace your Exams.

2. Why is studying from the RS Aggarwal book essential for Class 6 Maths Chapter 3?

RS Aggarwal is designed keeping in mind the needs of Class 6 students. The book follows the latest CBSE syllabus. Hence, it can be referred to while preparing for Class 6 Exams. It explains concepts in a clear and easy to understand manner. It is one of the best books when it comes to strengthening your basics and fundamentals. It has numerous solved Examples and Exercises that add to a student’s learning. It covers everything that is asked in Class 6 Examination. Hence, students are advised to study from this book for better preparation of the Examination.

3. What are the topics covered in Chapter 3 of the Class 6 RS Aggarwal Math book?

Chapter 3- Whole Systems begins with an introduction of Number Systems. There are different kinds of numbers on the number line such as natural numbers, Whole Numbers, Integers, rational and irrational numbers. Students will further learn about Whole Numbers in detail with the help of different Exercises. They will also learn about different properties of Whole Numbers and will study how to perform addition, subtraction, division, and multiplication on Whole Numbers following different rules.The last section of the book contains several Exercises for students to solve.

4. Is it necessary to solve all the Exercises of RS Aggarwal Whole Number Chapter?

It is always better to solve all the Chapter Exercises as these give you practice. Math is not a subject that you can just read or memorize. It requires hard work and practice. RS Aggarwal has Examples and Exercises after every section. After going through each section, go through the solved Examples and understand them completely. Then move on to the Exercises and try to solve them. There are chances of the same questions coming in the Examination so students are advised to practice the sums in the Exercises well.

5. How to score well in Class 6 Math Chapter 3 Whole Numbers?

Practicing Math is the only way to score well in Class 6 Math. Solve all the Chapter Exercises. This will improve your problem-solving ability and improve your speed and efficiency. You can make notes of important formulas, definitions, and equations in a notebook and revise them regularly. Solve sample papers and question papers of previous years within a time limit. This will get you familiar with the paper pattern, question type as well as improve your time management skills. Revise regularly so that you’re able to retain all you’ve studied for a longer period.