NCERT Solutions | Class 6 Maths Chapter 7

NCERT Solutions | Class 6 Maths Chapter 7 | Fractions 

CBSE Solutions | Maths Class 6

Check the below NCERT Solutions for Class 6 Maths Chapter 7 Fractions Pdf free download. NCERT Solutions Class 6 Maths  were prepared based on the latest exam pattern. We have Provided Fractions Class 6 Maths NCERT Solutions to help students understand the concept very well.

NCERT | Class 6 Maths

NCERT Solutions Class 6 Maths

Book:	National Council of Educational Research and Training (NCERT)
Board:	Central Board of Secondary Education (CBSE)
Class:	6th
Subject:	Maths
Chapter:	7
Chapters Name:	Fractions
Medium:	English

Fractions | Class 6 Maths | NCERT Books Solutions

You can refer to MCQ Questions for Class 6 Maths Chapter 7 Fractions to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise 7.1

Ex 7.1 Class 6 Maths Question 1.

Write the fraction representing the shaded portion.

Solution:

The fraction representing the shaded portion in the given diagram are as under:

Ex 7.1 Class 6 Maths Question 2.

Colour the part according to the given fraction

Solution:

The figures are shaded as per indicated fraction shown against them.

Ex 7.1 Class 6 Maths Question 3.

Identify the error, if any?

Solution:

In all the figures, the shaded portions do not represent the given fractions.

Ex 7.1 Class 6 Maths Question 4.

What fraction of a day is 8 hours?

Solution:

Since, there are 24 hours in a day, therefore, the required fraction
\(=\frac { 8 }{ 24 } =\frac { 1 }{ 3 } \).

Ex 7.1 Class 6 Maths Question 5.

What fraction of an hour is 40 minutes?

Solution:

Since, there are 60 minutes in an hour, therefore, the required fraction \(=\frac { 40 }{ 60 } =\frac { 2 }{ 3 } \).

Ex 7.1 Class 6 Maths Question 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?

Solution:

(a) To divide 2 sandwiches brought by Arya equally among Arya, Abhimanyu and Vivek (i.e., 3 persons), we have to divide each sandwich into 3 equal parts. Then two parts thus obtained be given to each of them.
(b) \(\frac { 1 }{ 3 } \) of a sandwich will be received by each boy but in total each will get \(\frac { 2 }{ 3 } \).

Ex 7.1 Class 6 Maths Question 7.

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

Solution:

Total number of dresses = 30
Work finished = 20
∴ The fraction of dresses she has finished =\(=\frac { 20 }{ 30 } =\frac { 2 }{ 3 } \).

Ex 7.1 Class 6 Maths Question 8.

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

Solution:

Natural numbers from 2 to 12 are:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 i.e., 11 in number.
Prime numbers out of these numbers are:
2, 3, 5, 7, 11 i.e., 5 in number.
∴ Required fraction = \(=\frac { 4 }{ 12 } =\frac { 1 }{ 3 } \)

Ex 7.1 Class 6 Maths Question 9.

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

Solution:

Natural numbers from 102 to 113 are:
102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113 i.e., 12 in number.
Prime numbers out of the above numbers are:
103, 107, 109, 113 i.e., 4 in number.
∴ Required fraction =\(=\frac { 4 }{ 12 } =\frac { 1 }{ 3 } \)

Ex 7.1 Class 6 Maths Question 10.

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

Solution:

∴Required fraction = \(=\frac { 4 }{ 8 } =\frac { 1 }{ 2 } \)

Ex 7.1 Class 6 Maths Question 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?

Solution:

Total number of CDs = 3 + 5 = 8
Number of CDs purchased = 3
Fraction of CDs purchased = \(\frac { 3 }{ 8 } \)
Fraction of CDs received as gift = \(\frac { 5 }{ 8 } \) .

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise 7.2

Ex 7.2 Class 6 Maths Question 1.

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

Solution:

(a) We know that \(\frac { 1 }{ 2 } \) is greater than zero and less than 1, so it should lie 2 between 0 and 1.
To show \(\frac { 1 }{ 2 } \) on the number line, we divide the gap between 0 and 1 into two equal parts and the point P represents the fraction \(\frac { 1 }{ 2 } \) .

To represent \(\frac { 1 }{ 4 } ,\frac { 3 }{ 4 } ,\frac { 4 }{ 4 } \) on the number line, we divide the gap between 0 and 1 into 4 equal parts, then the points P, R and A respectively represent the fraction \(\frac { 1 }{ 4 } ,\frac { 3 }{ 4 } \) and \(\frac { 4 }{ 4 } \) .

(b) To rfepresent \(\frac { 1 }{ 8 } ,\frac { 2 }{ 8 } ,\frac { 3 }{ 8 } \) and \(\frac { 7 }{ 8 } \) on the number line, we divide the gap between 0 and 1 into 8 equal parts, then the points P, Q, R and S respectively represent the fraction \(\frac { 1 }{ 8 } ,\frac { 2 }{ 8 } ,\frac { 3 }{ 8 } \) and \(\frac { 7 }{ 8 } \) .

(c) To represent \(\frac { 2 }{ 5 } ,\frac { 3 }{ 5 } \) and \(\frac { 4 }{ 5 } \) on the number line, we divide the gap between 0 and 1 into 5 equal parts, then the points P, Q and R respectively represent the fraction \(\frac { 2 }{ 5 } ,\frac { 3 }{ 5 } \) and \(\frac { 4 }{ 5 } \) .

For representing \(\frac { 8 }{ 5 } \)
Draw a line. Take a point 0 on it. Let it represent 0.
Now, \(\frac { 8 }{ 5 } =1\quad \frac { 3 }{ 5 } =1+\frac { 3 }{ 5 } \)

From O, set off unit distances to the right. Let these segments be OA, AB. Then, clearly the points A and B represent 1 and 2 respectively. Take 1 full unit length to the right of O. Divide the 2nd unit AB into 5 equal parts. Take 3 parts out of these 5 parts to reach P. Then, P represents \(\frac { 8 }{ 5 } \).

Ex 7.2 Class 6 Maths Question 2.

Express the following as mixed fractions:

Solution:

Ex 7.2 Class 6 Maths Question 3.

Express the following as improper fractions:

Solution:

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise 7.3

Ex 7.3 Class 6 Maths Question 1.

Write the fractions. Are all these fractions equivalent?

Solution:

Ex 7.3 Class 6 Maths Question 2.

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

Solution:

Ex 7.3 Class 6 Maths Question 3.

Replace □ in each of the following by the correct number:

Solution:

Ex 7.3 Class 6 Maths Question 4.

Find the equivalent fraction of \(\frac { 3 }{ 5 } \) having
(a) denominator 20
(b) numerator 9
(c) denominator 30
(d) numerator 27

Solution:

Ex 7.3 Class 6 Maths Question 5.

Find the equivalent fraction of \(\frac { 36 }{ 48 } \) with
(a) numerator 9
(b) denominator 4

Solution:

(a) ∵ 36 ÷ 9 = 4
∴ We divide the numerator and denominator by 4
\(\frac { 36 }{ 48 } =\frac { 36\div 4 }{ 48\div 4 } =\frac { 9 }{ 12 } \)
(b) ∵ 48 ÷ 4 = 12
∴ We divide the numerator and denominator by 12
\(\frac { 36 }{ 48 } =\frac { 36\div 12 }{ 48\div 12 } =\frac { 3 }{ 4 } \)

Ex 7.3 Class 6 Maths Question 6.

Check whether the given fractions are equivalent:

Solution:

Ex 7.3 Class 6 Maths Question 7.

Reduce the following fractions to simplest form:

Solution:

Ex 7.3 Class 6 Maths Question 8.

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 their of her/his pencils?

Solution:

Fractions of pencils used by Ramesh, Sheelu and Jamaal are \(\frac { 10 }{ 20 } ,\frac { 25 }{ 50 } \) and \(\frac { 40 }{ 80 } \) respectively.

Thus, these fractions are equal.

Ex 7.3 Class 6 Maths Question 9.

Match the equivalent fractions and write two more for each:

Solution:

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise 7.4

Ex 7.4 Class 6 Maths Question 1.

Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign ‘>’, ‘=’, ‘>’ between the fractions:

Solution:

Ex 7.4 Class 6 Maths Question 2.

Compare the fractions and put an appropriate sign.

Solution:

Ex 7.4 Class 6 Maths Question 3.

Make five more such pairs and put appropriate signs.

Solution:

Five more such pairs may be taken as under:
Compare the fractions and put an appropriate sign.

Ex 7.4 Class 6 Maths Question 4.

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

Make five more such problems and solve them with your friends.

Solution:

Ex 7.4 Class 6 Maths Question 5.

Five more such problems are as under:
Look at the figures given in question 5 and write ‘<’ or ‘>’ or ‘=’ between the pairs of fractions.

Solution:

Ex 7.4 Class 6 Maths Question 6.

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

Solution:

Ex 7.4 Class 6 Maths Question 7.

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

Solution:

On separating them into three groups of equivalent fractions, we have

Ex 7.4 Class 6 Maths Question 8.

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

Solution:

Ex 7.4 Class 6 Maths Question 9.

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

Solution:

Ex 7.4 Class 6 Maths Question 10.

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?

Solution:

Ex 7.4 Class 6 Maths Question 11.

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

Solution:

Fraction of students getting first class in class A
\(=\frac { 20 }{ 25 } =\frac { 20\div 5 }{ 25\div 5 } =\frac { 4 }{ 5 } \)
Fraction of students getting first class in class B
\(=\frac { 24 }{ 30 } =\frac { 24\div 6 }{ 30\div 6 } =\frac { 4 }{ 5 } \)
Clearly, an equal number of students got 1st class in both the classes.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise 7.5

Ex 7.5 Class 6 Maths Question 1.

Write these fractions appropriately as additions or subtractions:

Solution:

Ex 7.5 Class 6 Maths Question 2.

Solve:

Solution:

Ex 7.5 Class 6 Maths Question 3.

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?

Solution:

Portion of wall painted by Shubham = \(\frac { 2 }{ 3 } \)
Portion of wall painted by Madhavi = \(\frac { 1 }{ 3 } \)
Wall painted by both of them = \(\frac { 2 }{ 3 } +\frac { 1 }{ 3 } =\frac { 2+1 }{ 3 } =\frac { 3 }{ 3 } =1\)
i.e., full wall was painted by them.

Ex 7.5 Class 6 Maths Question 4.

Fill in the missing fractions.

Solution:

Ex 7.5 Class 6 Maths Question 5.

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

Solution:

Portion of oranges received by Javed = \(\frac { 5 }{ 7 } \)
Portion of oranges left in the basket

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise 7.6

Ex 7.6 Class 6 Maths Question 1.

Solve:

Solution:

Ex 7.6 Class 6 Maths Question 2.

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?

Solution:

Ribbon bought of Sarita = \(\frac { 2 }{ 5 } \) m
Ribbon bought of Lalita = \(\frac { 3 }{ 4 } \) m
Total length of the ribbon bought = \(\left( \frac { 2 }{ 5 } +\frac { 3 }{ 4 } \right) \) m

Ex 7.6 Class 6 Maths Question 3.

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.

Solution:

Number of pieces of cake consumed by Naina = \(1\frac { 1 }{ 2 } \)
Number of pieces of cake consumed by Najma = \(1\frac { 1 }{ 3 } \)
Total amount of cake consumed = \(1\frac { 1 }{ 2 } +1\frac { 1 }{ 3 } \)

Ex 7.6 Class 6 Maths Question 4.

Fill in the boxes:

Solution:

Ex 7.6 Class 6 Maths Question 5.

Complete the addition-subtraction box.

Solution:

Ex 7.6 Class 6 Maths Question 6.

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?

Solution:

Total length of wire = \(\frac { 7 }{ 8 } \) metre
Length of a piece of wire = \(\frac { 1 }{ 4 } \) metre
∴ Other piece of wire =\(\left( \frac { 7 }{ 8 } -\frac { 1 }{ 4 } \right) \) metre

Ex 7.6 Class 6 Maths Question 7.

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

Solution:

Total distance of Nandini’s house from her school = \(\frac { 9 }{ 10 } \) km
Distance for which bus was taken = \(\frac { 1 }{ 2 } \) km
∴ Distance walked by Nandini for home

Ex 7.6 Class 6 Maths Question 8.

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

Solution:

Ex 7.6 Class 6 Maths Question 9.

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?

Solution:

NCERT Class 6 Maths

Class 6 Maths Chapters | Maths Class 6 Chapter 7

NCERT Solutions for Class 6 Maths

NCERT Solutions of Maths Class 6 Chapter-wise

Chapter-wise NCERT Solutions for Class 6 Maths

NCERT Solutions For Class 6 Maths Chapter 1 Knowing Our Numbers
NCERT Solutions For Class 6 Maths Chapter 2 Whole Numbers
NCERT Solutions For Class 6 Maths Chapter 3 Playing With Numbers
NCERT Solutions For Class 6 Maths Chapter 4 Basic Geometrical Ideas
NCERT Solutions For Class 6 Maths Chapter 5 Understanding Elementary Shape
NCERT Solutions For Class 6 Maths Chapter 6 Integers
NCERT Solutions For Class 6 Maths Chapter 7 Fractions
NCERT Solutions For Class 6 Maths Chapter 8 Decimals
NCERT Solutions For Class 6 Maths Chapter 9 Data Handling
NCERT Solutions For Class 6 Maths Chapter 10 Mensuration
NCERT Solutions For Class 6 Maths Chapter 11 Algebra
NCERT Solutions For Class 6 Maths Chapter 12 Ratio and Proportion
NCERT Solutions For Class 6 Maths Chapter 13 Symmetry
NCERT Solutions For Class 6 Maths Chapter 14 Practical Geometry

NCERT Solutions for Class 6 to 12

NCERT Solutions for Class 6 All Subjects
NCERT Solutions for Class 7 All Subjects
NCERT Solutions for Class 8 All Subjects
NCERT Solutions for Class 9 All Subjects
NCERT Solutions for Class 10 All Subjects
NCERT Solutions for Class 11 All Subjects
NCERT Solutions for Class 12 All Subjects

NCERT SOLUTIONS