NCERT Solutions for Class 6 Maths Chapter 3: Playing with Numbers - Exercise 3.4

Exercise 3.4

Refer to page 11 for Exercise 3.4 in the PDF

1. Find the common factors of:

(a)  \[20 \] and  \[28 \]

Ans: Factors of   \[20 \] are  \[ = 1,2,4,5,10,20 \]

Factors of  \[28 \] are  \[ = 1,2,4,7,14,28 \]

The numbers  \[1,2 \] and  \[4 \] are factors of both  \[20 \] and  \[28 \]. Therefore,  \[1,2 \] and \[4 \] are the common factors of  \[20 \] and  \[28 \].

(b)  \[15 \] and  \[25 \]

Ans: Factors of  \[15 \] are  \[ = 1,3,5,15 \]

         Factors of  \[25 \] are  \[ = 1,5,25 \]

The numbers  \[1 \] and  \[5 \] are factors of both  \[15 \] and  \[25 \].Therefore,   \[1 \] and  \[5 \] are the common factors of  \[15 \] and  \[25 \].

(c)  \[{\text{35}} \] and  \[{\text{50}} \]

Ans: Factors of  \[{\text{35}} \] are  \[ = 1,5,7,35 \]

        Factors of  \[{\text{50}} \] are  \[ = 1,5,10,25,50 \]

The numbers  \[1 \] and  \[{\text{5}} \] are factors of both  \[{\text{35}} \] and  \[{\text{50}} \]. Therefore,  \[1 \] and  \[{\text{5}} \] are the common factors of  \[{\text{35}} \] and  \[{\text{50}} \].

(d)  \[{\text{56}} \] and  \[{\text{120}} \]

Ans: Factors of  \[{\text{56}} \] are  \[ = 1,2,4,6,7,8,14,28,56 \]

Factors of  \[{\text{120}} \] are  \[ = 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120 \]

The numbers  \[1,2,4,6 \] and  \[8 \] are factors of both  \[{\text{56}} \] and  \[{\text{120}} \]. Therefore,  \[1,2,4,6 \] and  \[8 \] are the common factors of   \[{\text{56}} \] and  \[{\text{120}} \].

2. Find the common factors of:

(a)  \[4,8 \] and  \[12 \]

Ans: Factors of  \[4 \] are  \[ = 1,2,4 \]

        Factors of  \[8 \] are  \[ = 1,2,4,8 \]

        Factors of  \[12 \] are  \[ = 1,2,3,4,6,12 \]

The numbers  \[1,2 \]and  \[4 \] are factors of both  \[4,8 \]and  \[12 \]. Therefore, \[1,2 \]and  \[4 \]  are the common factors of  \[4,8 \]and  \[12 \].

(b)  \[5,15 \]and \[25 \]

Ans: Factors of  \[5 \]are \[ = 1,5 \]

Factors of  \[15 \]are \[ = 1,3,5,15 \]

Factors of  \[25 \]are \[ = 1,5,25 \]

The numbers  \[1 \]and \[5 \] are factors of both  \[5,15 \]and \[25 \]. Therefore,  \[1 \]and \[5 \] are the common factors of \[5,15 \]and \[25 \].

3. Find first three common multiples of:

(a)  \[6 \]and \[8 \]

Ans: Multiples of  \[6 \]are \[6,12,18,24,30,36,42,48,54,60,66,72.... \]

         Multiples of  \[8 \]are \[8,16,24,32,40,48,56,72,80,.... \]

The first three numbers common in both multiples of  \[6 \]and  \[8 \]are  \[24,48 \]and  \[72 \]. Therefore, the numbers \[24,48 \]and  \[72 \]are the first three common multiples

 of  \[6 \]and  \[8 \]. 

(b)  \[12 \]and  \[18 \]

Ans: Multiples of  \[12 \]are  \[12,24,36,48,60,72,84,96,108,120,.... \]

         Multiples of  \[18 \]are  \[18,36,54,72,90,108,126,144,162,180,.... \]

The first three numbers common in both multiples of \[12 \] and  \[18 \]are  \[36,72 \]and \[108 \]. Therefore, the numbers  \[36,72 \]and  \[108 \]are the first three common multiples

 of  \[12 \]and  \[8 \].

4. Write all the numbers less than  \[100 \] which are common multiples of  \[3 \]and \[4 \].

Ans: Multiples of  \[3 \]less than  \[100 \] are \[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99 \]

        Multiples of  \[4 \] less than  \[100 \] are \[4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96 \]

The numbers  \[12,24,36,48,60,72,84 \] and  \[96 \]are the common multiples of \[3 \] and \[4 \] less than  \[100 \].

5. Which of the following numbers are co-prime?

(a)  \[18 \] and  \[35 \]

Ans: Factors of  \[18 \]are  \[ = 1,2,3,6,9,18 \]

         Factors of  \[35 \] are  \[ = 1,5,7,35 \]

The common factor between  \[18 \]and  \[35 \] is  \[1 \] ,therefore  \[18 \]and  \[35 \] , are co-prime numbers.

(b)  \[15 \] and \[37 \]

Ans: Factors of  \[15 \]are  \[ = 1,3,5,15 \]

         Factors of  \[37 \] are  \[ = 1,37 \]

The common factor between  \[15 \]and  \[37 \] is  \[1 \] ,therefore  \[15 \]and  \[37 \] , are co-prime numbers.

(c)  \[30 \] and \[415 \]

Ans: Factors of  \[30 \]are  \[ = 1,2,3,5,6,10,15,30 \]

         Factors of  \[415 \]are  \[ = 1,5,83,415 \]

The common factors between  \[30 \]and  \[415 \]are \[1 \] and  \[5 \],i.e., other than 1,therefore  \[30 \]and \[415 \], are not co-prime numbers.

(d)  \[17 \] and \[68 \]

Ans: Factors of  \[17 \]are  \[ = 1,17 \]

         Factors of  \[68 \]are  \[ = 1,2,4,17,34,68 \]

The common factors between  \[17 \]and  \[68 \]are \[1 \]and  \[17 \],i.e. other than  \[1 \],therefore  \[17 \]and \[68 \], are not co-prime numbers.

(e) \[216 \] and \[215 \]

Ans: Factors of  \[216 \]are  \[ = 1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216 \]

         Factors of  \[215 \] are  \[ = 1,5,43,215 \]

The common factor between  \[216 \]and  \[215 \] is  \[1 \] ,therefore  \[216 \]and \[215 \], are co-prime numbers.

(f)  \[81 \] and \[16 \]

Ans: Factors of  \[81 \]are  \[ = 1,3,9,27,81 \]

         Factors of  \[16 \] are  \[ = 1,2,4,8,16 \]

The common factor between  \[81 \]and  \[16 \] is  \[1 \] ,therefore  \[81 \]and \[16 \], are co-prime numbers.

6. A number is divisible by both  \[5 \] and  \[12 \].By which other number will that number be always divisible?

Ans: Factors of  \[5 \] are  \[ = 1,5 \]

    Factors of  \[12 \]are  \[ = 1,2,3,4,6,12 \]

Because the common factor between  \[5 \]and  \[12 \] is  \[1 \] , therefore  \[5 \]and  \[12 \], are co-prime numbers.

If a number is divisible by co-prime numbers  then that number is always divisible by product of those co-prime numbers. Therefore  \[5 \cdot 12 = 60 \],is the other number by which that number will always be divisible.

7. A number is divisible by  \[12 \] . By what other numbers will that number be divisible?

Ans: If a number ‘b’ is divisible  by a number ‘c’ , then ‘b’ is also divisible by factors of number ‘c’.

Factors of  \[12 \] are  \[ = 1,2,3,4,6,12 \]

Therefore, that number is also divisible by  \[1,2,3,4,6 \] and  \[12 \].

Maths Class 6 Chapter 3 – Playing With Numbers

The NCERT Solutions for Exercise 3.4 and other exercises, that are provided by Vedantu, help to follow and study the new concepts involving numbers. This chapter particularly concentrates on educating students of Class 6 about how to apply common sense and solve puzzle-like problems using mathematical skills. While studying this chapter, a student might need more insights regarding the problems prescribed in the exercises apart from what the school teachers have mentioned. This is where the use of our Maths NCERT solutions Class 6 Chapter 3 Exercise 3.4 will be appropriate. Once the chapter is over, a student can easily find out the solutions by referring to these solutions and understand how to solve any problem quickly during an exam. 

The examples used in different sections such as Class 6 Maths Exercise 3.4 will explain to the students about what kind of problems they will encounter and solve using numerical skills. The prime reason for introducing this chapter in the upgraded syllabus of NCERT Class 6 Maths is to make the students use all the mathematical skills they have learned and use in the previous chapters and classes. On slowly progressing to the next levels, using our NCERT Class 6 Maths Chapter 3 Ex 3.4 solutions will be a great support for a student who wants to learn well and grab the new concepts ideally. 

This chapter has the following sections fabricated scientifically to make a student enter the new dimension of numbers and problems related to it.

Introduction

Factors and Multiples

Prime and Composite Numbers

Tests For Divisibility Numbers 

Common Factors and Common Multiples

Some more divisibility rules

Prime factorization

Highest Common Factor (HCF)

Lowest Common Multiple (LCM)

Problems with HCF and LCM 

What have we discussed?

Introduction

The first section of Class 6 Chapter 3 Playing with Numbers is the introduction to the new concept of arithmetic where the students will face problems regarding numbers and their properties. It is a very interesting introduction configured by the NCERT experts in order to engage the students in the fun of solving mathematical problems using different numbers and their properties. This part of the chapter will provide a few examples through which a student will be eased into the new concepts. The example of marbles in the first segment will tell the students how entities can be positioned to form a particular arrangement. 

By taking the example of 6 marbles, the chapter will tell the students how many ways they can be arranged to form a pattern. The concept of rows and columns will be inculcated by this section. In fact, the concept of factors, which the students have studied and solved problems with earlier, will also be introduced in such a way that they can understand how old concepts are utilized to solve advanced problems in the future. On proceeding further, this section will also tell about a composite number and its factors. It will also recollect how a number can be factorized and its factors are used to solve a problem using them as clues. The Class 6 Maths Exercise 3.4 solutions will also tell you how to use this prime concept in the firsthand to grab hold of a problem and finds its solution. After completing this section, a student will understand how factors and multiples can be used in different types of problems later on.

Factors and Multiples

On proceeding further, the next section will take you to an advanced level of factors and multiples. This section will create a foundation for the students of Class 6 where they will be using the concepts of multiples and factors in solving problems other than LCM and HCF. On revising the old concepts of division and multiplication, the importance of reminders will come into action. In this section, the examples taken by NCERT will discuss how a number, its factors and multiples are found. It will also tell what divisor, dividend, and remainder stands for. 

On proceeding further, the description of factors and multiples will also tell the students how and why factors are less in value than the original number. On the other hand, it will also discuss why the multiples are greater than a particular number. As you can see, this chapter in this book has been designed to impart knowledge about factors and multiples from the grass root level. 

Several games have also been delivered in this segment as examples for the new concepts. The students will be able to engage themselves and find out new concepts brimming in their minds. The concept of the remainder and where it fits into the concepts of multiples and factors will also be cleared occasionally. The Maths Class 6 Chapter 3 Exercise 3.4 solutions designed by the experts of Vedantu will also explain how the samples in the form of examples can be used to solve problems later. By referring these solutions, you will also find out why the examples have been used by the experts of NCERT.

The examples will also direct the students to do some interesting activities. On properly doing the activities by following the teacher’s instructions, they will find out how the concept of factors of a number fits in. This is the beginning of upcoming new concepts of arithmetic that will include factors and multiples at a huge scale. Defining what are factors and how they can be calculated will the prime motive of this section. On proceeding further, a student will discover executed examples. In this segment, different types of problems will be displayed and solved using the simplest methods designed. On referring the Ch 3 Class 6 Maths Ex 3.4 solutions designed by our experts, you will understand how important it is to follow the examples in the first section of this chapter. The exercise following this section will contain problems such as factorization, finding the multiples, and matching the following,

Prime and Composite Numbers

After completely describing the new concepts of factors and multiples in the previous section, you will proceed to this segment where the chapter will describe prime numbers and composite numbers. The prime numbers will have a different set of factors. As this section will progress further, the difference between a prime number and composite number will be discussed and verified using tabular presentations and examples.

A table will discuss how the prime numbers have only two factors, 1 and the number itself. On the other hand, the composite numbers will have more than two factors except these two mentioned above. On setting proper examples, this section will tell you what are the basic differences between prime and composite numbers and how the new problems will be approached. The definition of prime numbers along with examples will help the students to understand what the properties of these numbers are. Similar, the definition and examples of composite numbers will also tell the students about specific features and differences. Proceeding further, the chapter will also discuss how the number ‘1’ is absolutely different from the others. It neither falls in the prime number sets nor in the composite number section. The basic difference between 1 and other prime and composite numbers will be clarified with perfect reasoning. 

The history of Eratosthenes in defining the properties of numbers 1 to 100 will be elaborately discussed with an example. The students will also do an activity mentioned in this chapter to imbibe the new fundamentals of prime and composite numbers properly. A new method called the ‘Sieve of Eratosthenes’ will be discussed and described so that the students can easily find out whether a number is a prime number or a composite one. This section moves forward to a set of examples worked out according to the understanding of a Class 6 student so that the newly learned concepts can be verified and understood. This section is then followed by an exercise where students will find new problems encircling the latest concept they learned about composite and prime numbers.

Tests for Divisibility of Numbers

Moving forward to the next level, the fourth section of this chapter will discuss elaborately how numbers can be divided with their factors. Asking simple questions to the students, this section will tickle the inquisitive mind of the students to think deeper and find out the relation between a number and its factors. On progress, the chapter will tell about how to find the right factors of a number that can be used to divide it without leaving a remainder.

This chapter has been formatted in such a way that it can answer all the questions rising in the young minds about the divisibility of certain numbers. Every number is connected to a few factors and there are ways to find out by using simple mathematical tricks and clues whether it will be divisible by a particular number or not. The next level of this section will teach the students about how to find whether a number is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11.

The solution for Class 6 Maths Chapter 3 Exercise 3.4 in this section will discuss how a number can be judged using simple mathematical tricks without going for a long division method to find out whether it is divisible by the numbers mentioned above. A proper fragmentation of this section regarding the rules of divisibility by 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11 will make it easier for the students to understand and practice on their own. These tricks are developed and displayed in such a way that a student of Class 6 can find out the inner concept and easily implement them later to solve problems in exams. On referring the solution formulated by the Vedantu experts, it will also be easier for you to grab hold of the new concepts of divisibility and find the easiest ways to solve problems without any hassle. This will help the students to save time and use this new knowledge for solving problems in higher classes later. Follow the solutions and techniques mentioned in the solution PDF you have downloaded from the website whenever you want to conveniently find out how the divisibility problems can be solved. Practicing these problems and solutions will help the students to create a strong foundation for this particular section and then proceed to the next section.

Common Factors and Common Multiples

Once the concept of dealing with the factors and multiples of single numbers are over, this section will take you to the next level where the factors of more than one number will be considered. This is the section where you will use your old techniques of LCM and HCF to find out the common multiples and common factors of a set of numbers described in a problem. This section will concentrate on recollecting the old concepts of LCM and HCF. After describing a few solved problems, the students will be able to recollect the old concepts. Performing a few solutions will also make it clear to the students regarding LCM and HCF.

After solving the examples in this section and understanding the connection between factors and multiples to find the divisor of a particular number, the students will be able to understand new concepts perfectly. Using the knowledge of previous sections in this chapter, a new exercise will be delivered. The problems in this section will concentrate on sharpening the skill to find out the factors and multiples of numbers learned by the students in this chapter. This exercise is a simple one and will not impart any challenge to the students as all the questions are based on the old concept of LCM and HCF. Om completing this exercise, a student will be ready to move forward to clarify new advanced concepts of divisibility. On seeking the solutions for Class 6 Maths Exercise 3.4, students will find out how these problems can be solved within a very short period. On downloading the solution for this section, a student can conveniently refer to the solutions provided by the experts and grab hold of the concepts to proceed to advanced sections of this chapter.

Some More Divisibility Rules

The next step in this chapter will take you to an advanced level of factors and multiples. In this section, you will find out how common factors and multiples are found between a set of numbers. Initially, the chapter will start by asking a few questions about what the composite numbers are made of and how the common factors can be found. It will also teach how and why a set of factors can also divide a bigger composite number when its smaller factor has the same set of numbers as factors. The simplest examples will trigger the students to think about how common factors are determined and the concept can be used to find out solutions for different types of problems.

Setting a few simple examples, this section will make the students of Class 6 understand how common factors can be determined. In fact, it will also teach the students the relation between co-prime factors of two composite numbers. For instance, if a number is divisible by two co-prime numbers, then the product of the co-prime numbers will also be able to divide the composite number. On proceeding further to an advanced level, the second concept delivered by this segment is that the sum of two numbers can be divided by a number when both the number can be individually divided by that number without leaving a remainder. In fact, it will also be clear to the students that the difference between the two composite numbers will also be divisible by the same number when the criteria match.

This advanced set of concepts will be very helpful for the students. The only challenge is to understand and apply them to solve problems. For this, considering the NCERT solutions for Class 6 Maths Chapter 3 Exercise 3.4 PDF solution for the particular problems will be ideal. The experts have considered the steps guided by NCERT and fabricated the best way to make the students understand how these problems will be executed. On referring the solutions, a student will be able to perceive the best approaches and get the solutions by picking up the clues all by himself. Consider referring the solution PDF for this section so that you can meet the challenging sums and get the answers without wasting time.

Prime Factorization

On progressing further, the chapter will lead to the new section where the old concepts of prime factorization will be revised. The students will be able to remember what they have learned about prime factorization in the previous classes by going through the examples used in Chapter 3 NCERT Maths solution Class 6 Exercise 3.4. 

These examples will describe how prime factorization of a composite number is done and to what extent a student will proceed. Every step of factorization will lead to the discovery of prime numbers present in a composite number as factors. This step will continue until the factors cannot be segregated into further factors. On viewing the examples, you will be able to understand and recollect the methods you have practiced previously. 

This section will take you to an advanced level of factorization called ‘Factor Tree’. In this method, a student will be directed to use a tree-type configuration to break down bigger composite factors of a number into smaller factors by utilizing flow designs. In fact, the students can also use the old method of factorization when a bigger composite number is prescribed. This section will then lead to an exercise where the students will find a set of problems designed by NCERT for the understanding of a new concept here. By using the solutions developed by experts for Class 6 Maths Chapter 3 Exercise 3.4, you can precisely learn how to approach these problems and solve them accordingly. This exercise will follow a new type of question pattern that will need support from our solutions. These questions are based on simple number fundamentals where a student will have to use his insights to solve them accordingly. Most of the questions are based on hints that a student has to figure out and get accustomed to the patterns so that he can find the solutions of these problems easily in an exam.

Highest Common Factor (HCF)

As directed in the previous sections, you will gradually learn how to find the factors of a composite number using general and new concepts. In this section, you will progress to find the highest common factor of two given numbers. This is the section where the concept of factors & multiples and prime factorization will be used.

It is easy to find the common factors of two numbers but you will need to learn a few tricks to find out the highest common factor. After doing prime factorization of the provided numbers in an example, you will have to find out the biggest common number among the factors of every composite number. 

This section will also describe why the highest common factor (HCF) is also called the greatest common divisor (GCD). GCD is similar to HCF as the biggest factor common to a set of composite numbers will be able to divide the numbers individually. Hence, it can also be considered as the greatest common divisor of given composite numbers.

On learning the concepts of how to calculate HCF or GCD, the section will lead to an exercise where the students will find new problems. In this section, the new patterns of questions will be encountered. On preferring the NCERT Maths Class 6 Chapter 3 Exercise 3.4 solution PDF, you will be able to find out the easiest ways to approach these problems. The experts have explained how to solve the problems as per the guidelines of NCERT so that the students can understand and apply them accordingly. Use this solution for reference in the future and practice how to solve HCF problems.

Lowest Common Multiple (LCM)

On proceeding further, you will reach the section where you will be taught about lowest common multiples. This part of the chapter will describe the definition of the lowest common multiple (LCM) of a set of numbers and how it is calculated. After setting a few examples, this section will tell the students how to approach a problem and solve it using the concepts.

Every example in this section of NCERT Class 6 Maths Chapter 3 Ex 3.4 is elaborately discussed in a stepwise method so that the students can easily understand how a problem is approached and solved. A step is described in such a way that it will inculcate the fundamental of the LCM concept. The numbers in a problem with similar prime factors will have a different approach than those who have different sets of prime numbers in their factors.

A common stepwise method will be taught to the students where more than two composite numbers can be set to calculate their lowest common multiple in an easy way. This method is the quickest way to find the LCM of a set of numbers and should be used in every problem.

Some Problems On HCF and LCM

After grabbing the new concept of performing the LCM of a set of numbers in a composite way, a student will proceed to learn to use these concepts in an arithmetic problem. In this segment, the examples will focus on how the concept of factors & multiples, HCF, and LCM can be used in specific problems. The instances used in this section will be elaborately discussed in simple steps so that the students can understand how the concept is being twisted and used. 

By following our NCERT solution for Class 6 Maths Chapter 3 Exercise 3.4, you can easily find out how this chapter has slowly grown the concept of factors, multiples and factorization so that you can play with numbers. The perfectly-scribed descriptions and problems related to them are ideal to create a conscience. Follow our solutions for the enlisted problems in different exercises so that you can develop a better understanding of the chapter and start solving the problems on your own.

Other Chapters in Class 6 NCERT Maths Book

Chapter 1 Knowing Our Numbers

This chapter will introduce a new concept of numbers. Here, it will be discussed how the digits can be arranged to form different numbers. The formation of the highest and smallest numbers will be discussed by arranging the given digits in particular places. How shifting digits in different places of a number creates a new number will also be described in Chapter 1. 

On moving further, the student will also proceed to understand numbers above 10,000 and 100,000. The introduction of thousand’s place and one lakh’s place will teach the students about how bigger numbers are formed. The numbers containing 7 and 8 digits will be discussed elaborately.

Chapter 2 Whole Numbers

In Chapter 2, the students will be introduced to whole numbers, integers, natural numbers and other related concepts. On proceeding further, the number line will be introduced in the syllabus with a proper description of examples. With the aid of number line, the commutative law of addition, multiplication, subtraction and division will be clearly explained to the young minds.

Moving on to the next level, a student will come to know about the distributive law of multiplication and division. In this section, he will learn how this concept can be used to solve problems with complex multiplication and divisions. 

Moving forward, the students will also learn to find specific patterns in the whole numbers. After observing these patterns, a student will be able to build new concepts of how whole numbers behave. For further reference, you can seek the solutions provided by the Vedantu experts for this particular chapter.

Chapter 3 Playing With Numbers

To be precise, it is an important chapter that will take the students to a new journey of how numbers can be very interesting. The concepts mentioned in the different sections will deliver a new foundation where the students will be able to build logical reasoning power for the future.

Chapter 4 Basic Geometrical Ideas

This is the chapter where a student will be introduced to basic geometric shapes and ideas. It will start with an introduction to the evolution of geometry. The concepts linked to points, straight lines, line segments, and intersecting lines will be delivered. Moving ahead, this chapter will discuss what parallel lines are and how they are formed.

The second section of this chapter will discuss the closed geometrical shapes and figures. It will discuss how the names to particular closed figures are given and their properties. This is where the concept of angles will be introduced. Ideas about triangles and circles will also be discussed.

Chapter 5 Understanding Elementary Shapes

The elementary shapes such as triangles, circles, polygons, etc will be discussed here in an elaborate manner. In this chapter, how a line is drawn using pencil, scale, and a divider will be discussed stepwise. It will also discuss the different types of angles and how to measure them. Moving forward, it will discuss different types of triangles based on their properties. It will also discuss concisely polygons and solid figures.

Chapter 6 Integers

This chapter is a continuation of whole numbers and will discuss integers using the number line concept. The next section of this chapter will tell you about how addition and subtraction are done using a number line. 

Chapter 7 Fractions

After completing whole numbers and integers, this chapter will introduce you to the concepts of fractions. It will tell you about how fractions can also be interpreted using a number line. The description of proper fractions, improper fractions and mixed fractions will be covered in the next section.

In the next part, a student will come to know how fractions are compared to each other. Using different examples, this chapter will discuss how two fractions can be compared. Here, the concept of HCF and LCM will be used for computing different concepts and finding out the relation between two or more given fractions.

Moving forward, the next section will tell you how to perform addition and subtraction of different types of fractions.

Chapter 8 Decimals

The concept of fractions will be taken to the next level by introducing decimals. It will also discuss how a fraction is represented using decimals. On representing fractions with decimals, it will also be shown how to put them on a number line. The next section will tell you how to compare decimals and interpret them into different dimensions such as length and mass. The exercise will tell you how to perform addition and subtraction with decimal numbers.

Chapter 9 Data Handling

This is a new concept of data handling that the students of Class 6 will be introduced to. In this chapter, the student will learn how to collect data, record them, organize them and arrange in a particular format for ease of calculation. 

The next segment will discuss how pictographs are used to handle data and interpret it according to the questions. The students will also learn how to draw a bar graph using data interpreted as taught in the previous sections.

Chapter 10 Mensuration

The concepts delivered about closed figures and polygons will now be used in this chapter of mensuration where a student will have to figure out the dimensions of an object or a shape. Using simple formulas and ideas, the students will be taught how closed figures can be divided into simpler shapes and then perimeter or other dimensions are calculated. New formulas about perimeter and area of rectangles, squares, triangles, and circles will be taught. In the next segment, this section will also teach about how the area of irregular shapes can be determined using graph papers.

Chapter 11 Algebra

In the 11th chapter of Class 6 NCERT Maths book, the concept of algebra will be introduced. The students will learn what a variable is and how a formula of variables can be derived from the given hints. There will be elaborate examples and exercises to help the student understand the new concepts and practice them accordingly. First, the common rules will be used to make you understand about variables. In this section, the commutative law of addition will also be clarified. The next step will be to introduce the concept of creating formulas according to the given conditions. A small introduction about equations of single variables and how to solve them will be taught.

Chapter 12 Ratio and Proportion

The 12th chapter will discuss the definitions of ratio and proportion. With suitable examples, the students will understand what the symbols are and what their interpretations are. On using a few examples, the application of ratio and proportion will be discussed. On progressing further, the relation between two ratios will also be discussed. You will also learn how to use the unitary method to solve problems. Follow the examples given in this chapter. You can also use our solution for this chapter to make it easier for you. On solving the problems in its exercises, you will be able to understand your depth regarding this new chapter.

Chapter 13 Symmetry

Symmetry is an interesting chapter where a student will be taught how to find symmetry in different objects and figures. First, it will discuss how to identify whether an object is symmetrical or not. On following the examples, you will know how to draw a line of symmetry and check whether the provided figure is symmetric or not. On progressing further, you will also learn how to draw more than one symmetric line and find out whether an object or a figure is symmetric or not. The exercises will show different images and shapes where you will have to use your knowledge and solve the problems.

Chapter 14 Practical Geometry

This is the last chapter of your NCERT Class 6 Maths Book that will teach you how to draw closed figures using the tools in your geometry box. This chapter will discuss the easiest ways to draw a circle first in the first section. The students will also practice it in the first exercise. They will also learn how to measure or draw a line segment. They will learn how to draw perpendiculars using geometry tools. On learning how to use a ruler and a compass, students will be able to draw such figures with confidence. They will also learn how to draw different angles using a ruler and a compass.

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Vedantu has always taken a step ahead for the students by formulating the ideal NCERT solutions for Class 6 Maths Chapter 3 Exercise 3.4 so that the students can find learning new concepts at ease. It is our experts who have found the right ways to describe a problem and find a solution that a Class 6 student will easily understand. Download Maths NCERT solutions Class 6 Chapter 3 Exercise 3.4 PDF from our website and take references to understand the enlisted problems. Grow your knowledge and bridge the gap to solve any problem regarding numbers during exams.