# NCERT Solutions for Class 6 Maths Chapter 7 Fractions

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

### NCERT Solutions for Class 6 Maths Chapter 7 Fractions Ex 7.1

Free download NCERT Solutions for Class 6 Maths Chapter 7 Exercise 7.1, Ex 7.2, Ex 7.3, Ex 7.4, Ex 7.5 and Ex 7.6 Fractions PDF for CBSE 2020 Exams.

Topics and Sub Topics in Class 6 Maths Chapter 6 Integers

 Section Name Topic Name 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 7.9.1 Comparing Like Fractions 7.9.2 Comparing Unlike Fractions 7.10 Addition and Subtraction of Fractions 7.10.1 Adding or Subtracting like fractions 7.10.2 Adding or Subtracting fractions 7.10.3 How do we add or Subtract mixed fractions

### Fractions Class 6 Ex 7.1

Ex 7.1 Class 6 Maths Question 1.
Write the fraction representing the shaded portion.

Solution:
(i) Total number of parts = 4
Number of shaded parts = 2
∴ Fraction = 2/4

(ii) Total number of parts = 9
Number of shaded parts = 8
∴ Fraction = 8/9

(iii) Total number of parts = 8
Number of shaded parts = 4
∴ Fraction = 4/8

(iv) Total number of parts = 4
Number of shaded parts = 1
∴ Fraction = 1/4

(v) Total number of parts = 7
Number of shaded parts = 3
∴ Fraction = 3/7

(vi) Total number of parts = 12
Number of shaded parts = 3
∴ Fraction = 3/12

(vii) Total number of parts = 10
Number of shaded parts = 10
∴ Fraction = 10/10

(viii) Total number of parts = 9
Number of shaded parts = 4
∴ Fraction = 4/9

(ix) Total number of parts = 8
Number of shaded parts = 4
∴ Fraction = 4/8

(x) Total number of parts = 2
Number of shaded part = 1
∴ Fraction = 1/2

Ex 7.1 Class 6 Maths Question 2.
Colour the part according to the given fraction.

Solution:

Ex 7.1 Class 6 Maths Question 3.
Identify the error, if any.

Solution:
(a) Since the shaded part is not half.
∴ This is not 1/2.

(b) Since, the parts are not equal.
∴ Shaded part is not 1/4 .

(c) Since, the part are not equal.
∴ Shaded part is not 3/4.

Ex 7.1 Class 6 Maths Question 4.
What fraction of a day is 8 hours?
Solution:
Since, a day has 24 hours and we have 8 hours,
∴ Required fraction = 8/24

Ex 7.1 Class 6 Maths Question 5.
What fraction of a hour is 40 minutes?
Solution:
Since I hours = 60 minutes
∴ Fraction of 40 minutes = 40/60

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) Arya has divided his sandwich into three equal parts.
So, each of them will get one part.
(b) Each one of them will receive 1/3 part.
∴ Required fraction = 1/3

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 to be dyed = 30
Number of dresses finished = 20
∴ Required fraction = 20/30 = 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 between 2 and 12 are;
2,3,4, 5, 6, 7, 8, 9, 10,11, 12
Number of given natural numbers = 11
Number of prime numbers = 5
∴ Required fraction = 5/11

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
Total number of given natural numbers = 12
Prime numbers are 103, 107, 109, 113
∴ Number of prime numbers = 4
∴ Required fraction = 4/12 = 1/3

Ex 7.1 Class 6 Maths Question 10.
What fraction of these circles have X’s in them?

Solution:
Total number’of circles = 8
Number of circles having X’s in them = 4
Required fraction = 4/8 = 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:
Number of CDs bought by her from the market = 3
∴ Total number of CDs = 3 + 5 = 8
∴ Fraction of CD (bought) = 3/8 and the fraction of CDs (gifted) = 5/8

### Fractions Class 6 Ex 7.2

Ex 7.2 Class 6 Maths Question 1.
Draw number lines and locate the points on them.

Solution:

We have divided the number line from 0 to 1 into four equal parts.
C represents 2/4 i,e., 1/2
B represents 1/4
D represents 3/4
and E represents 4/4 , i.e., 1.

We have divided the number line from 0 to 1 into eight equal parts.
B represents 1/8
C represents 2/8
D represents 3/8
and H represents 7/8

From the above number line, we have
C represents 2/5
D represents 3/5
E represents 4/5
and I represents 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:

### Fractions Class 6 Ex 7.3

Ex 7.3 Class 6 Maths Question 1.
Write the fractions. Are all these fractions equivalent?

Solution:

Since all the fractions in their simplest form are not equal.
∴ They are not equivalent fractions.

Ex 7.3 Class 6 Maths Question 2.
Write the fractions and pair up the equivalent fractions from each row.

Solution:

The following pairs fractions:represent the equivalent fractions.
(a) and (ii) = 1/2
(b) and (iv) = 2/3
(c) and (i) = 1/3
(d) and (v) = 1/4
(e) and (iii) = 3/4

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 3/5 having
(a) denominator 20
(b) numerator 9
(c) denominator 30
(d) numerator 27
Solution:
(a) Here, we require denominator 20.
Let N be the numerator of the fractions.

∴ The required fraction is 12/20

(b) Here, we required numerator 9.
Let D be the denominator of the fraction.

∴ The required fraction is 9/15.

(c) Here, we required denominator 30.
Let N be the numerator of the fraction.

∴ The required fraction is 18/30.

(d) Here, we required numerator 27.
Let D be the denominator of the fraction.

∴ The required fraction is 27/45.

Ex 7.3 Class 6 Maths Question 5.
Find the equivalent fraction of 36/48 with
(a) numerator 9
(b) denominator 4
Solution:
(a) Given that numerator = 9

So, the equivalent fraction is 9/12.

(b) Given that denominator = 4
∴ N4 = 36/48 ⇒ N x 48 = 4 x 36
⇒ N = 4x36/48 = 3
So, the equivalent fraction is 3/4 .

Ex 7.3 Class 6 Maths Question 6.
Check whether the given fractions are equivalent:

Solution:
(a) 5/9 and 30/54
We have 5 x 54 = 270
and 9 x 30 = 270
Here 5 x 54 = 9 x 30
∴ 5/9 and 30/54 are equivalent fractions.

(b) 3/10 and 12/50
We have 3 x 50 = 150
and 10 x 12 = 120
Here 3 x 50 ≠ 10 x 12
∴ 3/10 and 12/50 are not equivalent fractions.

(c) 7/13 and 5/11
We have 7 x 11 = 77 and 5 x 13 = 65
Here 7 x 11 ≠ 5 x 13
∴ 7/13 and 5/11 are not equivalent fractions.

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 28 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.
Solution:
Ramesh used up 10 pencils out of 20 pencils.

Sheelu used up 25 pencils out of 50 pencils.

Jamaal used up 40 pencils out of 80 pencils.

Yes, each has used up an equal fractions, i.e., 1/2.

Ex 7.3 Class 6 Maths Question 9.
Match the equivalent fractions and write two more for each.

Solution:

Two additional examples of equivalent fractions are

Two additional examples of equivalent fractions are

Two additional examples of equivalent fractions are

Two additional examples of equivalent fractions are

Two additional examples of equivalent fractions are

### Fractions Class 6 Ex 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.

(c) Show 2/4 , 4/6 , 8/6 and 6/6 on the number line. Put appropriate signs between the fractions given.

Solution:
(a) Total number of divisions = 8
(i) Number of shaded parts = 3
∴ Fraction = 3/8

(ii) Total number of divisions = 8
Number of shaded parts = 6
∴ Fraction = 6/8

(iii) Total number of divisions = 8
Number of shaded parts = 4
∴ Fraction = 4/8

(iv) Total number of divisions = 8
Number of shaded part = 1
∴ Fraction = 1/8
Now the fractions are:
3/86/84/8 and 1/8 with same denominator.

(b)(i) Total number of divisions = 9
Number of shaded parts = 8
∴ Fraction = 8/9
(ii) Total number of divisions = 9
Number of shaded parts = 4
∴ Fraction = 4/9
(iii) Total number of divisions = 9
Number of shaded parts = 3
∴ Fraction = 3/9
(iv) Total number of divisions = 9
Number of shaded parts = 6
∴ Fraction = 6/9
∴ Fractions are 8/94/93/96/9 with same denominator.

Ex 7.4 Class 6 Maths Question 2.
Compare the fractions and put an appropriate sign.

Solution:

Here, denominators of the two fractions are same and 3 < 5.

Here, numerators of the fractions are same and 7 > 4.

Here, denominators of the two fractions are same and 4 < 5.

Here, numerators of the two fractions are same and 5 < 7.

Ex 7.4 Class 6 Maths Question 3.
Make five more such pairs and put appropriate signs.
Solution:

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:

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

Ex 7.4 Class 6 Maths Question 5.
How quickly can you do this? Fill appropriate sign. ‘<‘, ‘=’, ‘>’.

Solution:

Ex 7.4 Class 6 Maths Question 6.
The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.

Solution:

Now grouping the above fractions into equivalent fractions, we have

Ex 7.4 Class 6 Maths Question 7.
Find answers to the following. Write and indicate how you solved them.

Solution:

By cross-multiplying, we get
5 x 5 = 25 and 4 x 9 = 36
Since 25 ≠ 36

By cross-multiplying, we get
9 x 9 = 81 and 16 x 5 =80
Since 81 ≠ 80

By cross-multiplying, we get
4 x 20 = 80 and 5 x 16 = 80
Since 80 = 80

By cross-multiplying, we get
1 x 30 = 30 and 4 x 15 = 60

Ex 7.4 Class 6 Maths Question 8.
Ila read 25 pages of a book containing 100 pages.
Solution:
Ila reads 25 pages out of 100 pages.

Lalita reads 2/5 of the same book.
Comparing 1/4 and 2/5 , we get
1 x 5 = 5 and 2 x 4 = 8
Since 5 < 8
∴ 1/4 < 2/5

Ex 7.4 Class 6 Maths Question 9.
Rafiq exercised for 3/6 of an hour, while Rohit exercised for 3/4 of an hour. Who exercised for a longer time?
Solution:
Rafiq exercised for 3/6 of an hour.
Rohit exercised for 3/4 of an hour.
Comparing 3/6 and 3/4 , we get
3 x 4 = 1/2 and 3 x 6 = 1/8
Since 1/2 < 1/8
∴ 3/4 > 3/6
Hence Rohit exercised for longer time.

Ex 7.4 Class 6 Maths Question 10.
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:
In class A, 20 students passed in first class out of 25 students.
∴ Fraction of students getting first class

In class B, 24 students passed in first class out of 30 students.
∴ Fraction of students getting first class

Comparing the two fractions, we get 4/5 = 4/5
Hence, both the class A and B have the same fractions.

### Fractions Class 6 Ex 7.5

Ex 7.5 Class 6 Maths Question 1.
Write these fractions appropriately as additions or subtractions.

Solution:
(a) The given figure represents the addition of

Thus the given diagrams can be represented as

(b) The given figure represents the difference between 1 and 3/5.

Thus, the given diagrams can be represented as

(c) The given figure represents addition of 2/6 and 3/6.

Thus, the given diagrams can be represented as

Ex 7.5 Class 6 Maths Question 2.
Solve:

Solution:

Ex 7.5 Class 6 Maths Question 3.
Shubham painted 2/3 of the wall space in his room. His sister Madhavi helped and painted 1/3 of the wall space. How much did they paint together?
Solution:
Fraction of wall painted by Shubham = 2/3
Fraction of wall painted by Madhavi = 1/3
Fraction of wall painted by Shubham and Madhavi

Thus the fraction of wall painted by both = 1

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 5/7 of a basket of oranges. What fraction of oranges was left in the basket?
Solution:
Fraction of basket of oranges = 5/7
Fraction of basket as a whole can be taken as 1.
∴ Fraction of basket of oranges left

Thus, the required fraction = 2/7 .

### Fractions Class 6 Ex 7.6

Ex 7.6 Class 6 Maths Question 1.
Solve

Solution:

Ex 7.6 Class 6 Maths Question 2.
Sarita bought 2/5 metre of ribbon and Lalita 3/4 metre of ribbon. What is the total length of the ribbon they bought?
Solution:
Length of ribbon bought by Sarita = 2/5 metre
Length of ribbon bought by Lalita = 3/4 metre
∴ Length of ribbon bought by Sarita and Lalita

Hence, the required length = 23/20 metre

Ex 7.6 Class 6 Maths Question 3.

Ex 7.6 Class 6 Maths Question 4.
Fill in the boxes:

Solution:

Here, missing number is 1/4 more than 5/8 .

Here, missing number is 1/2 more than 1/5 .

Here, missing number is 1/6 less than 1/2.

Ex 7.6 Class 6 Maths Question 5.

Solution:

Thus the box may be completed as follows:

Hence, Asha’s shelf is full more than Samuel’s shelf.

So, the time take to cover the same distance by Rahul is less than that of Jaidev.

Hence, Rahul takes 9/20 minutes less to across the school ground.

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