# NCERT Solutions Class 6 Maths Chapter 7

The fundamental components of fraction are covered in the CBSE Mathematics syllabus for Class 6. A fraction is a number that represents a portion of a whole. The whole may be a single or a collection of objects with equal portions. A fraction is also said to be in its simplest (or lowest) form if the numerator and denominator share no common factor other than 1.

The questions of Chapter 7 of Class 6 Mathematics would seem to be a little difficult for students to solve because several subtopics of the chapter deal with different forms of fractions. If you're looking for a good study guide to help you answer the chapter's questions, look no further. NCERT Solutions Class 6 Mathematics Chapter 7 at Extramarks assists you in dealing with difficult questions and saving time with  correct answers.

## NCERT Solutions for Class 6 Mathematics Chapter 7 - Fractions

Access NCERT Solutions for Mathematics Class 6 Chapter 7 – Fractions

### NCERT Solutions For Class 6 Mathematics Chapter 7 PDF –

Once students have gone through the chapter, the next step is to solve the exercise questions given at the end of the chapter, which assesses the contents of the chapter. Answering these questions increases student’s engagement with the lesson. It not only helps them get better grades, but it also opens up a number of doors for them to pursue their goals in the future. NCERT Solutions for Class 6 Mathematics Chapter 7 Fractions assist students in effectively learning the concepts covered in the chapters by providing detailed answers.

NCERT Solutions for Class 6 Mathematics Chapter 7 include answers to the chapter’s questions with detailed explanations, illustrations, and more. It aids students in preparing for final exams.

Core Sections of Fraction Chapter for Class 6 Contains

As mastering the fundamentals is essential for achieving the desired result, you should be familiar with all of Fraction's main components.

### Class 6 Mathematics Chapter 7 Contains the Following Sections

Learning and practising the NCERT Solutions gives students the confidence they need to solve any fractions problems they come across. The following are the themes and sub topics addressed in Chapter 7 Fractions:

• 7.1 – Introduction
• 7.2 – A Fraction
• 7.3 – Fraction on the 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
• 7.10 – Addition and Subtraction of Fractions

The first part of the chapter will provide you with a thorough introduction to the concept of fractions. The second portion, in which fraction is thoroughly described using various examples and graphs. The third section covers fractions on the number line, as well as associated facts and examples.

In the next session, students will delve deeper into proper fractions.

Improper and mixed fractions are examined in depth in the fifth part.

The next section explains what equivalent  fraction is and how to calculate it in basic ways.

### Benefits of Opting for NCERT Solutions for Class 6 Chapter 7

Regular practice of the NCERT solutions can help you improve your problem solving skills and achieve better grades in the test.Students get detailed and authentic solutions without having to look anywhere else. NCERT Solutions are complete in every way for students to learn and grasp with better understanding and score well in their examinations. The solutions to the difficult questions are broken into smaller parts and explained in detail. The fact that the NCERT Solutions for Class 6 Biology Chapter 7 are prepared by subject matter experts makes them a reliable material for students to refer.

### We Cover All Exercises in the Chapter Given Below

NCERT Solutions for Class 6 Mathematics is regarded as the best study resource available, since it clears students’ doubts by providing in-depth answers to the  end of the chapter questions. The solutions offered by Extramarks's topic experts include extensive explanations of all of the questions found in the NCERT textbooks.

NCERT Solutions for Class 6 Mathematics Chapter 7 are available on Extramarks in an easy-to-understand format so students can access and study them whenever it's convenient. Subject matter experts provide in-depth explanations so that students  get conceptual clarity  without much difficulty.

Students who are looking for comprehensive CBSE Class 6 Mathematics Solutions for all chapters need not look any further. They can discover straightforward and easy-to-understand Solutions for NCERT books exercises on this page. Students gearing up for their Class 6 exams should consult these NCERT Solutions Class 6 Mathematics Chapter 7 to take their exam preparations to the next level.

With the help of NCERT Solutions Class 6 Mathematics, students will become adept in writing better answers for their exams. Extramarks provides Solutions for NCERT Solutions for Class 6 Mathematics Chapter 7 to assist you in your test preparation.

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• Accuracy is a crucial component that can be found in all NCERT Solutions.  Subject matter experts have written these solutions which are authentic and reliable.
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Apart from that, the answers in NCERT Solution for Class 6 Mathematics Chapter 7 are presented in a lucid and well-structured way that students find easy to understand. As a result, NCERT Class 6 Mathematics Chapter 7 Solutions can be used as a study guide to help you enhance your grades.

Q.1 Write the fraction representing the shaded portion.

Ans-

$\begin{array}{l}\left(\text{i}\right)\frac{2}{4}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{ii}\right)\frac{8}{9}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{iii}\right)\frac{4}{8}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{iv}\right)\frac{1}{4}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\\ \left(\text{v}\right)\frac{3}{7}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{vi}\right)\frac{3}{12}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{vii}\right)\frac{10}{10}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\\ \left(\text{viii}\right)\frac{4}{9}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{ix}\right)\frac{4}{8}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{x}\right)\frac{1}{2}\end{array}$

Q.2 Colour the part according to the given fraction.

(a) (b)

(c)

(e)

Ans-

(a) (b)

(c) (d)

(e)

Q.3 Identify the error, if any
(a)

$\text{This is}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{1}{2}$

(b)

$\text{This is}\frac{1}{4}$

(c)

$\text{This is}\frac{3}{4}$

Ans-

(a)

This is

$\frac{1}{2}$

This is incorrect as the shaded portion does not represent the required fraction.
(b)

This is

$\frac{1}{4}$

This is incorrect as the shaded portion does not represent the required fraction.
(c)

This is

$\frac{3}{4}$

This is incorrect as the shaded portion does not represent the required fraction.

Q.4 What fraction of a day is 8 hours?

Ans-

Number of hours in a day = 24 hours

Fraction =

$\frac{8}{24}$

Q.5 What fraction of an hour is 40 minutes?

Ans-

Number of minutes in an hour = 60 minutes

Fraction =

$\frac{40}{60}$

Q.6 Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.
(a) How can Arya divide his sandwiches so that each person has an equal share?
(b) What part of a sandwich will each boy receive?

Ans-

(a) each sandwich will be divided into 3 equal parts, so that each one of them get equal share.

(b) Number of parts of sandwich = 6
Every one of them will get 2 pieces each, out of 6 pieces. Each boy will get part =

$\frac{2}{6}=\frac{1}{3}$

Q.7 Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?

Ans-

Total dresses to dye = 30

Dresses done dying = 20

Fraction

$=\frac{20}{30}$

Q.8 Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

Ans-

Natural numbers from 2 to 12 = 11

Prime numbers = 2, 3, 5, 7, 11

Fraction

$=\frac{5}{11}$

Q.9 Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

Ans-

Natural numbers from 102 to 113 = 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113.

Prime numbers among them = 103, 107, 109, 113

Fraction =

$\frac{4}{12}$

Q.10 What fraction of these circles have X’s in them?

Ans-

Number of circles having X’s in them = 4

Fraction =

$\frac{4}{8}$

Q.11 Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?

Ans-

CDs bought by Kristin = 3

Total = 8

Fraction of CDs she buy =

$\frac{3}{8}$

$\frac{5}{8}$

Q.12 Draw number lines and locate the points on them :

$\begin{array}{l}\left(\mathrm{a}\right)\text{\hspace{0.17em}\hspace{0.17em}}\frac{1}{2},\frac{1}{4},\frac{3}{4},\frac{4}{4}\end{array}$ $\begin{array}{l}\left(\mathrm{b}\right)\text{\hspace{0.17em}}\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{7}{8}\end{array}$ $\begin{array}{l}\left(\mathrm{c}\right)\text{\hspace{0.17em}}\frac{2}{5},\frac{3}{5},\frac{8}{5},\frac{4}{5}\end{array}$

Ans-

(a)

$\frac{1}{2},\frac{1}{4},\frac{3}{4},\frac{4}{4}$

(b)

$\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{7}{8}$

(c)

$\frac{2}{5},\frac{3}{5},\frac{8}{5},\frac{4}{5}$

Q.13 Express the following as mixed fractions :

$\begin{array}{l}\left(\mathrm{a}\right)\text{\hspace{0.17em}\hspace{0.17em}}\frac{20}{3}\text{\hspace{0.17em} \hspace{0.17em}}\left(\mathrm{b}\right)\text{\hspace{0.17em}}\frac{11}{5}\text{\hspace{0.17em}\hspace{0.17em}}\\ \left(\mathrm{c}\right)\text{\hspace{0.17em}\hspace{0.17em}}\frac{17}{7}\text{\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{d}\right)\frac{28}{5}\text{\hspace{0.17em}}\\ \left(\mathrm{e}\right)\text{\hspace{0.17em}}\frac{19}{6}\text{\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{f}\right)\frac{35}{9}\end{array}$

Ans-

$\begin{array}{l}\left(a\right)\frac{20}{3}=3\begin{array}{c}\hfill 6\\ \hfill \overline{)\begin{array}{l}\text{}20\\ \underset{¯}{-18}\\ \underset{¯}{\text{}2}\end{array}}\end{array}\\ \text{​}\text{​}\text{​}\text{​}\text{​}\text{​}\text{​}\text{​}\text{​}\text{​}\text{​}\text{​}\text{​}\text{​}\text{​}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=6\frac{2}{3}\\ \left(b\right)\text{\hspace{0.17em}}\frac{11}{5}=5\begin{array}{c}\hfill 2\\ \hfill \overline{)\begin{array}{l}\text{11}\\ \underset{¯}{-10}\\ \underset{¯}{\text{1}}\end{array}}\end{array}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=2\frac{1}{5}\\ \left(c\right)\text{\hspace{0.17em}}\frac{17}{7}=7\begin{array}{c}\hfill 2\\ \hfill \overline{)\begin{array}{l}\text{17}\\ \underset{¯}{-14}\\ \underset{¯}{\text{3}}\end{array}}\end{array}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=2\frac{3}{7}\\ \left(d\right)\text{\hspace{0.17em}}\frac{28}{5}=5\begin{array}{c}\hfill 5\\ \hfill \overline{)\begin{array}{l}\text{28}\\ \underset{¯}{-25}\\ \underset{¯}{\text{3}}\end{array}}\end{array}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=5\frac{3}{5}\\ \left(e\right)\text{\hspace{0.17em}}\frac{19}{6}=6\begin{array}{c}\hfill 3\\ \hfill \overline{)\begin{array}{l}\text{19}\\ \underset{¯}{-18}\\ \underset{¯}{\text{1}}\end{array}}\end{array}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=3\frac{1}{6}\\ \left(f\right)\text{\hspace{0.17em}}\frac{35}{9}=9\begin{array}{c}\hfill 3\\ \hfill \overline{)\begin{array}{l}\text{35}\\ \underset{¯}{-27}\\ \underset{¯}{\text{8}}\end{array}}\end{array}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=3\frac{8}{9}\end{array}$

Q.14 Express the following as improper fractions :

$\begin{array}{l}\left(\mathrm{a}\right)\text{\hspace{0.17em}}7\frac{3}{4}\text{\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{b}\right)5\frac{6}{7}\\ \left(\mathrm{c}\right)2\frac{5}{6}\text{\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{d}\right)10\frac{3}{5}\\ \left(\mathrm{e}\right)9\frac{3}{7}\text{\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{f}\right)8\frac{4}{9}\end{array}$

Ans-

$\begin{array}{l}\left(\mathrm{a}\right)\text{\hspace{0.17em}}7\frac{3}{4}=7+\frac{3}{4}=\frac{7×4+3}{4}=\frac{31}{4}\\ \left(\mathrm{b}\right)\text{\hspace{0.17em}}5\frac{6}{7}=5+\frac{6}{7}=\frac{5×7+6}{7}=\frac{41}{7}\\ \left(\mathrm{c}\right)\text{\hspace{0.17em}}2\frac{5}{6}=2+\frac{5}{6}=\frac{2×6+5}{6}=\frac{17}{6}\\ \left(\mathrm{d}\right)\text{\hspace{0.17em}}10\frac{3}{5}=10+\frac{3}{5}=\frac{10×5+3}{5}=\frac{53}{5}\\ \left(\mathrm{e}\right)\text{\hspace{0.17em}}9\frac{3}{7}=9+\frac{3}{7}=\frac{9×7+3}{7}=\frac{66}{7}\\ \left(\mathrm{f}\right)\text{\hspace{0.17em}}8\frac{4}{9}=8+\frac{4}{9}=\frac{8×9+4}{9}=\frac{76}{9}\end{array}$

Q.15 Write the fractions. Are all these fractions equivalent ?
(a)

(b)

Ans-

(a)

$\text{Here,}\frac{1}{2},\frac{\overline{)2}}{\overline{)4}}=\frac{1}{2},\frac{\overline{)3}}{\overline{)6}}=\frac{1}{2},\frac{\overline{)4}}{\overline{)8}}=\frac{1}{2}$

So, all these fractions are equivalent.

(b)

$\text{Here,}\frac{4}{12}=\frac{1}{3},\frac{3}{9}=\frac{1}{3},\frac{2}{6}=\frac{1}{3},\frac{6}{15}=\frac{2}{5}.$

Q.16 Write the fractions and pair up the equivalent fractions from each row.

Ans-

Equivalent fractions are shown below :

Q.17 Write the fractions and pair up the equivalent fractions from each row.

Ans-

Equivalent fractions are shown below :

Q.18 Write the fractions and pair up the equivalent fractions from each row.

Ans-

Equivalent fractions are shown below :

Q.19 Replace in each of the following by the correct number :

$\left(\text{a}\right)\frac{2}{7}=\frac{8}{}\left(\text{b}\right)\frac{5}{8}=\frac{10}{}\left(\text{c}\right)\frac{3}{5}=\frac{}{20}\left(\text{d}\right)\frac{45}{60}=\frac{15}{}\left(\text{e}\right)\frac{18}{24}=\frac{}{4}$

Ans-

$\begin{array}{l}\text{(a)}\frac{2}{7}=\frac{8}{}\\ ⇒\frac{2}{7}=\frac{2×4}{7×4}=\frac{8}{28}\\ \text{(b)}\frac{5}{8}=\frac{10}{}\\ ⇒\frac{5}{8}=\frac{2×5}{8×2}=\frac{10}{16}\\ \left(c\right)\frac{3}{5}=\frac{}{20}\\ ⇒\frac{3}{5}=\frac{3×4}{5×4}=\frac{12}{20}\\ \left(d\right)\frac{45}{60}=\frac{15}{}\\ ⇒\frac{45÷3}{60÷3}=\frac{15}{20}\\ \left(e\right)\frac{18}{24}=\frac{}{4}\\ ⇒\frac{18÷6}{24÷6}=\frac{3}{4}\end{array}$

Q.20 Find the equivalent fraction of having
(a) denominator 20 (b) numerator 9
(c) denominator 30 (d) numerator 27

Ans-

$\begin{array}{l}\left(\text{a}\right)\text{Denominator 2}0\\ \frac{3}{5}=\frac{}{20}\\ ⇒\frac{3}{5}=\frac{3×4}{5×4}=\frac{12}{20}\\ \left(\text{b}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{Numerator 9}\\ \text{}\frac{3}{5}=\frac{9}{}\\ ⇒\frac{3}{5}=\frac{3×3}{5×3}=\frac{9}{15}\\ \left(\text{c}\right)\text{Denominator 3}0\\ \text{}\frac{3}{5}=\frac{}{30}\\ ⇒\frac{3}{5}=\frac{3×6}{5×6}=\frac{18}{30}\\ \left(\text{d}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{Numerator 27}\\ \text{}\frac{3}{5}=\frac{27}{}\\ ⇒\frac{3}{5}=\frac{3×9}{5×9}=\frac{27}{45}\end{array}$

Q.21 Find the equivalent fraction of

$\frac{36}{48}$

having
(a) numerator 9 (b) denominator 4

Ans-

$\begin{array}{l}\left(\text{a}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{Numerator 9}\\ \frac{36}{48}=\frac{9}{}\\ ⇒\frac{36÷4}{48÷4}=\frac{9}{12}\\ \left(\text{b}\right)\text{\hspace{0.17em}}\text{Denominator 4}\\ \text{}\frac{36}{48}=\frac{}{4}\\ ⇒\frac{36÷12}{48÷12}=\frac{3}{4}\end{array}$

Q.22 Check whether the given fractions are equivalent :

$\begin{array}{l}\left(\text{a}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{5}{9},\frac{30}{54}\text{\hspace{0.17em}}\\ \left(\text{b}\right)\frac{3}{10},\frac{12}{50}\\ \left(\text{c}\right)\frac{7}{13},\frac{5}{11}\end{array}$

Ans-

(a)

$\frac{5}{9},\frac{30}{54}$

The given fractions will be equivalent if the product of numerator of one fraction with denominator of another fraction is equal.

Here, 5 × 54 = 9 × 30. So, the fractions are equivalent.

(b)

$\frac{3}{10},\frac{12}{50}$

The given fractions will be equivalent if the product of numerator of one fraction with denominator of another fraction is equal.

$\text{Here,}50×3\ne 12×10\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{So},\text{these fractions are not equivalent}.$ $\left(c\right)$ $\frac{7}{13},\frac{5}{11}$ $\text{The given fractions will be equivalent if the product of numerator of one fraction with denominator of another fraction is equal}.\phantom{\rule{0ex}{0ex}}\text{\hspace{0.17em}}\text{Here, 11}×7\ne 13×5\text{\hspace{0.17em}}\text{So},\text{these fractions are not equivalent}.$

Q.23 Reduce the following fractions to simplest form :

$\begin{array}{l}\left(\mathrm{a}\right)\text{\hspace{0.17em}}\frac{48}{60}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{b}\right)\frac{150}{60}\\ \left(\mathrm{c}\right)\text{\hspace{0.17em}}\frac{84}{98}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{d}\right)\frac{12}{52}\\ \left(\mathrm{e}\right)\text{\hspace{0.17em}}\frac{7}{28}\end{array}$

Ans-

$\begin{array}{l}\left(\mathrm{a}\right)\text{\hspace{0.17em}}\frac{48}{60}=\frac{12×4}{12×5}=\frac{4}{5}\\ \left(\mathrm{b}\right)\text{\hspace{0.17em}}\frac{150}{60}=\frac{15×10}{6×10}=\frac{15}{6}=\frac{5}{2}\\ \left(\mathrm{c}\right)\text{\hspace{0.17em}}\frac{84}{98}=\frac{14×6}{14×7}=\frac{6}{7}\\ \left(\mathrm{d}\right)\text{\hspace{0.17em}}\frac{12}{52}=\frac{4×3}{4×13}=\frac{3}{13}\\ \left(\mathrm{e}\right)\text{\hspace{0.17em}}\frac{7}{28}=\frac{1×7}{4×7}=\frac{1}{4}\end{array}$

Q.24 Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils ?

 Total pencils Used pencils Fraction Equivalent fraction Ramesh 20 10 $\frac{10}{20}$ $\frac{1}{2}$ Sheelu 50 25 $\frac{25}{50}$ $\frac{1}{2}$ Jamaal 80 40 $\frac{40}{80}$ $\frac{1}{2}$

Here, we can see that Ramesh, Sheelu and Jamaal has used up an equal fraction of his/her pencils.

Ans-

 Total pencils Used pencils Fraction Equivalent fraction Ramesh 20 10 $\frac{10}{20}$ $\frac{1}{2}$ Sheelu 50 25 $\frac{25}{50}$ $\frac{1}{2}$ Jamaal 80 40 $\frac{40}{80}$ $\frac{1}{2}$

Here, we can see that Ramesh, Sheelu and Jamaal has used up an equal fraction of his/her pencils.

Q.25 Match the equivalent fractions and write two more for each :

 (i) $\frac{250}{400}$ (a) $\frac{2}{3}$ (ii) $\frac{180}{200}$ (b) $\frac{2}{5}$ (iii) $\frac{660}{990}$ (c) $\frac{1}{2}$ (iv) $\frac{180}{360}$ (d) $\frac{5}{8}$ (v) $\frac{220}{550}$ (e) $\frac{9}{10}$

Ans-

 (i) $\frac{250}{400}$ (d) $\frac{5}{8},\text{}\frac{10}{16},\text{}\frac{15}{24}$ (ii) $\frac{180}{200}$ (e) $\frac{9}{10},\text{}\frac{18}{20},\text{}\frac{27}{30}$ (iii) $\frac{660}{990}$ (a) $\frac{2}{3},\text{}\frac{4}{6},\text{}\frac{6}{9}$ (iv) $\frac{180}{360}$ (c) $\frac{1}{2},\text{}\frac{2}{4},\text{}\frac{3}{6}$ (v) $\frac{220}{550}$ (b) $\frac{2}{5},\text{}\frac{4}{10},\text{}\frac{6}{15}$

Q.26 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.27 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)

$\frac{5}{6}\overline{)>}\frac{2}{6},\text{}\frac{3}{6}\overline{)>}0,\text{}\frac{1}{6}\overline{)<}\frac{6}{6},\text{}\frac{8}{6}\overline{)>}\frac{5}{6}$

Q.28 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.29 Compare the fractions and put an appropriate sign.

$\begin{array}{l}\left(\mathrm{a}\right)\text{\hspace{0.17em}\hspace{0.17em}}\frac{3}{6}\left[\text{\hspace{0.17em}}\right]\frac{5}{6}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\phantom{\rule{0ex}{0ex}}\left(\text{b}\right)\text{\hspace{0.17em}}\frac{1}{7}\left[\text{\hspace{0.17em}}\right]\frac{1}{4}\text{}\\ \left(\text{c}\right)\text{\hspace{0.17em}}\frac{4}{5}\left[\text{\hspace{0.17em}}\right]\frac{5}{5}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\phantom{\rule{0ex}{0ex}}\left(\mathrm{d}\right)\frac{3}{5}\left[\text{\hspace{0.17em}}\right]\frac{3}{7}\text{}\end{array}$

Ans-

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

Q.30 et 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.31 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.32 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-

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

Q.33 How quickly can you do this ? Fill appropriate sign. ( ‘<’, ‘=’, ‘>’)

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

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.34 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.35 Find answers to the following. Write and indicate how you solved them.

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

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.36  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 :

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

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.

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.

Write these fractions appropriately as additions or subtractions :

Solve :

$\begin{array}{l}\left(\text{a}\right)\text{ }\frac{\text{1}}{\text{18}}\text{+}\frac{\text{1}}{\text{18}}\\ \left(\text{b}\right)\text{ }\frac{\text{8}}{\text{15}}\text{+}\frac{\text{3}}{\text{15}}\\ \left(\mathrm{c}\right)\text{ }\frac{7}{5}-\frac{7}{5}\\ \left(\mathrm{d}\right)\text{ }\frac{1}{22}+\frac{21}{22}\\ \left(\mathrm{e}\right)\text{ }\frac{12}{15}-\frac{7}{15}\\ \left(\mathrm{f}\right)\text{ }\frac{5}{8}+\frac{3}{8}\\ \left(\mathrm{g}\right)\text{ }1-\frac{2}{3}\left(1=\frac{3}{3}\right)\\ \left(\mathrm{h}\right)\text{ }\frac{1}{4}+\frac{0}{4}\\ \left(\mathrm{i}\right)\text{ }3-\frac{12}{5}\end{array}$

Ans-

$\begin{array}{l}\text{(a)}\frac{1}{18}+\frac{1}{18}\\ \text{}=\frac{1+1}{18}\\ \text{}=\frac{2}{18}\end{array}$ $\begin{array}{l}\text{(b)}\frac{8}{15}+\frac{3}{15}\\ \text{}=\frac{8+3}{15}\\ \text{}=\frac{11}{15}\end{array}$ $\begin{array}{l}\text{}\end{array}$

$\begin{array}{l}\text{(c)}\frac{7}{7}-\frac{5}{7}\\ \text{}=\frac{7-5}{7}\\ \text{}=\frac{2}{7}\end{array}$ $\begin{array}{l}\text{}\end{array}$ $\begin{array}{l}\text{(d)}\frac{1}{22}+\frac{21}{22}\\ \text{}=\frac{1+21}{22}\\ \text{}=\frac{22}{22}=1\end{array}$ $\begin{array}{l}\text{}\end{array}$ $\begin{array}{l}\text{(e)}\frac{12}{15}-\frac{7}{15}\\ \text{}=\frac{12-7}{15}\\ \text{}=\frac{5}{15}=\frac{1}{3}\end{array}$

$\begin{array}{l}\begin{array}{l}\text{(f)}\frac{5}{8}+\frac{3}{8}\\ \text{ }=\frac{8}{8}=1\end{array}\\ \text{​​}\left(\text{g}\right)\text{}1–\frac{2}{3}\text{​}\\ \text{ }=\frac{3}{3}–\frac{1}{3}\text{​}\\ \text{ }=\frac{2}{3}\end{array}$ $\begin{array}{l}\text{}\end{array}$ $\begin{array}{l}\text{(h)}\frac{1}{4}+\frac{0}{4}\\ \text{}=\frac{1}{4}+0\\ \text{}=\frac{1}{4}\end{array}$ $\begin{array}{l}\end{array}$ $\begin{array}{l}\left(\text{i) 3}-\frac{12}{5}\\ \text{}=\frac{3×5}{5}-\frac{12}{5}\\ \text{}=\frac{15}{5}-\frac{12}{5}\\ \text{}=\frac{3}{5}\end{array}$

Shubham painted

$\frac{2}{3}$

of the wall space in his room. His sister Madhavi helped and painted

$\frac{1}{3}$

of the wall space. How much did they paint together?

Ans-

$\begin{array}{l}\text{Space painted by shubham =}\frac{2}{3}\text{of the room}\\ \text{Space painted by Madhvi =}\frac{1}{3}\text{of the room}\\ \text{Hence, together they painted =}\frac{2}{3}+\frac{1}{3}=1\\ \text{}\mathrm{i}.\mathrm{e}.\text{the complete wall.}\end{array}$

Fill in the missing fractions :

$\begin{array}{l}\left(\text{a}\right)\text{ }\frac{\text{7}}{\text{10}}-\overline{)}\text{ = }\frac{\text{3}}{\text{10}}\text{ }\\ \left(\text{b}\right)\text{ }\overline{)}\text{ }-\frac{\text{3}}{\text{21}}\text{=}\frac{\text{5}}{\text{21}}\\ \left(\text{c}\right)\text{ }\overline{)}\text{ }-\frac{\text{3}}{\text{6}}\text{ = }\frac{\text{3}}{\text{6}}\\ \left(\text{d}\right)\text{ }\overline{)}\text{ + }\frac{\text{5}}{\text{27}}\text{ = }\frac{\text{12}}{\text{27}}\end{array}$

Ans-

$\begin{array}{l}\left(\text{a)}\frac{7}{10}-\overline{)}=\frac{3}{10}\\ ⇒\overline{)}=\frac{7}{10}-\frac{3}{10}\\ ⇒\overline{)}=\frac{4}{10}\\ \left(\text{b)}\overline{)}-\frac{3}{21}=\frac{5}{21}\\ ⇒\overline{)}=\frac{3}{21}+\frac{5}{21}\\ ⇒\overline{)}=\frac{8}{21}\\ \text{(c)}\overline{)}-\frac{3}{6}=\frac{3}{6}\\ ⇒\overline{)}=\frac{3}{6}+\frac{3}{6}\\ ⇒\overline{)}=\frac{6}{6}=1\\ \text{(d)}\overline{)}+\frac{5}{27}=\frac{12}{27}\\ ⇒\overline{)}=\frac{12}{27}-\frac{5}{27}\\ ⇒\overline{)}=\frac{12-5}{27}=\frac{7}{27}\end{array}$

Javed was given

$\frac{5}{7}$

of a basket of oranges. What fraction of oranges was left in the basket?

Ans-

Fractions given to Javed =

$\frac{5}{7}$

$=1-\frac{5}{7}\phantom{\rule{0ex}{0ex}}=\frac{7}{7}-\frac{5}{7}\phantom{\rule{0ex}{0ex}}=\frac{2}{7}$

1. How to easily solve fractions for Class 6 (problems)?

Students should focus on clearing concepts first before attempting to solve complex problems. The main topics can be difficult to grasp at first, but with consistent effort, advanced ways can be learned gradually.

This chapter contains several parts and characteristics of fraction that necessitate more attention and effort at first. Once you’ve grasped the fundamentals, the subject will begin to take on a life of its own. Mathematics NCERT Solutions Class 6 Chapter 7 assists in providing the best answers that improve quick problem-solving skills while also guiding you to improve your analytical skills..

2. How can I access the NCERT Solutions for Mathematics Chapter 7 in Class 6 online?

Students may access NCERT Solutions for Class 6 Mathematics Chapter 7 easily from Extramarks,one of the leading  educational platforms for all classes from 1 to 12. They can go to the website and access all the NCERT Solutions anytime, anywhere, as per their convenience. The systemic and well-laid-out balanced study plan boosts their performance naturally and effortlessly.

3. What are the differences between proper, improper, and mixed fractions?

When the numerator is less than the denominator, the fraction is called proper. Proper fractions include 5/7, 4/9, and 35.

Fractions with a numerator higher than the denominator are called improper fractions. Examples of improper fractions are 13/7 and 15/9.

A mixed fraction is a fraction in which a whole number and a proper fraction are both present.

4. How do you define fractions for Class 6 Mathematics Chapter 7?

A fraction is the fractional part of a whole  number. The numerator is the component of the fraction that is higher, while the denominator is the part that is lower. Let’s use the number 7/19 as an example. The numerator is seven, and the denominator is nineteen. Always represent the fraction in the simplest form possible.

5. What are the most important concepts in Chapter 7 of Mathematics for Class 6?

Chapter 7 of Class 6 Mathematics is all about fractions. The following topics are covered in the chapter:

• The different concepts related to fractions.
• Addition, subtraction, multiplication, and division of fractions.
• Different methods are used for adding like and unlike fractions.
• Proper, improper, and mixed fractions.
• Techniques for solving different fractions

6. How can I improve in Class 6 Mathematics?

The only way to improve and score higher in Class 6 Mathematics is to practise. Students can refer to online learning materials such as sample papers, mock tests, and solutions to practise and improve their problem solving skills.

7. Who prepares these NCERT Solutions?

Extramarks prepare these NCERT Solutions with the help of experienced  subject matter experts while following the latest CBSE syllabus.