NCERT Solutions for Class 6 Maths, Chapter 7 - Fractions

When expressing a situation of counting parts to write a fraction, it must be ensured that all parts are equal. A fraction is a number representing a part of a whole. The whole may be a single object or a group of objects. This chapter will help you in understanding the concepts of fractions.

In NCERT Maths Book Class 6, Chapter 7 Solutions, as you progress through the chapter you will learn fractions. A fraction means a part of a group or of a region. For example – 5/12 is a fraction. Here 5 is called the numerator and 12 is called the denominator. As you move further in this chapter you will learn proper, improper and mixed fractions, equivalent fractions, simplest form and comparing fractions. Towards the end of this chapter, you will study the addition and subtraction of fractions.

Let’s take a look at topics and sub-topics of class 6 Maths Chapter 7, Fractions

7.1 Introduction

7.2 A Fraction

7.3 Fraction On A Number Line

7.4 Proper Fractions

7.5 Improper And Mixed Fractions

7.6 Equivalent Fractions

7.7 Simplest Form Of A Fraction

7.8 Like Fractions

7.9 Comparing Fractions

              7.9.1 Comparing Like Fractions

              7.9.2 Comparing Unlike Fractions

7.10 Addition And Subtractions Of Fractions

              7.10.1  Adding or subtracting like fractions

              7.10.2  Adding and subtracting fractions

In Class 6 Maths NCERT Solutions Chapter 7, you will learn – 

Section 7.2 –  This section will brief you about fractions. A fraction is a number representing a part of a whole. A fraction means a part of a group or of a region. 5/12 is a fraction. We read it as “five-twelfths”. What does “12” stand for? It is the number of equal parts into which the whole has been divided. What does “5” stand for? It is the number of equal parts which have been taken out. Here 5 is called the numerator and 12 is called the denominator. You can also understand fractions with the help of a game. Take many copies of a grid. Consider any fraction, say 1/2. Each one of you should shade 1/2 of the grid. You will observe that only 2 copies of the grid can be taken out so that each part is 1/2 of the grid.

Section 7.3 –  In this section, you will learn how to represent fractions on a number line. You have learnt to show whole numbers like 0,1,2… on a number line. You can also show fractions on a number line. Let us draw a number line and try to mark 1/2 on it. We know that 1/2 is greater than 0 and less than 1, so it should lie between 0 and 1. Since we have to show 1/2, we divide the gap between 0 and 1 into two equal parts and show 1 part as 1/2. Suppose we want to show 1/3 on a number line. Into how many equal parts should the length between 0 and 1 be divided?  We divide the length between 0 and 1 into 3 equal parts and show one part as 1/3.

Section 7.4 –  You already know about fractions. Now you will study the first category of fractions which is proper fractions. In a proper fraction, the numerator is less than the denominator. In fact, all the fractions we have learnt so far are less than 1. These are proper fractions. In the next section, you will study the next two categories of fractions – improper and mixed fractions.

Section 7.5 –  This section will teach you improper and mixed fractions. An improper fraction can be written as a combination of a whole and, a part; and such fraction then called mixed fractions. Thus, fractions like 3/2, 12/7 and 18/5, are all improper fractions. Fractions such as 1 1/4 and 2 1/2 are called mixed fractions because they are the combination of a whole and a part.

Section 7.6 –  Now you will study equivalent fractions. Each proper or improper fraction has many equivalent fractions. To find an equivalent fraction of a given fraction, we may multiply or divide both the numerator and the denominator of the given fraction by the same number. 1/2, 2/4, 3/6, 36/72, …, are all equivalent fractions. They represent the same part of a whole. To find an equivalent fraction of a given fraction, you may multiply both the numerator and the denominator of the given fraction by the same number.

Section 7.7 – In this section, you will study the simplest form of a fraction. A fraction is said to be in the simplest (or lowest) form if its numerator and the denominator have no common factor except 1. Take an example –  36/54, let us try to get an equivalent fraction in which the numerator and the denominator have no common factor except 1. How do we do it? We see that both 36 and 54 are divisible by 2. 36/54 = (36÷2)/ (54÷2) = 18/27. But 18 and 27 also have common factors other than one. The common factors are 1, 3, 9; the highest is 9. Therefore, 18/27 = (18÷9)/(27÷9) = 2/3. Now 2 and 3 have no common factor except 1; we say that the fraction 2/3 is in the simplest form. The shortest way to find the equivalent fraction in the simplest form is to find the HCF of the numerator and denominator, and then divide both of them by the HCF.

Section 7.8 – This section will teach you like fractions. Fractions with same denominators are called like fractions. Thus, 1/15, 2/15, 3/15, 8/15, …, are all like fractions. Are 7/27 and 7/28 like fractions? Their denominators are different. Therefore, they are not like fractions. They are called, unlike fractions.

Section 7.9 – Now you will learn how to compare like and unlike fractions.  If the numerator is the same in two fractions, the fraction with the smaller denominator is greater of the two. Thus, 1/8 > 1/10,  3/5 > 3/7, 4/9 > 4/11 and so on. Let us arrange 2/1, 2/13, 2/9, 2/5, 2/7 in increasing order. All these fractions are unlike, but their numerator is the same. Hence, in such a case, the larger the denominator, the smaller is the fraction. The smallest is 2/13, as it has the largest denominator. The next three fractions in order are 2/9, 2/7, 2/5. The greatest fraction is 2/1 (It is with the smallest denominator). The arrangement in increasing order, therefore, is 2/13, 2/9, 2/7, 2/5, 2/1.

Section 7.10 – Towards the end of this chapter, you will study the addition and subtraction of fractions. All fractions cannot be added orally. We need to know how they can be added in different situations and learn the procedure for it. What added to 1/5 gives 1/2? This means subtract 1/5 from 1/2 to get the required number. Since 1/5 and 1/2 are unlike fractions, in order to subtract them, we first find their equivalent fractions with the same denominator. These are 2/10 and 5/10 respectively.

In this chapter, you are provided with several examples along with their solutions for a clear understanding of fractions. To know more about NCERT Solutions for Class 6 Maths Chapter 7 Fractions, you should explore the exercises below. You can also download the Fractions Class 6 NCERT Solutions PDF, solved by expert maths trainers. You can also refer online to Class 6 Maths Chapter 7 Worksheet PDF.