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NCERT Solutions for Class 6 maths Chapter 7: Fractions

65 Solved Questions & Exercises18 min estimated readingUpdated 2026-09-16
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NCERT Solutions • Class 6 Mathematics (Ganita Prakash)
Chapter 7: Fractions
Latest Rationalised Syllabus (NEP 2026-27)

Get the simplifiedClass 6 Maths NCERT Solutionsof Ganita Prakash Chapter 7 Fractions textbook exercise questions with complete explanation.

Ganita Prakash Class 6 Maths Chapter 7 Solutions Fractions

Question 1 (7)

1 Fractional Units and Equal Shares Figure it Out (Page No. 152 – 153)

Fill in the blanks with fractions.

Question 1


Three guavas together weigh 1 kg. If they are roughly of the same size, each guava will roughly weigh ____kg.

Solution:
Question 2


A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is _________ kg.
Solution:

Question 3


Four friends ordered 3 glasses of sugarcane juice and shared it equally. Each one drank ____________ glass of sugarcane juice.

Solution:


As total quantity is 3 which is to be divided into four equal parts. So, the required fraction is .
Question 4


The bis fish weighs kg. The small one weighs kg. Together they weigh ____ kg.
Solution:

Given the weighs of big fish = kg and the weighs of small fish = kg
Total weight of both fish = kg
= kg

Fractions Diagram 1

Question 5


Arrange these fraction words in order of size from the smallest to the biggest in the empty box below: One and a half, three quarters, one and a quarter, half, quarter, two and a half.
Solution:

∴ The fractions from smallest to the biggest are as follows: quarter, half, three quarters one and a quarter, one and a half, two and a half.

Fractions Diagram 2

Question 2 (7)

2 Fractional Units as Parts of a Whole Figure it Out (Page No. 155)

Question 1

The figure below shows different fractional units of a whole chikki. How much of a whole chikki is each piece?

Solution:
(a)

Total no. of pieces formed of given size = 12
Required fraction =
(b)

Total no. of pieces formed of given size = 4
Required fraction =
(c)

Total no. of pieces formed of given size = 8
Required fraction =
(d)

Total no. of pieces formed of given size = 6
Required fraction =

Fractions Diagram 3

Fractions Diagram 4

Fractions Diagram 5

Fractions Diagram 6

Fractions Diagram 7

(e)

Total no. of pieces formed of given size = 8
Required fraction =

Fractions Diagram 8

(f)

Total no. of pieces formed of given size = 8
Required fraction =

Fractions Diagram 9

Fractions Diagram 10

(g)

Total no. of pieces formed of given size = 24
Required fraction =

Fractions Diagram 11

(h)

Total no. of pieces formed of given size = 12
Required fraction =

Fractions Diagram 12

Question 3 (7)

3 Measuring Using Fractional Units Figure it Out (Page No. 158)

Question 1


Continue this table of for 2 more steps.

Solution:

Fractions Diagram 13

Question 2


Can you create a similar table for ?
Solution:
Yes.

Fractions Diagram 14

Question 3


Make using a paper strip. Can you use this to also make ?
Solution:
Take a strip of paper.

Fold the strip into three equal parts and then open up.

Yes, we can also make using a paper strip by folding 6 again the above strip.

Fractions Diagram 15

Fractions Diagram 16

Question 4


Draw a picture and write an addition statement as above to show:
(a) 5 times of a roti
Solution:

5 times of a roti
=

Fractions Diagram 17

(b) 9 times of a roti
Solution:

9 times of a roti
=

Fractions Diagram 18

Fractions Diagram 19

Question 5


Match each fractional unit with the correct picture:

Solution:

Fractions Diagram 20

Fractions Diagram 21

Question 4 (7)

4 Marking Fraction Lengths on the Number Line Figure it Out (Page No. 160)

Question 1


On a number line, draw lines of length , , and .

Solution:

Divide the unit into 10 equal parts and point A represents .

Divide a unit into 10 equal parts and point B represents .

Divide a unit into 5 equal parts and point C represents .

Fractions Diagram 22

Fractions Diagram 23

Fractions Diagram 24

Question 2


Write five more fractions of your choice and mark them on the number line.
Solution:
The fractions are and .
Their number line representations are:

Fractions Diagram 25

Question 3


How many fractions lie between 0 and 1? Think, discuss with your classmates, and write your answer.
Solution:
There are an infinite number of fractions between 0 and 1.
Example: etc.

Question 4


What is the length of the pink line and black line shown below? The distance between 0 and 1 is 1 unit long, and it is divided into two equal parts. The length of each part is . So the pink line is y units long. Write the fraction that gives the length of the black line in the box.

Solution:
Length of black line is ;
Length of black line is + +
Fraction that gives length of black line =

Fractions Diagram 26

Question 5


Write the fraction that gives the lengths of the black lines in the respective boxes.

Solution:

Fractions Diagram 27

Fractions Diagram 28

Intext Questions

Question 1


Here, the fractional unit is dividing a length of 1 unit into three equal parts. Write the fraction that gives the length of the pink line in the box or in your notebook. (Page 159)

Solution:
Here number line OR is divided into three equal parts OP, PQ and QR.
Hence length of pink line = OP + PQ =

Fractions Diagram 29

Question 2


Here, a unit is divided into 5 equal parts. Write the fraction that gives the length of the pink lines in the respective boxes or in your notebook.

Solution:
Here number line OT = 1 unit is divided into five equal parts OP, PQ, QR, RS and ST.
Hence length of pink line OQ = OP + PQ =
Now, length of pink line OS = OP + PQ + QR + RS =
Hence, OQ = OS =

Fractions Diagram 30

Question 3


Now, a unit is divided into 8 equal parts. Write the appropriate fractions in your notebook Solution:Here number line OH is divided into 8 equal parts OA, AB, BC, CD, DE, EF, FG and GH.
Solution:

Also, OA = , OB = , OC = , OH = = 1

Fractions Diagram 31

Question 5 (7)

5 Mixed Fractions Figure it Out (Page No. 162)

Question 1


How many whole units are there in ?

Solution:

So, there are 3 whole units in .
Question 2


How many whole units are there in and in ?
Solution:

So, there are 1 whole unit in .

So, there are 2 whole units in .

Question 6 (7)

5 Mixed Fractions Figure it Out (Page No. 162)

Question 1


Figure out the number of whole units in each of the following fractions:
(a)
(b)
(c)

Solution:
(a) 2
(b) 2
(c) 2
Question 2


Can all fractions greater than 1 be written as such mixed numbers?
Solution:
Yes.

Question 3


Write the following fractions as mixed fractions (e.g. = 4)
(a)
Solution:
= 4

(b)
Solution:
= 1

(c)
Solution:
= 1

(d)
Solution:
= 5

(e)
Solution:
= 1

(f)
Solution:
= 3

Question 7 (7)

5 Mixed Fractions Figure it Out (Page No. 163)

Question 1


Write the following mixed numbers as fractions:
(a) 3
(b) 7
(c) 9
(d) 3
(e) 2
(f) 3

Solution:

Fractions Diagram 32

Question 8 (7)

6 Equivalent Fractions Figure it Out 7.7 Simplest form of a Fraction Figure it Out (Page No. 165)

Question 1


Are equivalent fractions? Why?

Solution:
Here, simplest form of [HCF of 3 and 6 is 3]
and simplest form of is [HCF of 4 and 8 is 4]
and simplest form of is [HCF of 5 and 10 is 5]
Hence, are equivalent fractions.
Question 2


Write two equivalent fractions for .
Solution:
From the fractional wall we can choose any two fractions that denote the same length as

Question 3


= ___________ = ___________ = ___________ = ___________________
(Write as many as you can)
Solution:
Here,

Fractions Diagram 33

Intext Questions

Solution:
the following questions after looking at the fraction wall: [Page 164]

Fractions Diagram 34

Question 1


Are the lengths and equal?
Solution:
Yes, here lengths and =
Lengths are equal.

Question 2


Are and equivalent fractions? Why?
Solution:
Yes, lengths and = are equivalent fraction, as they have same length.

Question 3


How many pieces of length will make a length of ?
Solution:
Total no.of pieces = = 3
Hence three pieces of length will make a length of

Question 4


How many pieces of length will make a length of ?
Solution:
Total no. of pieces = = 2
Hence two pieces of length will make a length of .

Question 9 (7)

7 Simplest form of a Fraction Figure it Out (Page No. 166)

Question 1


Three rotis are shared equally by four children, show the division in the picture and write a fraction of how much each child gets. Also, write the corresponding division facts, addition facts, and, multiplication facts.

The fraction of roti each child gets is ___________
Division fact:
Addition fact:
Multiplication fact:
Compare your picture and answer with your classmates!

Solution:
One roti is shared as shown in the figure below:

The four shares must be equal to each other!
Similar distribution will be done for the second and third roti also.
So, each child will get a piece of roti.
The division fact is 3 ÷ 4 =
The addition fact is 3 =
The multiplication fact is 3 = 4 ×

Fractions Diagram 35

Fractions Diagram 36

Question 2


Draw a picture to show how much each child gets when 2 rotis are shared equally by 4 children. Also, write the corresponding division facts, addition facts, and multiplication facts.
Solution:
One roti is shared as shown in the figure below:

The four shares must be equal to each other!
A similar distribution will be done for the second roti also.
So, each child will get part from a rod.
So, the total fraction of roti received by each child from 2 rotis = =
The division fact is 2 ÷ 4 =
The addition fact is =
The multiplication fact is 2 = 4 ×

Fractions Diagram 37

Question 3

Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get?
Solution:
Anil would get part of the cake.

Question 10 (7)

7 Simplest form of a Fraction Figure it Out (Page No. 168 – 169)

Question 1


Find the missing numbers:
(a) 5 glasses of juice shared equally among 4 friends is the same as ____________ glasses of juice shared equally among 8 friends. So, = .
(b) 4 kg of potatoes divided equally in 3 bags is the same as 12 kgs of potatoes divided equally in ____________ bags. So, = .
(c) 7 rods divided among 5 children is the same as rods divided among children. So, = ____________

Solution:
(a) Here, the amount of juice each friend gets when 5 glasses are shared among 4 friends =
Now to determine how many glasses of juice would be needed to give each of the 8 friends the same amount = 8 ×
= 10 glasses
So, 10 glasses of juice shared equally among 8 friends is the same as 5 glasses of juice shared equally among 4 friends.
∴

(b) Here 4 kg of potatoes divided equally in 3 bags then amount of potatoes per bag = kg per bag
Let x is the number of bags for 12 kg of potatoes, where each bag has the same amount of potatoes then
kg per bag
⇒ 12 × 3 = 4 × x
⇒ 36 = 4x
⇒ x =
⇒ x = 9
∴

(c) Dividing 7 rotis among 4 children gives 7 each child = of a roti. We can find an
equivalent fraction by multiplying both the numerator and the denominator by the same number. For example, multiplying both by 2.

So, 7 rotis divided among 5 children is the same as 14 rotis divided among 10 children
∴

Intext Questions

Question 1


Find equivalent fractions for the given pairs of fractions such that the fractional units are the same. (Page 172)
(a) and
Solution:
Given fractions are and
Here, the denominators are 2 and 5.
And least common multiple of 2 and 5 is 10.
Hence for both fractions let’s have same denominator of 10.
Now for multiply both the numerator and the denominator by 5.

And for multiply both the numerator and the denominator by 2, we get,

Hence, the equivalent fractions with the same denominator are:
and

(b) and
Solution:
Given fractions are and
Here, the denominators are 3 and 6.
And least common multiple of 3 and 6 is 6.
Now for multiply both the numerator and the denominator by 2.

already have a denominator 6.
Hence, the equivalent fractions with the same denominator are:
and

(c) and
Solution:
Given fractions are and
Here, the denominators are 4 and 5.
And least common multiple of 4 and 5 is 20.
Now for multiply both the numerator and the denominator by 5.

And for multiply both the numerator and the denominator by 4, we get

So, the equivalent fractions with the same denominator are:
and

(d) and
Solution:
Given fractions are and
Here, the denominators are 7 and 5.
And least common multiple of 7 and 5 is 35.

Now for multiply both the numerator and the denominator by 5.

And for multiply both the numerator and the denominator by 7, we get

So, the equivalent fractions with the same denominator are:
and

(e) and
Solution:
Given fractions are and
Here, the denominators are 4 and 2.
And least common multiple of 4 and 2 is 4.
Now for multiply both the numerator and the denominator by 2.

and already have a denominator 4
So, the equivalent fractions with the same denominator are:
and

(f) and
Solution:
Given fractions are and and
Here, the denominators are 10 and 9.
And least common multiple of 10 and 9 is 90.
Now for multiply both the numerator and the denominator by 9.

And for 2 multiply both the numerator and the denominator by 10, we get

So, the equivalent fractions with the same denominator are:’
and

(g) and
Solution:
Given fractions are and
Here, the denominators are 3 and 4.
And least common multiple of 3 and 4 is 12.
Now for multiply both the numerator and the denominator by 4.

And for multiply both the numerator and the denominator by 3, we get

So, the equivalent fractions with the same denominator are:
and

(h) and
Solution:
Given fractions are and
Here, the denominators are 6 and 9.
And least common multiple of 6 and 9 is 18.

Now for multiply both the numerator and the denominator by 3.

And for multiply both the numerator and the denominator by 2, we get

So, the equivalent fractions with the same denominator are:
and

Question 11 (7)

7 Simplest form of a Fraction Figure it Out (Page No. 173)

Question 1


Express the following fractions in lowest terms:
(a)

Solution:

(b)
Solution:

(c)
Solution:

(d)
Solution:

Question 12 (7)

8 Comparing Fractions Figure it Out (Page No. 174)

Question 1


Compare the following fractions and justify your answers:
(a)
(b)
(c)
(d)
(e)

Solution:

Fractions Diagram 38

Fractions Diagram 39

Question 2


Write following fractions ascending order.
(a)
Solution:
The given fractions are
Let us find LCM of denominator 10, 15, 5

∴ LCM of 10, 15 and 5 = 2 × 3 × 5 = 30
Now let us make denominator of each fractions as LCM

Hence given fractions in ascending order are:

Fractions Diagram 40

Fractions Diagram 41

(b)
Solution:
The given fractions are
Here LCM of 24, 6, 12 is 24.

On arranging in ascending Order, we get

⇒

Fractions Diagram 42

Question 3


Write the following fractions in descending order.
(a)
Solution:

Fractions Diagram 43

(b)
Solution:

Fractions Diagram 44

Question 13 (7)

9 Relation to Number Sequences Figure it Out (Page No. 179)

Question 1


Add the following fractions using Brahmagupta’s method:
(a)

Solution:

=
=1

Fractions Diagram 45

(b)
Solution:

=
=
= 1

(c)
Solution:


= 1

(d)
Solution:

=

(e)
Solution:

=
= 1

(f)
Solution:

= 1

(g)
Solution:

= 1

(h)
Solution:

=

(i)
Solution:

= 5

(j)
Solution:

= 2

(k)
Solution:

= 1

(l)
Solution:

= 1

Fractions Diagram 46

(m)
Solution:

=

Question 2

Rahim mixes liters of yellow paint with liters of blue paint to make green paint What is the volume of green paint he has made?
Solution:
Quantity of yellow paint added = litres
Quantity of blue paint added = litres
Total quantity of green paint made = +
LCM of 3 and 4 is 12.



So, the total quantity of paint made is liters.

Fractions Diagram 47

Question 3


Geeta bought meter of lace and Shamim bought meter of the same lace to put a complete border on a table cloth whose perimeter is 1 meter long. Find the total length of the lace they both have bought. Will the lace be sufficient to cover the whole border?
Solution:
Length of lace bought by Geeta = m
Length of lace bought by Shamim = m
Total length of lace bought = +
LCM of 5 and 4 is 20.



This length is more than 1 m. So, lace is more than sufficient or will be left extra after covering the border.

Question 14 (7)

9 Relation to Number Sequences Figure it Out (Page No. 181)

Question 1


Solution:
Given
As fractional unit is same i.e., we shall simply subtract numerators keeping fractional unit as
Then
= (representing in simplest form)
Question 2



Solution:
Given
As fractional unit is same i.e., we shall simply subtract numerators keeping fractional unit as

=

Question 3



Solution:
Here
=
=

Question 15 (7)

9 Relation to Number Sequences Figure it Out (Page No. 182)

Question 1


Carry out the following subtractions using Brahmagupta’s method:
(a)

Solution:
Given
Fractional unit for both fractions is then

=

(b)
Solution:
Given
Here LCM of 5 and 15 is 15. Fractional unit for both fractions should be
then
=
=
=

(c)
Solution:
Given
Hence LCM of 6 and 9 is 18. Fractional unit for both fractions should be then

Fractions Diagram 48

(d)
Solution:
Given
Here LCM of 3 and 2 is 6. Fractional unit for both fractions should be

Fractions Diagram 49

Question 2


Subtract as indicated:
(a) from
Solution:
The denominators of the given fractions are 3 and 4. The LCM of 3 and 4 is 12.
Then
Therefore,

(b) from
Solution:
The denominators of the given fractions are 3 and 5.
The LCM of 3 and 5 is 15.
Then,
Therefore,

(c) from
Solution:
The denominators are same.
Therefore,

Question 3


Solve the following problems:
(a) Jaya’s school is km from her home. She takes an auto for km from her home daily, and then walks the remaining distance to reach her school. How much does she walk daily to reach the school?
Solution:
(a) Total distance between school and home = km
Distance travelled in Auto = km.
∴ Distance she walks daily to reach the school

Fractions Diagram 50

(b) Jeevika takes minutes to take a complete round of the park and her friend Namit takes minutes to do the same. Who takes less time and by how much?
Solution:
Time taken by Jeevika = minutes
and time taken by Narnit = minutes

Now, and
Clearly, >

∴ Jeevika takes less ti me by minutes
= minutes
= minutes.

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