NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Edited By Ramraj Saini | Updated on Nov 30, 2023 09:49 AM IST

NCERT Solutions for Class 6 Maths Chapter 7 Fractions are discussed here. Our Expert team designed these NCERT solutions kepping in mind lated syllabus of CBSE 2023. A fraction is a number representing part of a whole. The whole may be a single object or a group of the object and the parts have to be equal. In Class 4 and 5 NCERT, you have already learnt about the representation of fractions. In Fraction class 6, you will learn about the various operations and applications of fractions in mathematics. You can also refer to the NCERT Books for Class 6 Maths to solve the problems covered under NCERT solutions for Class 6.

Latest: Important Maths Formulas for Class 6 - Chapterwise

This Story also Contains

NCERT Solutions for Class 6 Maths Chapter 7 Fractions - Important Formulae
NCERT Solutions for Class 6 Maths Chapter 7 Fractions - Important Points
NCERT Solutions for Class 6 Maths Chapter 7 Fractions
NCERT Solutions for Class 6 Maths Chapter 7 Fractions (Intext Questions and Exercise)
NCERT Solutions for Class 6 Maths Topic: Fractions on the Number Line
NCERT Solutions for Class 6 Maths Topic: Proper Fractions
NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.2
NCERT Solutions for Class 6 Maths Topic: Simplest Form of a Fraction
NCERT Solutions for Class 6 Maths Topic: Equivalent Fractions
NCERT Solutions for Class 6 Maths Exercise: 7.3
NCERT Solutions for Class 6 Maths Topic: Comparing Fractions
NCERT Solutions for Class Maths Topic: Comparing Like Fractions
NCERT Class 6 Maths Chapter 7 Fractions Topic: Arrangement of Fractions
NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.4
NCERT Class 6 Maths Chapter 7 Fractions Topic: Addition and Subtraction of Fractions
NCERT Class 6 Maths Chapter 7 Fractions Topic: Adding or Substracting like Fractions
NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.5
NCERT Class 6 Maths Chapter 7 Fractions Topic: Addition and Subtraction of Fractions
NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.6
Fractions Class 6 Maths Chapter 7-Topics
Key features of NCERT Solutions for Class 6 Maths chapter 7

$NCERT Solutions for Class 6 Maths Chapter 7 Fractions$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

The subtopics covered under the NCERT Fraction class 6 are the representation of fractions on the number line, proper- improper and mixed fractions, the simplest form of the fractions, equivalent fractions, comparing fractions, comparing, unlike fractions, comparing like fractions, subtraction, and addition of fractions and adding or subtracting fractions. CBSE NCERT solutions for Class 6 Maths chapter 7 Fractions is covering the problems from each subtopic. In this chapter of NCERT Syllabus for Class 6 Maths, there are a total of 37 questions in 6 exercises. To help students in their preparation, we have designed NCERT solutions for class 6th math chapter 7. NCERT Solutions are also available class-wise and subject-wise.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions - Important Formulae

A fraction can be represented as A/B, where A is called the numerator and B is called the denominator. The denominator cannot be zero.
Mixed fraction =Quotient {Remainder/Divisor)
Addition and subtraction of fraction with same denominator

A/B + C/B = (A+C)/B

A/B - C/B = (A-C)/B

Addition and subtraction of fraction with different denominator

A/B + C/D = AD/BD + BC/BD = (AD + CB)/BD

A/B - C/D = AD/BD - BC/BD = (AD - CB)/BD

Multiplication: Multiply numerator to numerator and denominator to denominator

(A/B)(C/D) = AC/BD

Division: Flip the second fraction and then multiply with the first fraction.

(A/B) /(C/D) = (A/B)(D/C) = AD/BC

NCERT Solutions for Class 6 Maths Chapter 7 Fractions - Important Points

Fraction: A fraction represents a part of a whole or a part of a group. It is expressed as a/b, where 'a' is called the numerator and 'b' is called the denominator.

Types of Fractions: Fractions can be classified as proper fractions, improper fractions, and mixed fractions. In a proper fraction, the numerator is smaller than the denominator. In an improper fraction, the numerator is equal to or greater than the denominator. A mixed fraction is a combination of a whole number and a proper fraction.

Equivalent Fractions: Fractions that represent the same value are called equivalent fractions. They have different numerators and denominators but represent the same part of a whole.

Simplification of Fractions: Fractions can be simplified by dividing both the numerator and the denominator by their common factors. The simplified fraction is the one in which the numerator and the denominator have no common factors other than 1.

Comparing Fractions: Fractions can be compared by cross-multiplication. If the product of the numerator of one fraction and the denominator of the other fraction is greater, then the first fraction is larger. If the product is smaller, then the second fraction is larger.

Addition and Subtraction of Fractions: For adding or subtracting fractions, the denominators must be the same. If they are different, the fractions need to be converted to equivalent fractions with the same denominator before performing the operation.

Multiplication of Fractions: To multiply fractions, multiply the numerators and multiply the denominators. The product is the numerator of the resulting fraction, and the product is the denominator.

Division of Fractions: To divide fractions, multiply the first fraction by the reciprocal (flipped version) of the second fraction. In other words, multiply by the numerator of the second fraction and divide by the denominator of the second fraction.

Representation of Fractions on a Number Line: Fractions can be represented on a number line by dividing the line segment between 0 and 1 into equal parts based on the denominator of the fraction.

Operations on Fractions and Whole Numbers: To perform operations involving fractions and whole numbers, convert the whole number into a fraction by giving it a denominator of 1, and then proceed with the operation

Free download NCERT Solutions for Class 6 Maths Chapter 7 Fractions PDF for CBSE Exam.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

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NCERT Solutions for Class 6 Maths Chapter 7 Fractions (Intext Questions and Exercise)

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.1

Q1 Write the fraction representing the shaded portion.

1643038507901

Answer: (i) $\frac{2}{4}\ =\ \frac{1}{2}$

(ii) $\frac{8}{9}$

(iii) $\frac{4}{8}\ =\ \frac{1}{2}$

(iv) $\frac{1}{4}$

(v) $\frac{3}{7}$

(vi) $\frac{9}{12}\ =\ \frac{3}{4}$

(vii) $\frac{10}{10}\ =\ 1$

(viii) $\frac{4}{9}$

(ix) $\frac{4}{8}\ =\ \frac{1}{2}$

(x) $\frac{1}{2}$

Q2 Colour the part according to the given fraction.

1643038548278

Answer: The coloured parts are shown below :-

1643038564328

Q3 Identify the error if any

1643038594802 This is $\frac{1}{2}$

1643038605008 This is $\frac{1}{4}$

1643038615474 This is $\frac{3}{4}$

Answer: Yes, the above fractions are wrong. For these fractions to be correct areas of each part should be same. But clearly, in the given figure, the areas are not the same.

Q4 What fraction of a day is $8$ hours?

Answer: Total hours in 1 day $=\ 24$

Thus the required fraction is :-

$=\ \frac{8}{24}\ =\ \frac{1}{3}$

Q5 What fraction of an hour is $40$ minutes?

Answer: We know that 1 hour has 60 minutes.

Thus fraction of 40 minutes is :-

$=\ \frac{40}{60}\ =\ \frac{4}{6}\ =\ \frac{2}{3}$

Q6 (a) 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. How can Arya divide his sandwiches so that each person has an equal share?

Answer: Arya needs to divide one sandwich into 3 equal parts (as three persons are there.)

Thus each sandwich is divided into 3 parts.

Q6 (b) 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. What part of a sandwich will each boy receive?

Answer: Since they have to distribute 1 part in 3 people, hence the fraction received by each boy will be:-

$F\ =\ \frac{1}{3}$

Q7 Kanchan dyes dresses. She had to dye $30$ dresses. She has so far finished $20$ dresses. What fraction of dresses has she finished?

Answer: The required fraction is:-

$=\ \frac{20}{30}\ =\ \frac{2}{3}$

Q8 Write the natural numbers from $2$ to $12.$ What fraction of them are prime numbers?

Answer: We have :- 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

Prime number :- 2, 3, 5, 7, 11.

Thus the fraction of prime numbers is:- $\frac{5}{11}$

Q9 Write the natural numbers from $102$ to $113$ . What fraction of them are prime numbers?

Answer: The natural numbers are :- 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113.

Prime numbers are :- 103, 107, 109, 113.

Thus fraction is :-

Q10 What fraction of these circles have $X$ ’s in them?

1643038649229

Answer: The number of boxes with X in them = 4

Total number of boxes = 8.

The required fraction is :

$=\ \frac{4}{8}\ =\ \frac{1}{2}$

Q11 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?

Answer: The fraction of the CDs she bought is :

$=\ \frac{3}{8}$

And the fraction of CDs received as gifts is :

$=\ \frac{5}{8}$

NCERT Solutions for Class 6 Maths Topic: Fractions on the Number Line

Q1 Show $\frac{3}{5}$ on a number line.

Answer: First we write $1$ as $\frac{5}{5}$ and divide the number line into 5 equal parts.

3-batta-5

Q2 Show $\frac{1}{10},\frac{0}{10},\frac{5}{10}$ and $\frac{10}{10}$ on a number line.

Answer:

First, we write $1$ as $\frac{10}{10}$ and divide the number line in 10 equal parts.

1-batta-10

Q3 Can you show any other fraction between $0$ and $1$ ?Write five more fractions that you can show.

Answer:

Yes. There are infinite number of fraction between $0$ and $1$ (Numerator is less than denominator)

Five more fractions are: $\frac{4}{5}, \frac{6}{11}, \frac{4}{7}, \frac{3}{8}, \frac{11}{25}$

Q4 How many fractions lie between $0$ and $1$ ? Think, discuss and write your answer?

Answer: There are infinite number of fractions between $0$ and $1$ .

A fraction is of form $\frac{a}{b}$ and for a number lying between $0$ and $1$ , the numerator has to be less than the denominator.

NCERT Solutions for Class 6 Maths Topic: Proper Fractions

Q1 Give a proper fraction : (a) whose numerator is $5$ and the denominator is $7.$
(b) whose denominator is $9$ and the numerator is $5.$

(d) whose denominator is $4$ more than the numerator.

(Give any five. How many more can you make?)

Answer: A proper fraction whose:

(a) the numerator is $5$ and the denominator is $7.$ = $\frac{5}{7}$

(b) denominator is $9$ and numerator is $5.$ = $\frac{5}{9}$

Pairs of numbers having sum 10 = $(1,9),(2,8),(3,7),(4,6)(5,5)$

Therefore, the proper fractions are $\frac{1}{9}, \frac{2}{8}, \frac{3}{7}, \frac{4}{6}$

(d) denominator is $4$ more than the numerator. = $\frac{1}{5}, \frac{2}{6}, \frac{15}{19}, \frac{105}{109}, \frac{199}{203},$

Q2 A fraction is given. How will you decide, by just looking at it, whether, the fraction is

(a) less than $1$ ?

(b) equal to $1$ ?

Answer: (a) If the numerator is smaller than the denominator, then the fraction will be less than $1$ .

(b) If the numerator is equal to the denominator, then the fraction will be equal to $1$ .

Q3 Fill up using one of these: ‘ $>$ ’, ‘ $<$ ’ or ‘ $=$ ’

(a) $\frac{1}{2}\square 1$

(b) $\frac{3}{5}\square 1$

(d) $\frac{4}{4}\square 1$

(e) $\frac{2005}{2005}\square 1$

Answer: (a)

$\frac{1}{2}< 1$

(b)

$\frac{3}{5}< 1$

(c)

$1> \frac{7}{8}$

(d)

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

(e)

$\frac{2005}{2005}= 1$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.2

Q1 (a) Draw number lines and locate the points on them : $\frac{1}{2},\frac{1}{4},\frac{3}{4},\frac{4}{4}$

Answer: The number line is given below:-

1643038680325

Q1 (b) Draw number lines and locate the points on them : $\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{7}{8}$

Answer: The number line is shown below with the required points marked.

1643038705799

Q1 (c) Draw number lines and locate the points on them : $\frac{2}{5},\frac{3}{5},\frac{8}{5},\frac{4}{5}$

Answer: The number line locating the given fraction is shown below:-

1643038731961

Q2 Express the following as mixed fractions :

(a) $\frac{20}{3}$

(b) $\frac{11}{5}$

(d) $\frac{28}{5}$

(e) $\frac{19}{6}$

(f) $\frac{35}{9}$

Answer: (a) $\frac{20}{3}\ =\ \frac{18\ +\ 2}{3}\ =\ 6\frac{2}{3}$

(b) $\frac{11}{5}\ =\ \frac{10\ +\ 1}{5}\ =\ 2\frac{1}{5}$

(d) $\frac{28}{5}\ =\ \frac{25\ +\ 3}{5}\ =\ 5\frac{3}{5}$

(e) $\frac{19}{6}\ =\ \frac{18\ +\ 1}{6}\ =\ 3\frac{1}{6}$

(f) $\frac{35}{9}\ =\ \frac{27\ +\ 8}{9}\ =\ 3\frac{8}{9}$

Q3 Express the following as improper fractions :

(a) $7\frac{3}{4}$

(b) $5\frac{6}{7}$

(d) $10\frac{3}{5}$

(e) $9\frac{3}{7}$

(f) $8\frac{4}{9}$

Answer: The improper fractions of the mixed fractions are given below :-

(a) $7\frac{3}{4}\ =\ \frac{28\ +\ 3}{4}\ =\ \frac{31}{4}$

(b) $5\frac{6}{7}\ =\ \frac{35\ +\ 6}{7}\ =\ \frac{41}{7}$

(d) $10\frac{3}{5}\ =\ \frac{50\ +\ 3}{5}\ =\ \frac{53}{5}$

(e) $9\frac{3}{7}\ =\ \frac{63\ +\ 3}{7}\ =\ \frac{66}{7}$

(f) $8\frac{4}{9}\ =\ \frac{72\ +\ 4}{9}\ =\ \frac{76}{9}$

NCERT Solutions for Class 6 Maths Topic: Simplest Form of a Fraction

Q1 Write the simplest form of :

(i) $\frac{15}{75}$

(ii) $\frac{16}{72}$

(iii) $\frac{17}{51}$

(iv) $\frac{42}{28}$

(v) $\frac{80}{24}$

Answer: (i) $\frac{15}{75}=\frac{5}{25}=\frac{1}{5}$

(ii) $\frac{16}{72}=\frac{8}{36}=\frac{4}{18}=\frac{2}{9}$

(iii) $\frac{17}{51}=\frac{1}{3}$

(iv) $\frac{42}{28}=\frac{21}{14}=\frac{3}{2}$

(v) $\frac{80}{24}=\frac{40}{12}=\frac{20}{6}=\frac{10}{3}$

Q2 Is $\frac{49}{64}$ in its simplest form?

Answer: Yes, $\frac{49}{64}$ is in its simplest form because 49 and 64 has no common divisor.

NCERT Solutions for Class 6 Maths Topic: Equivalent Fractions

Q1 Are $\frac{1}{3}$ and $\frac{2}{7}$ ; $\frac{2}{5}$ and $\frac{2}{7}$ ; $\frac{2}{9}$ and $\frac{6}{27}$ and equivalent? Give reason

Answer: $\frac{1}{3}$ and $\frac{2}{7}$ ; $\frac{2}{5}$ and $\frac{2}{7}$ are not equivalent because

$\frac{1}{3}> \frac{2}{7}$ and

$\frac{2}{5}> \frac{2}{7}$

but

$\frac{2}{9}= \frac{6}{27}=0.222$

Q2 Give example of four equivalent fractions.

Answer: Four example of equivalent fractions are :

$\frac{2}{4}=\frac{4}{8};\frac{1}{3}=\frac{3}{9};\frac{8}{4}=\frac{12}{6};\frac{1}{5}=\frac{5}{25}$

Q3 Identify the fractions in each. Are these fractions equivalent?

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Answer:

seema

(i) $\frac{6}{8}$ (ii) $\frac{9}{12}$ (iii) $\frac{12}{16}$ (iv) $\frac{15}{20}$

all fractions in it simplest form is

$\frac{3}{4}$

So all fractions are equivalent

Q1 Find five equivalent fractions of each of the following:

(i) $\frac{2}{3}$

(ii) $\frac{1}{5}$

(iii) $\frac{3}{5}$

(iv) $\frac{5}{9}$

Answer: (i) $\frac{2}{3}=\frac{8}{12}$

(ii) $\frac{1}{5}=\frac{5}{25}$

(iii) $\frac{3}{5}=\frac{15}{25}$

(iv) $\frac{5}{9}=\frac{50}{90}$

NCERT Solutions for Class 6 Maths Exercise: 7.3

Q1 Write the fractions. Are all these fractions equivalent?

1643038760286

1643038770006

Answer: In the case of (a), we have:-

(i) $f_1\ =\ \frac{1}{2}$

(ii) $f_2\ =\ \frac{2}{4} =\ \frac{1}{2}$

(iii) $f_3\ =\ \frac{3}{6} =\ \frac{1}{2}$

(iv) $f_4\ =\ \frac{4}{8} =\ \frac{1}{2}$

Hence all fractions are equal in this case.

In the case of (b), we have:-

(i) $f_1\ =\ \frac{4}{12}\ =\ \frac{1}{3}$

(ii) $f_2\ =\ \frac{3}{9} =\ \frac{1}{3}$

(iii) $f_3\ =\ \frac{2}{6} =\ \frac{1}{3}$

(iv) $f_4\ =\ \frac{1}{3}$

(v) $f_5\ =\ \frac{6}{15}\ =\ \frac{2}{5}$

Q2 Write the fractions and pair up the equivalent fractions from each row.

1643038839251

Answer: The fractions of each are given below :-

(a) $f_a\ =\ \frac{1}{2}$

(b) $f_b\ =\ \frac{4}{6}\ =\ \frac{2}{3}$

(d) $f_d\ =\ \frac{2}{8}\ =\ \frac{1}{4}$

(e) $f_e\ =\ \frac{3}{4}$

Similarly,

(i) $f_1\ =\ \frac{6}{18}\ =\ \frac{1}{3}$

(ii) $f_2\ =\ \frac{4}{8}\ =\ \frac{1}{2}$

(iii) $f_3\ =\ \frac{12}{16}\ =\ \frac{3}{4}$

(iv) $f_4\ =\ \frac{8}{12}\ =\ \frac{2}{3}$

(v) $f_5\ =\ \frac{4}{16}\ =\ \frac{1}{4}$

Q3 (a) Replace box in each of the following by the correct number : $\frac{2}{7}=\frac{8}{\square }$

Answer: The correct number is 28.

$\frac{2}{7}\times \frac{4}{4} =\ \frac{8}{28}\ =\frac{8}{\square }$

Thus $\square\ =\ 28$ .

Q3 (b) Replace $\square$ in each of the following by the correct number : $\frac{5}{8}=\frac{10}{\square }$

Answer: (b) The correct answer is 16.

$\frac{5}{8}\times \frac{2}{2}=\frac{10}{16}$

Q3 (c) Replace $\square$ in each of the following by the correct number : $\frac{3}{5}=\frac{\square }{20}$

Answer: The required value is 12.

$\frac{3}{5}\times \frac{4}{4}=\frac{12 }{20}$

Q3 (d) Replace in each of the following by the correct number : $\frac{45}{60}=\frac{15}{\square }$

Answer: The required value is 20.

$\frac{45}{60}\times \frac{\frac{1}{3}}{\frac{1}{3}}=\frac{15}{20 }$

Q3 (e) Replace $\square$ in each of the following by the correct number : $\frac{18}{24}=\frac{4}{\square }$

Answer: The correct number is $\frac{48}{9}$ .

Multiplying numerator and denomenator by $\frac{4}{18}$ .

We have :- $\frac{18}{24}\times \frac {\frac{4}{18}}{\frac{4}{18}}\ =\ \frac{4}{\frac{96}{18}}\ =\ \frac{4}{\frac{48}{9}}$

Hence $\square\ =\ \frac{48}{9}$

Q4 Find the equivalent fraction of $\frac{3}{5}$ having

(a) denominator $20$

(b) numerator $9$

(d) numerator $27$

Answer: (a) Multiply numerator and denominator by 4, we have :

$\frac{3}{5}\times \frac{4}{4}\ =\ \frac{12}{20}$

(b) Multiply numerator and denominator by 3, we have :

$\frac{3}{5}\times \frac{3}{3}\ =\ \frac{9}{15}$

$\frac{3}{5}\times \frac{6}{6}\ =\ \frac{18}{30}$

(d) Multiply numerator and denominator by 9, we have :

$\frac{3}{5}\times \frac{9}{9}\ =\ \frac{27}{45}$

Q5 Find the equivalent fraction of $\frac{36}{48}$ with

(a) numerator $9$

(b) denominator $4$

Answer: The required equivalent fractions are given below :-

(a) Divide both numerator and denomenator by 4.

$\frac{36}{48}\times \frac{\frac{1}{4}}{\frac{1}{4}}\ =\ \frac{9}{12}$

(b) Divide both numerator and denomenator by 12.

$\frac{36}{48}\times \frac{\frac{1}{12}}{\frac{1}{12}}\ =\ \frac{3}{4}$

Q6 (a) Check whether the given fractions are equivalent : $\frac{5}{9},\frac{30}{35}$

Answer: Multiply both numerator and denominator by 6.

$\frac{5}{9}\times \frac{6}{6}\ =\ \frac{30}{54}\ \neq \frac{30}{35}$

Q6 (b) Check whether the given fractions are equivalent : $\frac{3}{10},\frac{12}{50}$

Answer:

Multiply both numerator and denominator by 4, we get :

$\frac{3}{10}\times \frac{4}{4}\ =\ \frac{12}{40}\ \neq \ \frac{12}{50}$

Q6 (c) Check whether the given fractions are equivalent : $\frac{7}{13},\frac{5}{11}$

Answer: Multiply both numerator and denominator by $\frac{5}{7}$ , we get :

$\frac{7}{13}\times \frac{\frac{5}{7}}{\frac{5}{7}}\ =\ \frac{5}{\frac{65}{7}}\ \neq \ \frac{5}{11}$

Hence these two fractions are not the same.

Q7 Reduce the following fractions to simplest form :

(a) $\frac{48}{60}$

(b) $\frac{150}{60}$

(d) $\frac{12}{52}$

(e) $\frac{7}{28}$

Answer: (a) $\frac{48}{60}\ =\ \frac{24}{30}\ =\ \frac{12}{15}\ =\frac{4}{5}$

(b) $\frac{150}{60}\ =\ \frac{15}{6}\ =\ \frac{5}{2}$

(d) $\frac{12}{52}\ =\ \frac{6}{26}\ =\ \frac{3}{13}$

(e) $\frac{7}{28}\ =\ \frac{1}{4}$

Q8 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?

Answer: The fraction of pencils used by Ramesh is:-

$=\ \frac{10}{20}\ =\ \frac{1}{2}$

The fraction of pencils used by Sheelu is:-

$=\ \frac{25}{50}\ =\ \frac{1}{2}$

The fraction of pencils used by Jamaal is:-

$=\ \frac{40}{80}\ =\ \frac{1}{2}$

Thus, the fractions of pencils used by each are the same.

Q9 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) $\frac{9}{10}$

Answer: (i) $\frac{250}{400}\ =\ \frac{25}{40}\ =\ \frac{5}{8}$

(ii) $\frac{180}{200}\ =\ \frac{18}{20}\ =\ \frac{9}{10}$

(iii) $\frac{660}{990}\ =\ \frac{66}{99}\ =\ \frac{22}{33}\ =\ \frac{2}{3}$

(iv) $\frac{180}{360}\ =\ \frac{18}{36}\ =\ \frac{2}{4}\ =\ \frac{1}{2}$

(v) $\frac{220}{550}\ =\ \frac{22}{55}\ =\ \frac{2}{5}$

NCERT Solutions for Class 6 Maths Topic: Comparing Fractions

Q1 You get one-fifth of a bottle of juice and your sister gets one-third of the same size of a bottle of juice. Who gets more?

Answer: My sister gets more because $\frac{1}{3}> \frac{1}{5}$

NCERT Solutions for Class Maths Topic: Comparing Like Fractions

Q1 Which is the larger fraction?

(i) $\frac{7}{10}$ or $\frac{8}{10}$

(ii) $\frac{11}{24}$ or $\frac{13}{24}$

(iii) $\frac{17}{102}$ or $\frac{12}{102}$

Answer: The fractions are shown below using greater than or less than sign

(i) $\frac{7}{10}$ $<$ $\frac{8}{10}$

(ii) $\frac{11}{24}$ $<$ $\frac{13}{24}$

(iii) $\frac{17}{102}$ $>$ $\frac{12}{102}$

Q2 Write these in ascending and also in descending order.

(a) $\frac{1}{8},\frac{5}{8},\frac{3}{8}$

(b) $\frac{1}{5},\frac{11}{5},\frac{4}{5},\frac{3}{5},\frac{7}{5}$

Answer: (a) $\frac{1}{8}< \frac{3}{8}< \frac{5}{8}$

$\frac{5}{8}>\frac{3}{8}> \frac{1}{8}$

(b) $\frac{1}{5}< \frac{3}{5}< \frac{4}{5}< \frac{7}{5}< \frac{11}{5}$

$\frac{11}{5}> \frac{7}{5}> \frac{4}{5}> \frac{3}{5}> \frac{1}{5}$

$\frac{13}{7}> \frac{11}{7}> \frac{7}{7}> \frac{3}{7}> \frac{1}{7}$

NCERT Class 6 Maths Chapter 7 Fractions Topic: Arrangement of Fractions

Q1 (1) Arrange the following in ascending and descending order :

$\frac{1}{12},\frac{1}{23},\frac{1}{5},\frac{1}{7},\frac{1}{50},\frac{1}{9},\frac{1}{17}$

Answer: (a) $\frac{1}{5}> \frac{1}{7}> \frac{1}{9}> \frac{1}{12}> \frac{1}{17}> \frac{1}{23}> \frac{1}{50}$

and $\frac{1}{50}< \frac{1}{23}< \frac{1}{17}< \frac{1}{12}< \frac{1}{9}< \frac{1}{7}< \frac{1}{5}$

Q1 (b) Arrange the following in ascending and descending order :

$\frac{3}{7},\frac{3}{11},\frac{3}{5},\frac{3}{2},\frac{3}{13},\frac{3}{4},\frac{3}{17}$

Answer: The following in ascending and descending order are :

(b) $\frac{3}{2}>\frac{3}{4}> \frac{3}{5}>\frac{3}{7}>\frac{3}{11}>\frac{3}{13}>\frac{3}{17}$

$\frac{3}{17}<\frac{3}{13}<\frac{3}{11}<\frac{3}{7}<\frac{3}{5}<\frac{3}{2}<\frac{3}{3}$

Q1 (c) Arrange the following in ascending and descending order :

Write 3 more similar examples and arrange them in ascending and descending order.

Answer: The following in ascending and descending order are:

(i) $\frac{3}{5},\frac{7}{5},\frac{4}{5}$

$\frac{3}{5}<\frac{4}{5}<\frac{7}{5}$

and $\frac{7}{5}>\frac{4}{5}>\frac{3}{5}$

(ii) $\frac{3}{11},\frac{7}{11},\frac{4}{11}$

$\frac{3}{11}<\frac{4}{11}<\frac{7}{11}$

and $\frac{7}{11}>\frac{4}{11}>\frac{3}{11}$

(iii) $\frac{3}{11},\frac{3}{7},\frac{3}{5}$

$\frac{3}{11}<\frac{3}{7}<\frac{3}{5}$

and $\frac{3}{5}>\frac{3}{7}>\frac{3}{11}$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.4

Q1 Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign $'<'\; '='\; '> '$ between the fractions:

1643038920076

1643038930022 (c) Show $\frac{2}{6},\frac{4}{6},\frac{8}{6}\; and\; \frac{6}{6}$ on the number line. Put appropriate signs between the fractions given

$\frac{5}{6}\square \frac{2}{6},$ $\frac{3}{6}\square 0,$ $\frac{1}{6}\square \frac{6}{6},$ $\frac{8}{6}\square \frac{5}{6},$

Answer: (a) $f_1\ =\ \frac{3}{8}$

$f_2\ =\ \frac{6}{8}\ =\ \frac{3}{4}$

$f_3\ =\ \frac{4}{8}\ =\ \frac{1}{2}$

$f_4\ =\ \frac{1}{8}$

$f_2\ >\ f_3\ >\ f_1\ >\ f_4$

(b) $f_1\ =\ \frac{8}{9}$

$f_2\ =\ \frac{4}{9}$

$f_3\ =\ \frac{3}{9}\ =\ \frac{1}{3}$

$f_4\ =\ \frac{6}{9}\ =\ \frac{2}{3}$

(c)

1643038946291

From the above number line we can compare the given numbers easily.

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

Q2 Compare the fractions and put an appropriate sign.

(a) $\frac{3}{6}\square \frac{2}{6}$

(b) $\frac{1}{7}\square \frac{1}{4}$

(d) $\frac{3}{5}\square \frac{3}{7}$

Answer: The comparison is given below :-

(a) $\frac{3}{6}\ >\ \frac{2}{6}$

(b) $\frac{1}{7}\ <\ \frac{1}{4}$

(d) $\frac{3}{5}\ >\ \frac{3}{7}$

Q3 Make five more such pairs and put appropriate signs.

Answer: The five pairs can be :-

$\frac{2}{3}\ > \frac{1}{3}$ , $\frac{5}{3}\ > \frac{2}{3}$ $\frac{5}{9}\ < \frac{4}{3}$ $\frac{2}{7}\ < \frac{5}{7}$ $\frac{1}{2}\ >\ \frac{1}{3}$

Q4 (a) Look at the figures and write $'< ' or '> ','='$ between the given pairs of fractions.

1643038973885

(a) $\frac{1}{6}\square \frac{1}{3}$

Answer: With the help of given diagram :

$\frac{1}{6}\ <\ \frac{2}{6}$

Thus $\frac{1}{6}\ <\ \frac{1}{3}$

Q4 (b) Look at the figures and write $'< ' or '> ','='$ between the given pairs of fractions.

1643038997226

(b) $\frac{3}{4}\square \frac{2}{6}$

Answer: From the diagram it is cleat that :

$\frac{3}{4}\ >\ \frac{2}{6}$

Q4 (c) Look at the figures and write $'< ' or '> ','='$ between the given pairs of fractions.

1643039020469

Answer: From the given diagram, we can clearly say that :-

$\frac{2}{3}\ >\ \frac{2}{4}$

Q4 (d) Look at the figures and write ‘<’ or ‘>’, ‘=’ between the given pairs of fractions.

1643039042715

(d) $\frac{6}{6}\ \square\ \frac{3}{3}$

Answer: From the diagram it is clear that :-

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

Q5 How quickly can you do this? Fill appropriate sign.

(a) $\frac{1}{2}\square \frac{1}{5}$

(b) $\frac{2}{4}\square \frac{3}{6}$

(d) $\frac{3}{4}\square \frac{2}{8}$

(e) $\frac{3}{5}\square \frac{6}{5}$

(f) $\frac{7}{9}\square \frac{3}{9}$

(g) $\frac{1}{4}\square \frac{2}{8}$

(h) $\frac{6}{10}\square \frac{4}{5}$

(i) $\frac{3}{4}\square \frac{7}{8}$

(j) $\frac{6}{10}\square \frac{3}{5}$

(k) $\frac{5}{7}\square \frac{15}{21}$

Answer: (a) $\frac{1}{2}\ >\ \frac{1}{5}$

(b) $\frac{2}{4}\ =\ \frac{3}{6}$

(d) $\frac{3}{4}\ >\ \frac{2}{8}$

(e) $\frac{3}{5}\ <\ \frac{6}{5}$

(f) $\frac{7}{9}\ >\ \frac{3}{9}$

(g) $\frac{1}{4}\ =\ \frac{2}{8}$

(h) $\frac{6}{10}\ <\ \frac{4}{5}$

(i) $\frac{3}{4}\ <\ \frac{7}{8}$

(j) $\frac{6}{10}\ =\ \frac{3}{5}$

(k) $\frac{5}{7}\ =\ \frac{15}{21}$

Q6 The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.

(a) $\frac{2}{12}$

(b) $\frac{3}{15}$

(d) $\frac{16}{100}$

(e) $\frac{10}{16}$

(f) $\frac{15}{75}$

(g) $\frac{12}{60}$

(h) $\frac{16}{96}$

(i) $\frac{12}{75}$

( j) $\frac{12}{72}$

(k) $\frac{3}{18}$

(l) $\frac{4}{25}$

Answer: (i) $\frac{2}{12}\times \frac{\frac{1}{2}}{\frac{1}{2}}\ =\ \frac{1}{6}$

(ii) $\frac{3}{15}\times \frac{\frac{1}{3}}{\frac{1}{3}}\ =\ \frac{1}{5}$

(iii) $\frac{8}{50}\times \frac{\frac{1}{2}}{\frac{1}{2}}\ =\ \frac{4}{25}$

(iv) $\frac{16}{100}\times \frac{\frac{1}{4}}{\frac{1}{4}}\ =\ \frac{4}{25}$

(v) $\frac{10}{16}\times \frac{\frac{1}{2}}{\frac{1}{2}}\ =\ \frac{5}{8}$

(vi) $\frac{15}{75}\times \frac{\frac{1}{15}}{\frac{1}{15}}\ =\ \frac{1}{5}$

(vii) $\frac{12}{60}\times \frac{\frac{1}{12}}{\frac{1}{12}}\ =\ \frac{1}{5}$

(viii) $\frac{16}{96}\times \frac{\frac{1}{16}}{\frac{1}{16}}\ =\ \frac{1}{6}$

(ix) $\frac{12}{75}\times \frac{\frac{1}{3}}{\frac{1}{3}}\ =\ \frac{4}{25}$

(x) $\frac{12}{72}\times \frac{\frac{1}{12}}{\frac{1}{12}}\ =\ \frac{1}{6}$

(xi) $\frac{3}{18}\times \frac{\frac{1}{3}}{\frac{1}{3}}\ =\ \frac{1}{6}$

(xii) $\frac{4}{25}$

Q7 (a) Find answers to the following. Write and indicate how you solved them.

Is $\frac{5}{9}$ equal to $\frac{4}{5}?$

Answer: No.

Multiply numerator and denomenator by $\frac{4}{5}$ .

We have : $\frac{5}{9}\times \frac{\frac{4}{5}}{\frac{4}{5}}\ =\ \frac{4}{\frac{36}{5}}$

Hence $\frac{5}{9}\ \neq \ \frac{4}{5}$

Q7 (b) Find answers to the following. Write and indicate how you solved them.

Is $\frac{9}{16}$ equal to $\frac{5}{9}$ ?

Answer: We have $\frac{9}{16}$ .

$\frac{9}{16}\ =\ \frac{9}{16}\times \frac{\frac{5}{9}}{\frac{5}{9}}\ =\ \frac{5}{\frac{80}{9}}\ \neq\ \frac{5}{9}$

Q7 (c) Find answers to the following. Write and indicate how you solved them.

Is $\frac{4}{5}$ equal to $\frac{16}{20}?$

Answer: Yes.

By multiplying numerator and denominator by 5, we get :

$\frac{4}{5}\times \frac{5}{5}\ =\ \frac{16}{20}$

Q7 (d) Find answers to the following. Write and indicate how you solved them.

Is $\frac{1}{15}$ equal to $\frac{4}{30}$ ?

Answer: No.

Multiply both numerator and denomenator by 2, we get :-

$\frac{1}{15}\times \frac{2}{2}\ =\ \frac{2}{30}\ \neq\ \frac{4}{30}$

Q8 Ila read $25$ pages of a book containing $100$ pages. Lalita read $\frac{2}{5}$ of the same book. Who read less?

Answer: The fraction of the book read by Ila is:-

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

So we can compare the fraction now:-

$\frac{1}{4}\ <\ \frac{2}{5}$

Hence Ila reads less.

Q9 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?

Answer: Who exercised for a longer time can be found by comparing the fraction of their work time.

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

Hence Rohit exercised for a longer time.

Q10 In a class A of $25$ students, $20$ passed with $60^{o}/_{o}$ or more marks; in another class B of $30$ students, $24$ passed with $60^{o}/_{o}$ or more marks. In which class was a greater fraction of students getting with $60^{o}/_{o}$ or more marks?

Answer: In class A, the fraction of students passed with $60 \%$ or above marks :

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

And, in class B, the fraction is :

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

Hence the required fraction is same in both the classes.

NCERT Class 6 Maths Chapter 7 Fractions Topic: Addition and Subtraction of Fractions

Q1 My mother divided an apple into $4$ equal parts. She gave me two parts and my brother one part. How much apple did she give to both of us together?

Answer: mother gave to me $\frac{1}{2}$ part

mother gave to my brother $\frac{1}{4}$ part

She gave both off us

$\frac{1}{2}+\frac{1}{4}=\frac{3}{4}$ part

Q2 Mother asked Neelu and her brother to pick stones from the wheat. Neelu picked one-fourth of the total stones in it and her brother also picked up one-fourth of the stones. What fraction of the stones did both pick up together?

Answer: Neelu picked stones

$=\frac{1}{4}$

brother picked up the stones

$=\frac{1}{4}$

The total fraction of the stones they both pick up together

$=\frac{1}{4}+\frac{1}{4}=\frac{1}{2}$ of total stones.

Q3 Sohan was putting covers on his note books. He put one fourth of the covers on Monday. He put another one fourth on Tuesday and the remaining on Wednesday. What fraction of the covers did he put on Wednesday?

Answer: He put covers on Monday= $\frac{1}{4}$

He put the cover on Tuesday = $\frac{1}{4}$

and the remaining on Wednesday.

Thus, the fraction of the covers he put on Wednesday = $1-(\frac{1}{4}+\frac{1}{4})$

$=1-(\frac{1}{2})$

$=\frac{1}{2}$

NCERT Class 6 Maths Chapter 7 Fractions Topic: Adding or Substracting like Fractions

Q1 Find the difference between $\frac{7}{8}$ and $\frac{3}{8}$ .

Answer: The difference between $\frac{7}{8}$ and $\frac{3}{8}$ is given by

$\frac{7}{8}-\frac{3}{8}=\frac{4}{8}=\frac{1}{2}$

Q2 Mother made a gud patti in a round shape. She divided it into $5$ parts. Seema ate one piece from it. If I eat another piece then how much would be left?

Answer: Seema ate = $\frac{1}{5}$

I eat = $\frac{1}{5}$

Total part eaten is

$\frac{1}{5}+\frac{1}{5}=\frac{2}{5}$

The left part would be

$=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}$

Q3 My elder sister divided the watermelon into $16$ parts. I ate $7$ out of them. My friend ate $4$ . How much did we eat between us? How much more of the watermelon did I eat than my friend? What portion of the watermelon remained?

Answer: I ate= $\frac{7}{16}$

My friend ate = $\frac{4}{16}$

we both eat

$\frac{7}{16}+\frac{4}{16}=\frac{7+4}{16}=\frac{11}{16}$

the watermelon more I eat than my friend is

$\frac{7}{16}-\frac{4}{16}=\frac{7-4}{16}=\frac{3}{16}$

The portion of the watermelon remained

$1-\frac{11}{16}=\frac{16-11}{16}=\frac{5}{16}$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.5

Q1 Write these fractions appropriately as additions or subtractions :

1643039073930

1643039101975 1643039087324

1643039121480

Answer: In case (a) - Addition

case (b) - Subtraction

case (c) - Addition

1643039131177

Q2 Solve :

(a) $\frac{1}{18} +\frac{1}{18}$

(b) $\frac{8}{15} +\frac{3}{15}$

(d) $\frac{1}{22} +\frac{21}{22}$

(e) $\frac{12}{15} -\frac{7}{15}$

(f) $\frac{5}{8} +\frac{3}{8}$

(g) $1-\frac{2}{3}\left ( 1=\frac{3}{3} \right )$

( h) $\frac{1}{4}+\frac{0}{4}$

(i) $3-\frac{12}{5}$

Answer: (a) $\frac{1}{18} +\frac{1}{18}\ =\ \frac{1+1}{18}\ =\ \frac{2}{18}\ =\ \frac{1}{9}$

(b) $\frac{8}{15} +\frac{3}{15}\ =\ \frac{8+3}{15}\ =\ \frac{11}{15}$

(d) $\frac{1}{22} +\frac{21}{22}\ =\ \frac{1+21}{22}\ =\ \frac{22}{22}\ =\ 1$

(e) $\frac{12}{15} -\frac{7}{15}\ =\ \frac{12-7}{15}\ =\ \frac{5}{15}\ =\ \frac{1}{ 3}$

(f) $\frac{5}{8} +\frac{3}{8}\ =\ \frac{5+3}{8}\ =\ \frac{8}{8}\ =\ 1$

(g) $1-\frac{2}{3}\ =\ \frac{3}{3}\ -\ \frac{2}{3}\ =\ \frac{3-2}{3}\ =\ \frac{1}{3}$

( h) $\frac{1}{4}+\frac{0}{4}\ =\ \frac{1+0}{4}\ =\ \frac{1}{4}$

(i) $3-\frac{12}{5}\ =\ \frac{15}{5}\ -\ \frac{12}{5}\ =\ \frac{15-12}{5}\ =\ \frac{3}{5}$

Q3 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?

Answer: Total wall painted = Wall painted by Subham + Wall pained by Madhavi

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

Hence the whole wall is painted by them.

Q4 Fill in the missing fractions.

(a) $\frac{7}{10}-\square =\frac{3}{10}$

(b) $-\square \frac{3}{21}=\frac{5}{21}$

(d) $\square+ \frac{5}{27}=\frac{12}{27}$

Answer: (a) $\frac{7}{10}-\square =\frac{3}{10}$

$\square\ =\ \frac{7}{10}\ -\ \frac{3}{10}$

or $\square\ =\ \frac{5}{10}\ =\ \frac{1}{2}$

(b) $-\square \frac{3}{21}=\frac{5}{21}$

$-\square =\frac{5}{3}$

or $\square\ =\ -\ \frac{5}{3}$

$\square\ =\ \frac{3}{6}\ +\ \frac{3}{6}\ =\ \frac{6}{6}\ =\ 1$

(d) $\square+ \frac{5}{27}=\frac{12}{27}$

$\square\ =\ \frac{12}{27}\ -\ \frac{5}{27}$

or $=\ \frac{7}{27}$

Q5 Javed was given $\frac{5}{7}$ of a basket of oranges. What fraction of oranges was left in the basket?

Answer: The total fraction of oranges in the basket are $\frac{7}{7}$ .

Thus the fraction of oranges left is :

$\frac{7}{7}\ -\ \frac{5}{7}\ =\ \frac{2}{7}$

NCERT Class 6 Maths Chapter 7 Fractions Topic: Addition and Subtraction of Fractions

Q1 Add $\frac{2}{5}$ and $\frac{3}{7}$ .

Answer: Addition of $\frac{2}{5}$ and $\frac{3}{7}$ is given by

$\frac{2}{5}+\frac{3}{7}=\frac{14+15}{35}=\frac{29}{35}$

Q2 Subtract $\frac{2}{5}$ from $\frac{5}{7}$ .

Answer: Subtraction of $\frac{2}{5}$ from $\frac{5}{7}$ is given by

$\frac{5}{7}-\frac{2}{5}=\frac{25-14}{35}=\frac{11}{35}$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.6

Q1 Solve

(a) $\frac{2}{3}+\frac{1}{7}$ (b) $\frac{3}{10}+\frac{7}{15}$ (c) $\frac{4}{9}+\frac{2}{7}$

(d) $\frac{5}{7}+\frac{1}{3}$ (e) $\frac{2}{5}+\frac{1}{6}$ (f) $\frac{4}{5}+\frac{2}{3}$

Answer: (a) $\frac{2}{3}+\frac{1}{7}\ =\ \frac{2\times 7\ +\ 1\times 3}{21}\ =\ \frac{17}{21}$

(b) $\frac{3}{10}+\frac{7}{15}\ =\ \frac{3\times 15\ +\ 7\times 10}{150}\ =\ \frac{115}{150}\ =\ \frac{23}{30}$

(d) $\frac{5}{7}+\frac{1}{3}\ =\ \frac{5\times 3\ +\ 1\times 7}{21}\ =\ \frac{22}{21}$

(e) $\frac{2}{5}+\frac{1}{6}\ =\ \frac{2\times 6\ +\ 1\times 5}{30}\ =\ \frac{17}{30}$

(f) $\frac{4}{5}+\frac{2}{3}\ =\ \frac{4\times 3\ +\ 2\times 5}{15}\ =\ \frac{22}{15}$

Q1 Solve

(g) $\frac{3}{4}-\frac{1}{3}$ (h) $\frac{5}{5}-\frac{1}{3}$ (i) $\frac{2}{3}+\frac{3}{4}+\frac{1}{2}$

(j) $\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$ (k) $1\frac{1}{3}+3\frac{2}{3}$ (l) $4\frac{2}{3}+3\frac{1}{4}$

(m) $\frac{16}{5}-\frac{7}{5}$ (n) $\frac{4}{3}-\frac{1}{2}$

Answer: (g) $\frac{3}{4}-\frac{1}{3}\ =\ \frac{3\times 3\ -\ 1\times 4}{12}\ =\ \frac{5}{12}$

(h) $\frac{5}{5}-\frac{1}{3}\ =\ \frac{5\times 3\ -\ 1\times 5}{15}\ =\ \frac{10}{15}\ =\ \frac{2}{3}$

(i) $\frac{2}{3}+\frac{3}{4}+\frac{1}{2}\ =\ \frac{2\times 4\ +\ 3\times 3}{12}\ +\ \frac{1}{2}\ =\ \frac{17}{12}\ +\ \frac{1}{2}\ =\ \frac{17\times 2\ +\ 1\times 12}{24}$

$=\ \frac{46}{24}\ =\ \frac{23}{12}$

(j) $\frac{1}{2}+\frac{1}{3}+\frac{1}{6}\ =\ \frac{1\times 3\ +\ 1\times 2}{6}\ +\ \frac{1}{6}\ =\ \frac{5}{6}\ +\ \frac{1}{6}\ =\ \frac{6}{6}\ =\ 1$

(k) $1\frac{1}{3}+3\frac{2}{3}\ =\ \frac{4}{3}\ +\ \frac{11}{3}\ =\ \frac{15}{3}\ =\ 5$

(l) $4\frac{2}{3}+3\frac{1}{4}\ =\ \frac{14}{3}\ +\ \frac{13}{4}\ =\ \frac{14\times 4\ +\ 13\times 3}{12}\ =\ \frac{95}{12}$ \

(m) $\frac{16}{5}-\frac{7}{5}\ =\ \frac{16\ -\ 7}{5}\ =\ \frac{9}{5}$

(n) $\frac{4}{3}-\frac{1}{2}\ =\ \frac{4\times2\ -\ 1\times3}{6}\ =\ \frac{5}{6}$

Q2 Sarita bought $\frac{2}{5}$ metre of ribbon and Lalita $\frac{3}{4}$ metre of ribbon. What is the total length of the ribbon they bought?

Answer: The total length of ribbon is given :-

$=\ \frac{2}{5}\ +\ \frac{3}{4}\ =\ \frac{2\times 4\ +\ 3\times 5}{20}\ =\ \frac{23}{20}$

Thus total length of ribbon is .

Q3 Naina was given $1\frac{1}{2}$ piece of cake and Najma was given $1\frac{1}{3}$ piece of cake. Find the total amount of cake was given to both of them.

Answer: Total amount of cake given to both = Cake given to Naina + Cake given to Najma

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

$=\ \frac{3}{2}\ +\ \frac{4}{3}$

$=\ \frac{3\times 3\ +\ 4\times 2 }{6}$

$=\ \frac{17 }{6}$

Q4 Fill in the boxes :

(a) $\square-\frac{5}{8}=\frac{1}{4}$

(b) $\square-\frac{1}{5}=\frac{1}{2}$

Answer: (a) $\square-\frac{5}{8}=\frac{1}{4}$ :-

$\square\ =\ \frac{1}{4}\ +\ \frac{5}{8}\ =\ \frac{1\times 8\ +\ 5\times 4}{32}\ =\ \frac{28}{32}\ =\ \frac{7}{8}$

(b) $\square-\frac{1}{5}=\frac{1}{2}$ :-

$\square\ =\ \frac{1}{2}\ +\ \frac{1}{5}\ =\ \frac{1\times 5\ +\ 1\times 2}{10}\ =\ \frac{7}{10}$

$\square\ =\ \frac{1}{2}\ -\ \frac{1}{6}\ =\ \frac{1\times 6\ -\ 1\times 2}{12}\ =\ \frac{4}{12}\ =\ \frac{1}{3}$

Q5 Complete the addition-subtraction box.

1643039159028

Answer: The required table is shown below:-

1643039168790

Q5 Complete the addition-subtraction box.

1643039199627

Answer: The required box is given below :-

1643039209377

Q6 A piece of wire $\frac{7}{8}$ metre long broke into two pieces. One piece was $\frac{1}{4}$ metre long. How long is the other piece?

Answer: Let the length of another piece of wire be x.

Thus, $x\ +\ \frac{1}{4}\ =\ \frac{7}{8}$

$x\ =\ \frac{7}{8}\ -\ \frac{1}{4}$

$=\ \frac{7\times 4\ -\ 1\times 8}{32}\ =\ \frac{20}{32}$

$=\ \frac{10}{16}\ =\ \frac{5}{8}$

Hence the length of other part is .

Q7 Nandini’s house is $\frac{9}{10}\; km$ from her school. She walked some distance and then took a bus for $\frac{1}{2}\; km$ to reach the school. How far did she walk?

Answer: The distance Nandini walked is given by :-

$\frac{9}{10}\ -\ \frac{1}{2}\ =\ \frac{9\times 2\ -\ 1\times 10 }{20}\ =\ \frac{8}{20}\ =\ \frac{2}{5}$

Hence she walked .

Q8 Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is $\frac{5}{6}th$ full and Samuel’s shelf is $\frac{2}{5}th$ full. Whose bookshelf is more full? By what fraction?

Answer: If we compare the bookshelves of both, we obtain that :

$\frac{5}{6}\ >\ \frac{2}{5}$

Also, $\frac{5}{6}\ -\ \frac{2}{5}\ =\ \frac{25-12}{30}\ =\ \frac{13}{30}$

Hence the bookshelf of Asha is more full and by $\frac{13}{30}$ fraction.

Q9 Jaidev takes $2\frac{1}{5}$ minutes to walk across the school ground. Rahul takes $\frac{7}{4}$ minutes to do the same. Who takes less time and by what fraction?

Answer: Firstly, let us convert the time taken by Jaidev in the improper fraction from mixed fraction.

$2\frac{1}{5}\ =\ \frac{10\ +\ 1}{5}\ =\ \frac{11}{5}$

Now, comparing both, we have :

$\frac{11}{5}\ >\ \frac{7}{4}$

Also, $\frac{11}{5}\ -\ \frac{7}{4}\ =\ \frac{11\times 4\ -\ 7\times 5}{20}\ =\ \frac{9}{20}$

Hence Rahul takes less time as compared to Jaidev by a fraction.

Fractions Class 6 Maths Chapter 7-Topics

A Fraction
Fraction of the Number Line
Proper Fraction
Improper and Mixed Fractions
Equivalent Fractions

NCERT Solutions for Class 6 Mathematics Chapter Wise

Chapters No.	Chapters Name
Chapter - 1	Knowing Our Numbers
Chapter - 2	Whole Numbers
Chapter - 3	Playing with Numbers
Chapter - 4	Basic Geometrical Ideas
Chapter - 5	Understanding Elementary Shapes
Chapter - 6	Integers
Chapter - 7	Fractions
Chapter - 8	Decimals
Chapter - 9	Data Handling
Chapter -10	Mensuration
Chapter -11	Algebra
Chapter -12	Ratio and Proportion
Chapter -13	Symmetry
Chapter -14	Practical Geometry

Key features of NCERT Solutions for Class 6 Maths chapter 7

Extensive Topic Coverage: The solutions for maths class 6 chapter 7 encompass all the important topics and subtopics of the chapter, ensuring that students have a thorough understanding of the content.

Focus on Exam Readiness: The NCERT Class 6 Maths Chapter 7 solutions adopt an exam-focused approach, equipping students with the necessary skills and strategies to approach exam questions effectively and perform well.

Interactive Learning: The NCERT class 6 maths chapter 7 promote interactive learning by incorporating illustrations, diagrams, and practical examples, making the learning process engaging and enjoyable for students.

Step-by-Step Solutions: Each problem in the fraction questions for class 6 is accompanied by a detailed step-by-step solution, enabling students to follow the logical thought process and learn problem-solving techniques.

NCERT Solutions for Class 6 Subject wise

NCERT Solutions for Class 6 Maths

NCERT Solutions for Class 6 Science

How to Use NCERT Solutions for Class 6 Maths Chapter 7 Fractions?

Learn the representation of fractions using the equal part concept.
Go through the text given in the textbook to learn various applications and concepts.
Have a glance through some examples to understand the answering of a particular kind of question with the help of NCERT Solutions for Class 6 .
Now you can jump to the practice problems.
While practicing you can use NCERT solutions for Class 6 Maths chapter 7 Fractions as a helping tool.

Keep learning and working hard!

Also Check NCERT Books and NCERT Syllabus here:

Frequently Asked Questions (FAQs)

1. How many exercise are solved in NCERT Solutions for Class 6 Maths Chapter 7 Fractions

A total of 6 exercise are discussed in the chapter 7 maths class 6. After practicing these exercises, Students get command on the concepts which ultimately lead to confidence during the exam and finaly able to score well in the exam.

Also Read

NCERT Solutions for Class 6 Science Chapter 3 Fibre to Fabric

NCERT Solutions for Class 6 Science Chapter 2 Components of Food

NCERT Solutions for Class 6 Science Chapter 1 Food Where Does It Come From

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

NCERT Solutions for Class 6 Maths Chapter 13 Symmetry

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Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

Option 1) less than 3	Option 2) more than 3 but less than 6
Option 3) more than 6 but less than 9	Option 4) more than 9

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

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NCERT Class 6 Maths Chapter 7 Fractions Topic: Addition and Subtraction of Fractions

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NCERT Class 6 Maths Chapter 7 Fractions Topic: Addition and Subtraction of Fractions

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