HomeNCERT SOLUTIONS6th CLASSNCERT Class 6 Maths Chapter 7: Fractions

# NCERT Class 6 Maths Chapter 7: 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 = $\frac { 2 }{ 4 }$

(iii) Total number of parts = 8
Number of shaded parts = 4
∴ Fraction = $\frac { 4 }{ 8 }$

(v) Total number of parts = 7
Number of shaded parts = 3
∴ Fraction = $\frac { 3 }{ 7 }$

(vii) Total number of parts = 10
Number of shaded parts = 10
∴ Fraction = $\frac { 10 }{ 10 }$

(viii) Total number of parts = 9
Number of shaded parts = 4
∴ Fraction = $\frac { 4 }{ 9 }$

(x) Total number of parts = 2
Number of shaded part = 1
∴ Fraction = $\frac { 1 }{ 2 }$

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 $\frac { 1 }{ 2 }$.

(c) Since, the part are not equal.
∴ Shaded part is not $\frac { 3 }{ 4 }$.

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 = $\frac { 8 }{ 24 }$

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 = $\frac { 40 }{ 60 }$

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

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 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 = $\frac { 5 }{ 11 }$

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 = $\frac { 4 }{ 12 }$ = $\frac { 1 }{ 3 }$

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

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

### 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 $\frac { 2 }{ 4 }$ i,e., $\frac { 1 }{ 2 }$
B represents $\frac { 1 }{ 4 }$
D represents $\frac { 3 }{ 4 }$
and E represents $\frac { 4 }{ 4 }$ , i.e., 1.

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

From the above number line, we have
C represents $\frac { 2 }{ 5 }$
D represents $\frac { 3 }{ 5 }$
E represents $\frac { 4 }{ 5 }$
and I 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:

### 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) = $\frac { 1 }{ 2 }$
(b) and (iv) = $\frac { 2 }{ 3 }$
(c) and (i) = $\frac { 1 }{ 3 }$
(d) and (v) = $\frac { 1 }{ 4 }$
(e) and (iii) = $\frac { 3 }{ 4 }$

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 $\frac { 3 }{ 5 }$ 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 $\frac { 12 }{ 20 }$

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

∴ The required fraction is $\frac { 9 }{ 15 }$.

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

∴ The required fraction is $\frac { 18 }{ 30 }$.

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

∴ The required fraction is $\frac { 27 }{ 45 }$.

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) Given that numerator = 9

So, the equivalent fraction is $\frac { 9 }{ 12 }$.

(b) Given that denominator = 4
∴ $\frac { N }{ 4 }$ = $\frac { 36 }{ 48 }$ ⇒ N x 48 = 4 x 36
⇒ N = $\frac { 4 x 36 }{ 48 }$ = 3
So, the equivalent fraction is $\frac { 3 }{ 4 }$ .

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

Solution:
(a) $\frac { 5 }{ 9 }$ and $\frac { 30 }{ 54 }$
We have 5 x 54 = 270
and 9 x 30 = 270
Here 5 x 54 = 9 x 30
∴ $\frac { 5 }{ 9 }$ and $\frac { 30 }{ 54 }$ are equivalent fractions.

(b) $\frac { 3 }{ 10 }$ and $\frac { 12 }{ 50 }$
We have 3 x 50 = 150
and 10 x 12 = 120
Here 3 x 50 ≠ 10 x 12
∴ $\frac { 3 }{ 10 }$ and $\frac { 12 }{ 50 }$ are not equivalent fractions.

(c) $\frac { 7 }{ 13 }$ and $\frac { 5 }{ 11 }$
We have 7 x 11 = 77 and 5 x 13 = 65
Here 7 x 11 ≠ 5 x 13
∴ $\frac { 7 }{ 13 }$ and $\frac { 5 }{ 11 }$ 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., $\frac { 1 }{ 2 }$.

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 $\frac { 2 }{ 4 }$ , $\frac { 4 }{ 6 }$ , $\frac { 8 }{ 6 }$ and $\frac { 6 }{ 6 }$ 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 = $\frac { 3 }{ 8 }$

(ii) Total number of divisions = 8
Number of shaded parts = 6
∴ Fraction = $\frac { 6 }{ 8 }$

(iii) Total number of divisions = 8
Number of shaded parts = 4
∴ Fraction = $\frac { 4 }{ 8 }$

(iv) Total number of divisions = 8
Number of shaded part = 1
∴ Fraction = $\frac { 1 }{ 8 }$
Now the fractions are:
$\frac { 3 }{ 8 }$, $\frac { 6 }{ 8 }$, $\frac { 4 }{ 8 }$ and $\frac { 1 }{ 8 }$ with same denominator.

(b)(i) Total number of divisions = 9
Number of shaded parts = 8
∴ Fraction = $\frac { 8 }{ 9 }$
(ii) Total number of divisions = 9
Number of shaded parts = 4
∴ Fraction = $\frac { 4 }{ 9 }$
(iii) Total number of divisions = 9
Number of shaded parts = 3
∴ Fraction = $\frac { 3 }{ 9 }$
(iv) Total number of divisions = 9
Number of shaded parts = 6
∴ Fraction = $\frac { 6 }{ 9 }$
∴ Fractions are $\frac { 8 }{ 9 }$, $\frac { 4 }{ 9 }$, $\frac { 3 }{ 9 }$, $\frac { 6 }{ 9 }$ 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.
Lalita read $\frac { 2 }{ 5 }$ of the same book. Who read less?
Solution:
Ila reads 25 pages out of 100 pages.

Lalita reads $\frac { 2 }{ 5 }$ of the same book.
Comparing $\frac { 1 }{ 4 }$ and $\frac { 2 }{ 5 }$ , we get
1 x 5 = 5 and 2 x 4 = 8
Since 5 < 8
∴ $\frac { 1 }{ 4 }$ < $\frac { 2 }{ 5 }$

Ex 7.4 Class 6 Maths Question 9.
Rafiq exercised for $\frac { 3 }{ 6 }$ of an hour, while Rohit exercised for $\frac { 3 }{ 4 }$ of an hour. Who exercised for a longer time?
Solution:
Rafiq exercised for $\frac { 3 }{ 6 }$ of an hour.
Rohit exercised for $\frac { 3 }{ 4 }$ of an hour.
Comparing $\frac { 3 }{ 6 }$ and $\frac { 3 }{ 4 }$ , we get
3 x 4 = 12 and 3 x 6 = 18
Since 12 < 18
∴ $\frac { 3 }{ 4 }$ > $\frac { 3 }{ 6 }$
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 $\frac { 4 }{ 5 }$ = $\frac { 4 }{ 5 }$
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 $\frac { 3 }{ 5 }$.

Thus, the given diagrams can be represented as

(c) The given figure represents addition of $\frac { 2 }{ 6 }$ and $\frac { 3 }{ 6 }$.

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 $\frac { 2 }{ 3 }$ 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:
Fraction of wall painted by Shubham = $\frac { 2 }{ 3 }$
Fraction of wall painted by Madhavi = $\frac { 1 }{ 3 }$
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 $\frac { 5 }{ 7 }$ of a basket of oranges. What fraction of oranges was left in the basket?
Solution:
Fraction of basket of oranges = $\frac { 5 }{ 7 }$
Fraction of basket as a whole can be taken as 1.
∴ Fraction of basket of oranges left

Thus, the required fraction = $\frac { 2 }{ 7 }$ .

### 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 $\frac { 2 }{ 5 }$ metre of ribbon and Lalita $\frac { 3 }{ 4 }$ metre of ribbon. What is the total length of the ribbon they bought?
Solution:
Length of ribbon bought by Sarita = $\frac { 2 }{ 5 }$ metre
Length of ribbon bought by Lalita = $\frac { 3 }{ 4 }$ metre
∴ Length of ribbon bought by Sarita and Lalita

Hence, the required length = $\frac { 23 }{ 20 }$ metre

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:
Piece of cake given to Naina = 1$\frac 1{ 1 }{ 2 }$
Piece of cake given to Najma = 1$\frac 1{ 1 }{ 3 }$
Piece of cake given to Naina and Najma

Hence the total amount of piece given to both = 2$\frac { 5 }{ 6 }$.

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

Solution:

Here, missing number is $\frac { 1 }{ 4 }$ more than $\frac { 5 }{ 8 }$ .

Here, missing number is $\frac { 1 }{ 2 }$ more than $\frac { 1 }{ 5 }$ .

Here, missing number is $\frac { 1 }{ 6 }$ less than $\frac { 1 }{ 2 }$.

Ex 7.6 Class 6 Maths Question 5.

Solution:

Thus the box may be completed as follows:

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 the wire = $\frac { 7 }{ 8 }$ metre
Length of one piece of wire = $\frac { 1 }{ 4 }$ metre
∴ Length of the other piece = $\frac { 7 }{ 8 }$ – $\frac { 1 }{ 4 }$
LCM of 8 and 4 = 8

Hence, the length of the other piece = $\frac { 5 }{ 8 }$ 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 far did she walk?
Solution:
Total distance from house to school = $\frac { 9 }{ 10 }$ km.
Distance travelled by Nandini by bus = $\frac { 1 }{ 2 }$ km
∴ Distance travelled by her on foot

Hence, the distance travelled by her on foot = $\frac { 2 }{ 5 }$km.

Ex 7.6 Class 6 Maths Question 8.
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?
Solution:
Asha’s shelf is $\frac { 5 }{ 6 }$ th full
and Samuel’s shelf is $\frac { 2 }{ 5 }$ th full
Comparing $\frac { 5 }{ 6 }$ and $\frac { 2 }{ 5 }$
LCM of 6 and 5 = 30

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

Hence, $\frac { 13 }{ 30 }$ th fraction is more full of Asha’s shelf.

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:
Jaidev takes 2$\frac { 1 }{ 5 }$ minutes 5
Rahul takes 2$\frac { 7 }{ 4 }$ minutes
Comparing 2$\frac { 1 }{ 5 }$ minutes and $\frac { 7 }{ 4 }$ minutes

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

Hence, Rahul takes $\frac { 9 }{ 20 }$ minutes less to across the school ground.

NCERT class 6 maths solutions have been provided by the most experienced teachers. A very simple approach has been followed while solving the questions and designing the class 6 maths NCERT solutions.

## NCERT Solutions for Class 6 Maths

NCERT Solutions for Class 6 Maths are given below for all chapters.

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