# NCERT Solutions for Class 6 Maths Chapter 7 Fractions (Ex 7.4) Exercise 7.4

## NCERT Solutions for Class 6 Maths Chapter 7 Fractions (Ex 7.4) Exercise 7.4

The NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 discuss the idea of Fractions, as the title would imply. This is demonstrated through real-world situations and brief games in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4. According to the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4, a Fraction is a Mathematical expression for a portion of a whole. Every Fraction has a point on the number line that corresponds to it. The section after that in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4, titled Fractions on the Number Line, explains this.

In these NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4, the following Fraction kinds will be introduced to students:

1. In a proper Fraction, the Numerator is less than the Denominator.
2. Incorrect Fractions: Numerator exceeds Denominator
3. Mixed Fractions: A mixed Fraction is one that combines a whole and a part in its writing.
4. Similar Fractions: Fractions that have the same Numerator
5. Unlike Fractions: Fractions with different Denominators

In addition to these concepts, a crucial subject is covered in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 which is, the idea of equivalent Fractions.

• Students can multiply the Numerator and Denominator of the given Fraction by the same number to find an equivalent Fraction of the given Fraction.
• They can divide the Numerator and Denominator by the same number to obtain an equivalent Fraction.

The Simplest Form of a Fraction is another topic covered in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 based on Fractions.

If a Fraction’s Numerator and Denominator only share one common factor, it is said to be in its simplest form.

Understanding how to compare Fractions comes next in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 after learning about Like and Unlike Fractions. Comparing comparable Fractions is simple, but doing so while comparing Fractions requires extra care because the common Denominator and LCM are needed. Under various sub-sections, the addition and subtraction of Fractions are explained with suitable examples:

• Adding or subtracting Like Fractions

### Access Other Exercises of Class 6 Maths Chapter 7

 Chapter 7 – Fractions Exercises Exercise 7.1 11 Questions & Solutions Exercise 7.2 3 Questions & Solutions Exercise 7.3 9 Questions & Solutions Exercise 7.5 5 Questions & Solutions Exercise 7.6 9 Questions & Solutions

## NCERT Solutions for Class 6 Maths Chapter 7 Fractions (Ex 7.4) Exercise 7.4

The NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 compare Like and Unlike Fractions that form the very foundation of the chapter. A lot of problems in everyday life can be resolved by teaching students how to compare Fractions.There are 10 questions in all with subparts based on arranging and comparing Fractions in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 based on Fractions.

Students must review all the ideas from the previous three exercises in order to complete the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 based on Fractions. The PDF link provided on the Extramarks website and mobile application can be used to access the concise solution set for the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4.

Through the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 students will learn how to correlate Unlike Fractions and Like Fractions (Fractions with the same Denominator) through the study of Fractions ( Fractions with different Denominators). When two distinct Fractions are compared, their equivalent Fractions with a Denominator that is a multiple of both Fractions’ Denominators are first found. Due to the fact that related Fractions share the same Denominator, the Fraction with the larger Numerator is larger.

The focus of the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4, is on conceptual comprehension of Fraction comparison. When dealing with the questions in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4, students can refer to the solved examples to help them comprehend the topics and ask teachers at Extramarks for assistance if necessary.

The NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 introduce Class 6 students to a crucial Mathematical concept, termed Fractions. A Fraction is a number that represents all or a portion of another number. In Chapter 2, students learned about Whole Numbers and the Number Line. It was previously advised to comprehend the number line because Fractions heavily rely on it. On a number line, Fractions can be represented. Every Fraction has a location on the number line that corresponds to it. The Numerator and Denominator are the two elements of a Fraction. Fractions can be of two types, namely, Proper Fractions and Improper Fractions, depending on the values of the Numerator and Denominator. The Numerator is less than the Denominator when referring to a Proper Fraction.

Improper Fractions are those in which the Numerator is higher than the Denominator. Mixed Fractions can also be used to represent Improper Fractions. A Mixed Fraction is an Improper Fraction that is represented as a combination of a whole and a portion of a number. After finishing the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4, students may grasp subsequent chapters like decimals and percentages, which have roots in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4. The new terminology used in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 on Fractions includes the following:

• Fractions and their types
• Comparing Fractions
• Operations on Fractions

## Access NCERT Solutions for Class 6 Maths Chapter 7- Fractions

Like and Unlike Fractions and their comparison are the ideas addressed in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4. It is well known that Unlike Fractions have a different Denominator from like Fractions, which are the opposite. The team of knowledgeable academics at Extramarks has answered the exercise-specific questions in detail. By using NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 to work through the text problems, students can raise their grade in the course.

The NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 are intended to help students perform better on their Maths exams. The topic of Fractions is covered in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4. Subject-matter experts associated with Extramarks have created the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4, which are meant to be detailed for a simpler understanding of the ideas.

The NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 addresses the depiction of a Fraction on a number line, proper Fractions, Improper Fractions, and Mixed Fractions, and these are just a few of the themes explored by the term “Fractions.” A Fraction is referred to as a piece of a whole. For instance, if a pizza is cut into five equal pieces, each piece is equal to one fifth of the whole. In Maths, a “Fraction” is a term used to define a specific area of a larger whole. It shows the same components of a whole number. The two primary components of a Fraction are a fixed Numerator and a fixed Denominator. One of the most crucial chapters for examinations is Chapter 7, for which the solutions are the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 by Extramarks.

The fact that Fractions have been around since the Egyptian era, one of the world’s oldest civilisations, may surprise students. However, Fractions were not considered to be numbers by the Egyptians. In reality, Fractions were used to compare whole numbers with Fractions. Fractions were used by the Egyptians to preserve the history of the region. The NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 can be accessed through the links offered on the Extramarks website and mobile application. The NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 will assist students in exploring the topic of Fractions in the most thorough manner possible.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise 7.4

Subject experts from Extramarks have carefully crafted the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 to ensure that every concept is covered in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 to the fullest extent possible. Due to the fact that they aid in executing mathematical operations, Fractions are a crucial subject that should be thoroughly studied with the aid of NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4. Students must organise their study time and go over all the material with these reliable resources in order to prepare well for tests. The Extramarks website and mobile application both provide links to download the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 in PDF format.

Students can effectively resolve all the problems in NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 by practising the aforementioned exercises on a regular basis. Students will be able to address advanced-level Fractions-related questions by consistently practising these ideas in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4. Below is a detailed examination of each task in NCERT solutions for Class 6 Maths Chapter 7 Fractions

• Class 6 Maths Chapter 7 Ex. 7.1–11 Questions
• Class 6 Maths Chapter 7 Ex. 7.2 – 3 Questions
• Class 6 Maths Chapter 7 Ex. 7.3–9 Questions
• Class 6 Maths Chapter 7 Ex. 7.4–10 Questions
• Class 6 Maths Chapter 7 Ex. 7.5, – 5 Questions
• Class 6 Maths Chapter 7 Ex 7.6 – 9 Questions

The depiction of Fractions on a number line, Proper and Improper Fractions, Mixed and Equivalent Fractions, the simplest form of a Fraction, lowest Fractions, and addition and subtraction of Fractions are all contained in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4.

There are a total of 47 questions in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4, of which 17 are easy, 5 are of moderate difficulty, and 23 are of the long answer variety.

Numerous fundamental ideas based on Fractions and their kinds are covered in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4, which is essential for bolstering the Mathematical foundation of students. This NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 contains information on how to apply various formulas and contains some key ideas, some of which are noted below:

• A Proper Fraction has a Numerator that is less than its Denominator. Fractions with a higher Numerator than the Denominator are considered Improper Fractions. A Mixed Fraction is what is used to describe an inappropriate Fraction that is expressed as a combination of a whole and a part.
• For any Proper or Improper Fraction, there are a number of corresponding Fractions. When the Numerator and Denominator are multiplied or divided by the same number, students can obtain an Equivalent Fraction of a given Fraction.
• The simplest (or lowest) variant of a Fraction is one in which the Numerator and Denominator share only the number 1.

The Fractions and their ideas presented in NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 are intended to assist students in improving their arithmetic abilities. Experts in Maths at Extramarks have crafted the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4, which thoroughly cover each and every subject. Thus, the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4, are excellent tools for students to acquire in-depth conceptual understanding.

The Fractions questions in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 cover a number of subjects that are all equally significant. Consistent practise is required for questions based on the types of Fractions and how they are represented on a number line. Every question from the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 must be practised if a student hopes to receive great grades.

The depiction of a Fraction on a Number Line, types of Fractions, Proper Fractions, Improper Fractions, addition and subtraction of Fractions, comparing Like and Unlike Fractions, and the simplest form of a Fraction are significant subjects discussed in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4. The NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4, go into great detail on each topic.

In the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4, there are formulas pertaining to Fractions, and students must be able to recall predefined concepts about them, such as the properties of Fractions, such as that the Numerator should be less than the Denominator in like Fractions and the Numerator should be significantly larger than the Denominator in Unlike Fractions. These notions in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 are also crucial for students to comprehend how to use arithmetic operators on Fractions.

By practising the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 students can develop their mathematical knowledge, logical thinking, and reasoning skills by using Fractions. These NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 were thoughtfully created by subject-matter specialists after extensive research to aid students in achieving the finest learning results. For better outcomes, students must also solve all the examples in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4.

Apart from the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4, Extramarks also provides NCERT solutions for other Maths chapters that students might want to refer to.

All of the textbook questions found in the NCERT coursebook are fully explained in the NCERT solutions for Class 6 Maths. The best cross-reference material is found in these answers since they offer a step-by-step explanation of all difficulties. Students may verify their responses and develop a sense of how to properly write answers to questions. Mathematical specialists have developed the NCERT solutions for Class 6 Maths. Extramarks’ experts invest a lot of time in finding the most accurate and efficient way to get the desired outcome. They also present the solutions in everyday terms so that students can easily understand the explanations.

The NCERT solutions for Class 6 Maths are used as a transitional tool between elementary and secondary education. They aid students in remembering the ideas they learned in junior classes and blend them with some brand-new ideas that signal the beginning of middle school. These solutions by Extramarks can be used for annual, half-yearly, and unit examinations for students in Class 6. They are also very good at preparing for competitive examinations like Olympiads. The CBSE NCERT solutions for Class 6 Maths make sure that students gain a solid conceptual grasp of fundamental mathematical concepts that will serve as the cornerstone for the remainder of their academic lives.

Numerous study hacks and ideas are included in the NCERT solutions for Class 6 Maths to speed up the learning process. Additionally, they make use of concrete examples, graphs, and situations from everyday life to help students relate to the subjects in a more effective way. The links on the Extramarks website and mobile application will take students to the well-organised and thorough solutions to all of the NCERT chapters.

The topics contained in the Class 6 chapters have principles that create the framework for higher-order teachings. If school students are not familiar with and well-versed with these things, it could prove problematic as they reach subsequent grades. Students should therefore frequently visit the above links to thoroughly review the chapters in order to avoid being perplexed during the exams.

The many topics connected to Fractions are explained in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 using enjoyable games and real-world situations. Students can learn about the many Fractional categories and how to manipulate different Fractions to get them into a form that can be used in mathematical operations.

The subjects covered in the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 include the depiction of Fractions on a number line, several forms of Fractions, including Improper, Mixed, Like, Unlike, and Equivalent Fractions, as well as their simplification and comparison. Additionally, the NCERT Solutions Class 6 Maths Chapter 7 Exercise 7.4 cover the addition and subtraction of these Fractions. Below is an overview of the chapter-wise NCERT Solutions for Class 6 Maths:

•  NCERT Solutions Class 6 Maths Chapter 1 – Knowing Our Numbers:

The Class 6 Maths NCERT solutions for “Knowing Our Numbers” are designed to help students develop a solid understanding of numbers and how they behave in various situations. Children are taught how to compare huge numbers, generate various numbers under specific conditions, and write the digit expansion.

•  NCERT Solutions Class 6 Maths Chapter 2 – Whole Numbers:

The NCERT solutions for Class 6 Maths based on Whole Numbers begin by explaining successors and predecessors to the students. The number line and how to use it for arithmetic operations are two of the most crucial ideas that youngsters will learn in this lesson. The characteristics of Whole numbers are another significant area that is covered.

•  NCERT Solutions Class 6 Maths Chapter 3 – Playing With Numbers

The ideas of Factors, Multiples, Prime and Composite numbers, as well as divisibility tests, are presented in the NCERT solutions for Class 6 Maths for the chapter titled Playing With Numbers as illustrative games that help pupils learn about these concepts in-depth while having fun.

• NCERT Solutions Class 6 Maths Chapter 4 – Basic Geometrical Ideas

The core concepts that make up the study of Geometry are the focus of the NCERT solutions for class 6 Maths. Children are exposed to fundamental forms like points, lines, and line segments, as well as many types of curves and their components, which will be examined in greater detail in subsequent lessons.

• NCERT Solutions Class 6 Maths Chapter 5 – Understanding Elementary Shapes

In continuation of the previous chapter, the NCERT solutions for Class 6 Maths on Understanding Elementary Shapes focus on line segments, angles, and how to classify triangles by the length of their sides and angles. A brief section on three-dimensional figures is included towards the end.

• NCERT Solutions Class 6 Maths Chapter 6 – Integers

Numbers having positive and negative signs, also referred to as Integers, are currently the subject of the NCERT solutions for Class 6 Maths. Students are taught how to order integers, display them on the number line, and perform arithmetic operations on them using numerous examples from everyday life.

• NCERT Solutions Class 6 Maths Chapter 7 – Fractions

The NCERT Solutions for Class 6 Maths cover a wide range of topics related to Fractions in fun games and practical contexts. In order to transform distinct Fractions into a form that can be used in mathematical operations, students can learn about the many types of fractions and how to manipulate various Fractions.

• NCERT Solutions Class 6 Maths Chapter 8 – Decimals

The relationship between Fractions and Decimals is established in the NCERT class 6 Maths Decimals to set up this lesson. The number line and other tools are used in this chapter to give kids a practical understanding of Decimals.

• NCERT Solutions Class 6 Maths Chapter 9 – Data Handling

The NCERT Solutions for Class 6 Maths based on Chapter 9 demonstrate how to arrange provided data into a form that can be used to carry out various statistical computations. In this chapter, representational methods like pictographs and bar graphs are also discussed in detail.

• NCERT Solutions Class 6 Maths Chapter 10 – Mensuration

NCERT solutions for Class 6 Maths based on Mensuration is one of the most significant lessons that students will study. It teaches learners about different 2D shapes as well as how to find their perimeter and area. These ideas will also be extensively utilised in subjects that are covered in higher grades.

• NCERT Solutions Class 6 Maths Chapter 11 – Algebra

The subject of Algebra from the NCERT Solutions for Class 6 Maths is possibly one of the most popular in business. It is used to carry out various arithmetic and geometric computations. This section presents to students the concept of a variable and how to evaluate expressions consisting of a variable.

• NCERT Solutions Class 6 Maths Chapter 12 – Ratio and Proportion

Students are taught how to successfully apply Ratios and Proportions to solve practical problems that call for the comparison of two amounts from the NCERT Solutions for Class 6 Maths based on Ratio and Proportion.

• NCERT Solutions Class 6 Maths Chapter 13 – Symmetry

A fascinating lesson utilising well-known forms like rectangles and a variety of actual composite shapes, the NCERT Solutions for Class 6 Maths based on Symmetry explains this intriguing idea. The link between symmetry and mirror reflection is also established in this chapter.

• NCERT Solutions Class 6 Maths Chapter 14 – Practical Geometry

The procedures taken to construct different figures and elements, such as Circles, Line Segments, and Angles given particular limits, are elaborated upon in the NCERT Solutions for Class 6 Maths Practical Geometry. Additionally, students learn how to effectively employ geometric tools like a compass and a ruler.

Q.1 Write shaded portions as fraction. Arrange them in ascending or descending order using the correct sign ‘<’ ‘=’ ‘>’ between the fractions.

$\begin{array}{l}\text{(c)}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\\ \text{Show}\frac{2}{6},\frac{4}{6},\frac{8}{6}\text{and}\frac{6}{6}\text{on the number line}\text{. Put appropriate}\\ \text{signs between the fractions given :}\\ \frac{5}{6}__\frac{2}{6},\text{}\frac{3}{6}__0,\text{}\frac{1}{6}__\frac{6}{6},\text{}\frac{8}{6}__\frac{5}{6}\end{array}$

Ans.

Since, they all are like fractions. They can be arranged in increasing order by observing numerator only.

So,

$\frac{1}{8}<\frac{3}{8}<\frac{4}{8}<\frac{6}{8}$

(b)

Since, they all are like fractions. They can be arranged in increasing order by observing numerator only.

So,

$\frac{3}{9}<\frac{4}{9}<\frac{6}{9}<\frac{8}{9}$

(c)

$\frac{5}{6}\begin{array}{|c|}\hline >\\ \hline\end{array}\frac{2}{6},\frac{3}{6}\begin{array}{|c|}\hline >\\ \hline\end{array}0,\frac{1}{6}\begin{array}{|c|}\hline <\\ \hline\end{array}\frac{6}{6},\frac{8}{6}\begin{array}{|c|}\hline >\\ \hline\end{array}\frac{5}{6}$

Q.2 Compare the fractions and put an appropriate sign.

$\begin{array}{l}\left(\mathrm{a}\right)\text{\hspace{0.17em}\hspace{0.17em}}\frac{3}{6}\left[\text{\hspace{0.17em}}\right]\frac{5}{6}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(b)\hspace{0.17em}}\frac{1}{7}\left[\text{\hspace{0.17em}}\right]\frac{1}{4}\text{}\\ \text{(c)\hspace{0.17em}}\frac{4}{5}\left[\text{\hspace{0.17em}}\right]\frac{5}{5}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{d}\right)\frac{3}{5}\left[\text{\hspace{0.17em}}\right]\frac{3}{7}\text{}\end{array}$

Ans.

$\begin{array}{l}\left(\mathrm{a}\right)\text{\hspace{0.17em}}\frac{3}{6}\left[\right]\frac{5}{6}\text{}\\ \text{Since},\text{these are like fractions and 3}<\text{5}.\text{So},\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\frac{3}{6}\left[<\right]\frac{5}{6}\text{}\\ \text{(b)\hspace{0.17em}}\frac{1}{7}\left[\right]\frac{1}{4}\text{}\\ \text{Here},\text{numerator of both the fractions are same}.\phantom{\rule{0ex}{0ex}}\text{So},\text{larger the denominator is},\text{smaller is the value of the fraction}.\\ \mathrm{So},\text{\hspace{0.17em}}\frac{1}{7}\left[<\right]\frac{1}{4}\\ \left(\mathrm{c}\right)\text{\hspace{0.17em}}\frac{4}{5}\left[\right]\frac{5}{5}\text{}\\ \text{Since},\text{these are like fractions and 4}<\text{5}.\text{So},\text{\hspace{0.17em}}\frac{4}{5}\left[<\right]\frac{5}{5}\text{}\\ \text{(d)\hspace{0.17em}}\frac{3}{5}\left[\right]\frac{3}{7}\text{}\\ \text{Here},\text{numerator of both the fractions are same}.\phantom{\rule{0ex}{0ex}}\text{So},\text{larger the denominator is},\text{smaller is the value of the fraction}.\\ \mathrm{So},\text{\hspace{0.17em}}\frac{3}{5}\left[>\right]\frac{3}{7}\text{}\end{array}$

Q.3 Let the pairs of fractions to compare is

$\begin{array}{l}\left(a\right)\text{\hspace{0.17em}}\frac{3}{7}\left[\right]\frac{5}{7}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{(b)}\text{\hspace{0.17em}}\frac{2}{7}\left[\right]\frac{2}{4}\text{}\\ \left(c\right)\text{\hspace{0.17em}}\frac{4}{9}\left[\right]\frac{5}{9}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(d\right)\frac{1}{5}\left[\right]\frac{1}{7}\text{}\\ \left(e\right)\text{\hspace{0.17em}}\frac{13}{15}\left[\right]\frac{23}{15}\text{}\end{array}$

Ans.

$\begin{array}{l}\left(\mathrm{a}\right)\frac{3}{7}\left[\right]\frac{5}{7}\text{}\\ \text{Since},\text{these are like fractions and 3}<\text{5}.\text{So},\\ \frac{3}{7}\left[<\right]\frac{5}{7}\text{}\\ \text{(b)}\frac{2}{7}\left[\right]\frac{2}{4}\text{}\\ \text{Here},\text{numerator of both the fractions are same}.\phantom{\rule{0ex}{0ex}}\text{So},\text{larger the denominator is},\text{smaller is the value of the fraction}.\\ \mathrm{So},\text{\hspace{0.17em}}\frac{2}{7}\left[<\right]\frac{2}{4}\\ \left(\mathrm{c}\right)\text{\hspace{0.17em}}\frac{4}{9}\left[\right]\frac{5}{9}\text{}\\ \text{Since},\text{these are like fractions and 4}<\text{5}.\text{So},\\ \frac{4}{9}\left[<\right]\frac{5}{9}\text{}\\ \text{(d)\hspace{0.17em}}\frac{1}{5}\left[\right]\frac{1}{7}\text{}\\ \text{Here},\text{numerators of both the fractions are same}.\phantom{\rule{0ex}{0ex}}\text{So},\text{larger the denominator is},\text{smaller is the value of the fraction}.\\ \mathrm{So},\text{\hspace{0.17em}\hspace{0.17em}}\frac{1}{5}\left[>\right]\frac{1}{7}\text{}\\ \text{(e)\hspace{0.17em}}\frac{13}{15}\left[\right]\frac{23}{15}\text{}\\ \text{Since},\text{these are like fractions and 13}<\text{23}.\text{So},\\ \frac{13}{23}\left[<\right]\frac{15}{23}\text{}\end{array}$

Q.4 Look at the figures and write ‘<’ or ‘>’, ‘=’ between the given pairs of fractions.

$\left(\text{a}\right)\frac{1}{6}\left[\right]\frac{1}{3}\phantom{\rule{0ex}{0ex}}\left(\text{b}\right)\frac{3}{4}\left[\right]\frac{2}{6}\phantom{\rule{0ex}{0ex}}\left(\text{c}\right)\frac{2}{3}\left[\right]\frac{2}{4}\phantom{\rule{0ex}{0ex}}\left(\text{d}\right)\frac{5}{6}\left[\right]\frac{5}{5}$

Ans.

$\left(\text{a}\right)\frac{1}{6}\left[<\right]\frac{1}{3}\phantom{\rule{0ex}{0ex}}\left(\text{b}\right)\frac{3}{4}\left[>\right]\frac{2}{6}\phantom{\rule{0ex}{0ex}}\left(\text{c}\right)\frac{2}{3}\left[>\right]\frac{2}{4}\phantom{\rule{0ex}{0ex}}\left(\text{d}\right)\frac{5}{6}\left[<\right]\frac{5}{5}$

Q.5 How quickly can you do this ? Fill appropriate sign. ( ‘<’, ‘=’, ‘>’)

$\begin{array}{l}\left(\text{a}\right)\frac{1}{2}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{1}{5}\left(\text{b}\right)\frac{2}{4}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{3}{6}\left(\text{c}\right)\frac{3}{5}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{2}{3}\\ \left(\text{d}\right)\frac{3}{4}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{2}{8}\left(\text{e}\right)\frac{3}{5}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{6}{5}\left(\text{f}\right)\frac{7}{9}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{3}{9}\\ \left(\text{g}\right)\frac{1}{4}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{2}{8}\left(\text{h}\right)\frac{6}{10}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{4}{5}\left(\text{i}\right)\frac{3}{4}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{7}{8}\\ \left(\text{j}\right)\frac{6}{10}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{4}{5}\left(\text{k}\right)\frac{5}{7}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{15}{21}\end{array}$

Ans.

$\begin{array}{l}\left(\mathrm{a}\right)\frac{1}{2}\overline{)>}\frac{1}{5}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{b}\right)\text{\hspace{0.17em}}\frac{2}{4}\overline{)=}\frac{3}{6}\text{\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{c}\right)\frac{3}{5}\overline{)<}\frac{2}{3}\\ \left(\mathrm{d}\right)\frac{3}{4}\overline{)>}\frac{2}{8}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{e}\right)\frac{3}{5}\overline{)<}\frac{6}{5}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{f}\right)\frac{7}{9}\overline{)>}\frac{3}{9}\\ \left(\mathrm{g}\right)\frac{1}{4}\overline{)=}\frac{2}{8}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{h}\right)\frac{6}{10}\overline{)<}\frac{4}{5}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{i}\right)\frac{3}{4}\overline{)<}\frac{7}{8}\\ \left(\mathrm{j}\right)\frac{6}{10}\overline{)<}\frac{4}{5}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{k}\right)\frac{5}{7}\overline{)=}\frac{15}{21}\end{array}$

Q.6 The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.

$\begin{array}{l}\left(\mathrm{a}\right)\frac{2}{12}\left(\mathrm{b}\right)\frac{3}{15}\left(\mathrm{c}\right)\frac{8}{50}\\ \left(\mathrm{d}\right)\frac{16}{100}\left(\mathrm{e}\right)\frac{10}{60}\left(\mathrm{f}\right)\frac{15}{75}\\ \left(\mathrm{g}\right)\frac{12}{60}\left(\mathrm{h}\right)\frac{16}{96}\left(\mathrm{i}\right)\frac{12}{75}\\ \left(\mathrm{j}\right)\frac{12}{72}\left(\mathrm{k}\right)\frac{3}{18}\left(\mathrm{l}\right)\frac{4}{25}\end{array}$

Ans.

$\begin{array}{l}\left(\mathrm{a}\right)\frac{2}{12}=\frac{1×2}{6×2}=\frac{1}{6}\left(\mathrm{b}\right)\frac{3}{15}=\frac{1×3}{5×3}=\frac{1}{5}\left(\mathrm{c}\right)\frac{8}{50}=\frac{4×2}{25×2}=\frac{4}{25}\\ \left(\mathrm{d}\right)\frac{16}{100}=\frac{4×4}{25×4}=\frac{4}{25}\left(\mathrm{e}\right)\frac{10}{60}=\frac{1×10}{6×10}=\frac{1}{6}\left(\mathrm{f}\right)\frac{15}{75}=\frac{1×15}{5×15}=\frac{1}{5}\\ \left(\mathrm{g}\right)\frac{12}{60}=\frac{1×12}{5×12}=\frac{1}{5}\left(\mathrm{h}\right)\frac{16}{96}=\frac{1×16}{6×16}=\frac{1}{6}\left(\mathrm{i}\right)\frac{12}{75}=\frac{3×4}{3×25}=\frac{4}{25}\\ \left(\mathrm{j}\right)\frac{12}{72}=\frac{1×12}{6×12}=\frac{1}{6}\left(\mathrm{k}\right)\frac{3}{18}=\frac{1×3}{6×3}=\frac{1}{6}\left(\mathrm{l}\right)\frac{4}{25}=\frac{1×4}{1×25}=\frac{4}{25}\end{array}$

The three different groups representing same fraction are
Fractions representing

$\frac{1}{6}$

:

$\frac{2}{12},\frac{10}{60},\frac{16}{96},\frac{12}{72},\frac{3}{18}$

Fractions representing

$\frac{1}{5}$

:

$\frac{3}{15},\frac{15}{75},\frac{12}{60}$

Fractions representing

$\frac{4}{25}$

:

$\frac{8}{50},\frac{16}{100},\frac{12}{75},\frac{4}{25}$

Q.7 Find answers to the following. Write and indicate how you solved them.

$\begin{array}{l}\left(\mathrm{a}\right)\mathrm{Is}\frac{5}{9}\mathrm{equal}\text{}\mathrm{to}\frac{4}{5}?\phantom{\rule{0ex}{0ex}}\left(\mathrm{b}\right)\mathrm{Is}\frac{9}{16}\mathrm{equal}\text{}\mathrm{to}\frac{5}{9}?\\ \left(\mathrm{c}\right)\mathrm{Is}\frac{4}{5}\mathrm{equal}\text{}\mathrm{to}\frac{16}{20}?\phantom{\rule{0ex}{0ex}}\left(\mathrm{d}\right)\mathrm{Is}\frac{1}{15}\mathrm{equal}\text{}\mathrm{to}\frac{4}{30}?\end{array}$

Ans.

(a) Let us convert both the fractions into like fractions.

$\begin{array}{l}\frac{5}{9}\text{and}\frac{4}{5}\\ \frac{5×5}{9×5}\text{and}\frac{4×9}{5×9}\\ \frac{25}{45}\text{and}\frac{36}{45}\\ \text{Since, 25 < 36}\text{. So,}\frac{5}{9}<\frac{4}{5}.\end{array}$

The fractions are not equal.
(b)
Let us convert both the fractions into like fractions.

$\begin{array}{l}\frac{9}{16}\text{and}\frac{5}{9}\\ \frac{9×9}{16×9}\text{and}\frac{5×16}{16×9}\\ \frac{81}{144}\text{and}\frac{80}{144}\\ \text{Since, 81>80}\text{. So,}\frac{9}{16}>\frac{5}{9}.\end{array}$

The fractions are not equal.
(c)
Let us convert both the fractions into like fractions.

$\begin{array}{l}\frac{16}{20}\text{and}\frac{4}{5}\\ \frac{16}{20}\text{and}\frac{4×4}{5×4}\\ \frac{16}{20}\text{and}\frac{16}{20}\\ \text{Since, 16 = 16}\text{. So,}\frac{16}{20}=\frac{4}{5}.\end{array}$

The fractions are equal.
(d)
Let us convert both the fractions into like fractions.

$\begin{array}{l}\frac{1}{15}\text{and}\frac{4}{30}\\ \frac{1×2}{15×2}\text{and}\frac{4}{30}\\ \frac{2}{30}\text{and}\frac{4}{30}\\ \text{Since, 2 < 4}\text{. So,}\frac{1}{15}<\frac{4}{30}.\end{array}$

Q.8 Ila read 25 pages of a book containing 100 pages. Lalita read

$\frac{2}{5}$

of the same book. Who read less?

Ans.

Pages read by Ila = 25

Fraction of pages read by Ila =

$\frac{25}{100}=\frac{1}{4}$

Fraction of pages read by Lalita =

$\frac{2}{5}$

Comparing both the fractions :

$\begin{array}{l}\frac{1}{4}\text{and}\frac{2}{5}\\ \frac{1×5}{4×5}\text{and}\frac{2×4}{4×5}\\ \frac{5}{20}\text{and}\frac{8}{20}\\ \text{Since, 5 < 8}\text{.}\\ \end{array}$

Q.9 Rafiq exercised for

$\frac{3}{6}$

of an hour, while Rohit exercised for

$\frac{3}{4}$

of an hour. Who exercised for a longer time?

Ans.

Rafiq exercised for

$\frac{3}{6}$

of an hour
Rohit exercised for

$\frac{3}{4}$

of an hour
Comparing both the fractions :
Since, numerator of both the fractions are same and denominators 4 < 6.
So, Rohit exercised longer.

Q.10 In a class A of 25 students, 20 passed in first class. In another class B of 30 students, 24 passes in first class. In which class was a greater fraction of students getting first class?

Ans.

Fraction of students of class A who passed in first class =

$\frac{20}{25}=\frac{4}{5}$

Fraction of students of class B who passed in first class =

$\frac{24}{30}=\frac{4}{5}$

So, equal fraction of students got first class.