NCERT Textbook: Fractions | Mathematics (Maths) Class 6 PDF Download

 Page 1


Recall that when some whole number of things are shared 
equally among some number of people, fractions tell us how 
much each share is.
Shabnam:  Do you remember, if one roti is divided equally 
between two children, how much 
roti will each child get?
Mukta: Each child will get half a roti.
Shabnam:  The fraction ‘one half’ is written as 
1
2
 . We also sometimes read this as 
‘one upon two.’
Mukta:  If one roti is equally shared among 
4 children, how much roti will one child get?
Shabnam: Each child’s share is 
1
4
 roti. 
Mukta: And which is more 
1
2
 roti or 
1
4
 roti? 
Shabnam: When 2 children share 1 roti 
equally, each child gets 
1
2
 roti. When 
4 children share 1 roti equally, each 
child gets 
1
4
 roti. Since, in the second 
group more children share the 
Fractions
7
Chapter 7_Fractions.indd   151 10-08-2024   17:52:17
Page 2


Recall that when some whole number of things are shared 
equally among some number of people, fractions tell us how 
much each share is.
Shabnam:  Do you remember, if one roti is divided equally 
between two children, how much 
roti will each child get?
Mukta: Each child will get half a roti.
Shabnam:  The fraction ‘one half’ is written as 
1
2
 . We also sometimes read this as 
‘one upon two.’
Mukta:  If one roti is equally shared among 
4 children, how much roti will one child get?
Shabnam: Each child’s share is 
1
4
 roti. 
Mukta: And which is more 
1
2
 roti or 
1
4
 roti? 
Shabnam: When 2 children share 1 roti 
equally, each child gets 
1
2
 roti. When 
4 children share 1 roti equally, each 
child gets 
1
4
 roti. Since, in the second 
group more children share the 
Fractions
7
Chapter 7_Fractions.indd   151 10-08-2024   17:52:17
Ganita Prakash | Grade 6
152
same one roti, each child gets a smaller share. So, 
1
2
 roti is 
more than 
1
4
 roti.
7.1 Fractional Units and Equal Shares 
Beni: Which fraction is greater? 
1
5
 or 
1
9
?
Arvin: 9 is bigger than 5. So I would guess that 
1
9
 is greater 
than 
1
5
. Am I right?
Beni: No! That is a common mistake. Think of these fractions 
as shares.
Arvin: If one roti is shared among 5 children, each one gets a 
share of 
1
5
 roti. If one roti is shared among 9 children, 
each one gets a share of 
1
9
 roti?
Beni: Exactly! Now think again - which share is higher?
Arvin: If I share with more people, I will get less. So 
1
9
 < 
1
5
.
Beni: You got it!
Oh, so 
1
100
 is bigger than 
1
200
!
When one unit is divided into several equal parts, each part is 
called a fractional unit. These are all fractional units: 
1
2
, 
1
3
, 
1
4
, 
1
5
, 
1
6
, …, 
1
10
, …, 
1
50
, …, 
1
100
, etc.
We also sometimes refer to fractional units as ‘unit fractions.’
 Figure it Out 
 Fill in the blanks with fractions.
1.   Three guavas together weigh 1 kg. If they are roughly of the same 
size, each guava will roughly weigh ____kg.
2.  A wholesale merchant packed 1 kg of rice in four packets 
of equal weight. The weight of each packet is ___ kg.
3.  Four friends ordered 3 glasses of sugarcane juice and 
shared it equally among themselves. Each one drank ____ 
glass of sugarcane juice
1
2
 > 
1
4
 
Math 
Talk
Math 
Talk
Chapter 7_Fractions.indd   152 10-08-2024   17:52:17
Page 3


Recall that when some whole number of things are shared 
equally among some number of people, fractions tell us how 
much each share is.
Shabnam:  Do you remember, if one roti is divided equally 
between two children, how much 
roti will each child get?
Mukta: Each child will get half a roti.
Shabnam:  The fraction ‘one half’ is written as 
1
2
 . We also sometimes read this as 
‘one upon two.’
Mukta:  If one roti is equally shared among 
4 children, how much roti will one child get?
Shabnam: Each child’s share is 
1
4
 roti. 
Mukta: And which is more 
1
2
 roti or 
1
4
 roti? 
Shabnam: When 2 children share 1 roti 
equally, each child gets 
1
2
 roti. When 
4 children share 1 roti equally, each 
child gets 
1
4
 roti. Since, in the second 
group more children share the 
Fractions
7
Chapter 7_Fractions.indd   151 10-08-2024   17:52:17
Ganita Prakash | Grade 6
152
same one roti, each child gets a smaller share. So, 
1
2
 roti is 
more than 
1
4
 roti.
7.1 Fractional Units and Equal Shares 
Beni: Which fraction is greater? 
1
5
 or 
1
9
?
Arvin: 9 is bigger than 5. So I would guess that 
1
9
 is greater 
than 
1
5
. Am I right?
Beni: No! That is a common mistake. Think of these fractions 
as shares.
Arvin: If one roti is shared among 5 children, each one gets a 
share of 
1
5
 roti. If one roti is shared among 9 children, 
each one gets a share of 
1
9
 roti?
Beni: Exactly! Now think again - which share is higher?
Arvin: If I share with more people, I will get less. So 
1
9
 < 
1
5
.
Beni: You got it!
Oh, so 
1
100
 is bigger than 
1
200
!
When one unit is divided into several equal parts, each part is 
called a fractional unit. These are all fractional units: 
1
2
, 
1
3
, 
1
4
, 
1
5
, 
1
6
, …, 
1
10
, …, 
1
50
, …, 
1
100
, etc.
We also sometimes refer to fractional units as ‘unit fractions.’
 Figure it Out 
 Fill in the blanks with fractions.
1.   Three guavas together weigh 1 kg. If they are roughly of the same 
size, each guava will roughly weigh ____kg.
2.  A wholesale merchant packed 1 kg of rice in four packets 
of equal weight. The weight of each packet is ___ kg.
3.  Four friends ordered 3 glasses of sugarcane juice and 
shared it equally among themselves. Each one drank ____ 
glass of sugarcane juice
1
2
 > 
1
4
 
Math 
Talk
Math 
Talk
Chapter 7_Fractions.indd   152 10-08-2024   17:52:17
Fractions
153
same one roti, each child gets a smaller share. So, 
1
2
 roti is 
more than 
1
4
 roti.
7.1 Fractional Units and Equal Shares 
Beni: Which fraction is greater? 
1
5
 or 
1
9
?
Arvin: 9 is bigger than 5. So I would guess that 
1
9
 is greater 
than 
1
5
. Am I right?
Beni: No! That is a common mistake. Think of these fractions 
as shares.
Arvin: If one roti is shared among 5 children, each one gets a 
share of 
1
5
 roti. If one roti is shared among 9 children, 
each one gets a share of 
1
9
 roti?
Beni: Exactly! Now think again - which share is higher?
Arvin: If I share with more people, I will get less. So 
1
9
 < 
1
5
.
Beni: You got it!
Oh, so 
1
100
 is bigger than 
1
200
!
When one unit is divided into several equal parts, each part is 
called a fractional unit. These are all fractional units: 
1
2
, 
1
3
, 
1
4
, 
1
5
, 
1
6
, …, 
1
10
, …, 
1
50
, …, 
1
100
, etc.
We also sometimes refer to fractional units as ‘unit fractions.’
 Figure it Out 
 Fill in the blanks with fractions.
1.   Three guavas together weigh 1 kg. If they are roughly of the same 
size, each guava will roughly weigh ____kg.
2.  A wholesale merchant packed 1 kg of rice in four packets 
of equal weight. The weight of each packet is ___ kg.
3.  Four friends ordered 3 glasses of sugarcane juice and 
shared it equally among themselves. Each one drank ____ 
glass of sugarcane juice
1
2
 > 
1
4
 
Math 
Talk
Math 
Talk
4.  The  big  fish  weighs 
1
2
 kg. The small one weighs 
1
4
 kg. 
Together they weigh ____ kg.
Knowledge from the past!
Fractions have been used and named in India since ancient 
times. In the Rig Veda, the fraction 
3
4
 is referred to as tri-
pada. This has the same meaning as the words for 
3
4
 in many 
Indian  languages  toda y ,  e.g.,  ?teen paav '  in  colloquial  Hindi  and
‘mukkaal’ in Tamil. Indeed, words for fractions used today in 
many Indian languages go back to ancient times. 
 Find out and discuss the words for fractions that are used in the 
different languages spoken in your home, city, or state. Ask your 
grandparents, parents, teachers, and classmates what words they use 
for different fractions, such as for one and a half, three quarters, one 
and a quarter, half, quarter, and two and a half, and write them here:
___________ ___________ ___________ ___________ ___________ ___________
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.
Write your answer here.
Chapter 7_Fractions.indd   153 10-08-2024   17:52:17
Page 4


Recall that when some whole number of things are shared 
equally among some number of people, fractions tell us how 
much each share is.
Shabnam:  Do you remember, if one roti is divided equally 
between two children, how much 
roti will each child get?
Mukta: Each child will get half a roti.
Shabnam:  The fraction ‘one half’ is written as 
1
2
 . We also sometimes read this as 
‘one upon two.’
Mukta:  If one roti is equally shared among 
4 children, how much roti will one child get?
Shabnam: Each child’s share is 
1
4
 roti. 
Mukta: And which is more 
1
2
 roti or 
1
4
 roti? 
Shabnam: When 2 children share 1 roti 
equally, each child gets 
1
2
 roti. When 
4 children share 1 roti equally, each 
child gets 
1
4
 roti. Since, in the second 
group more children share the 
Fractions
7
Chapter 7_Fractions.indd   151 10-08-2024   17:52:17
Ganita Prakash | Grade 6
152
same one roti, each child gets a smaller share. So, 
1
2
 roti is 
more than 
1
4
 roti.
7.1 Fractional Units and Equal Shares 
Beni: Which fraction is greater? 
1
5
 or 
1
9
?
Arvin: 9 is bigger than 5. So I would guess that 
1
9
 is greater 
than 
1
5
. Am I right?
Beni: No! That is a common mistake. Think of these fractions 
as shares.
Arvin: If one roti is shared among 5 children, each one gets a 
share of 
1
5
 roti. If one roti is shared among 9 children, 
each one gets a share of 
1
9
 roti?
Beni: Exactly! Now think again - which share is higher?
Arvin: If I share with more people, I will get less. So 
1
9
 < 
1
5
.
Beni: You got it!
Oh, so 
1
100
 is bigger than 
1
200
!
When one unit is divided into several equal parts, each part is 
called a fractional unit. These are all fractional units: 
1
2
, 
1
3
, 
1
4
, 
1
5
, 
1
6
, …, 
1
10
, …, 
1
50
, …, 
1
100
, etc.
We also sometimes refer to fractional units as ‘unit fractions.’
 Figure it Out 
 Fill in the blanks with fractions.
1.   Three guavas together weigh 1 kg. If they are roughly of the same 
size, each guava will roughly weigh ____kg.
2.  A wholesale merchant packed 1 kg of rice in four packets 
of equal weight. The weight of each packet is ___ kg.
3.  Four friends ordered 3 glasses of sugarcane juice and 
shared it equally among themselves. Each one drank ____ 
glass of sugarcane juice
1
2
 > 
1
4
 
Math 
Talk
Math 
Talk
Chapter 7_Fractions.indd   152 10-08-2024   17:52:17
Fractions
153
same one roti, each child gets a smaller share. So, 
1
2
 roti is 
more than 
1
4
 roti.
7.1 Fractional Units and Equal Shares 
Beni: Which fraction is greater? 
1
5
 or 
1
9
?
Arvin: 9 is bigger than 5. So I would guess that 
1
9
 is greater 
than 
1
5
. Am I right?
Beni: No! That is a common mistake. Think of these fractions 
as shares.
Arvin: If one roti is shared among 5 children, each one gets a 
share of 
1
5
 roti. If one roti is shared among 9 children, 
each one gets a share of 
1
9
 roti?
Beni: Exactly! Now think again - which share is higher?
Arvin: If I share with more people, I will get less. So 
1
9
 < 
1
5
.
Beni: You got it!
Oh, so 
1
100
 is bigger than 
1
200
!
When one unit is divided into several equal parts, each part is 
called a fractional unit. These are all fractional units: 
1
2
, 
1
3
, 
1
4
, 
1
5
, 
1
6
, …, 
1
10
, …, 
1
50
, …, 
1
100
, etc.
We also sometimes refer to fractional units as ‘unit fractions.’
 Figure it Out 
 Fill in the blanks with fractions.
1.   Three guavas together weigh 1 kg. If they are roughly of the same 
size, each guava will roughly weigh ____kg.
2.  A wholesale merchant packed 1 kg of rice in four packets 
of equal weight. The weight of each packet is ___ kg.
3.  Four friends ordered 3 glasses of sugarcane juice and 
shared it equally among themselves. Each one drank ____ 
glass of sugarcane juice
1
2
 > 
1
4
 
Math 
Talk
Math 
Talk
4.  The  big  fish  weighs 
1
2
 kg. The small one weighs 
1
4
 kg. 
Together they weigh ____ kg.
Knowledge from the past!
Fractions have been used and named in India since ancient 
times. In the Rig Veda, the fraction 
3
4
 is referred to as tri-
pada. This has the same meaning as the words for 
3
4
 in many 
Indian  languages  toda y ,  e.g.,  ?teen paav '  in  colloquial  Hindi  and
‘mukkaal’ in Tamil. Indeed, words for fractions used today in 
many Indian languages go back to ancient times. 
 Find out and discuss the words for fractions that are used in the 
different languages spoken in your home, city, or state. Ask your 
grandparents, parents, teachers, and classmates what words they use 
for different fractions, such as for one and a half, three quarters, one 
and a quarter, half, quarter, and two and a half, and write them here:
___________ ___________ ___________ ___________ ___________ ___________
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.
Write your answer here.
Chapter 7_Fractions.indd   153 10-08-2024   17:52:17
Ganita Prakash | Grade 6
154
7.2 Fractional Units as Parts of a Whole 
The picture shows a whole chikki.
 By dividing the whole chikki into 6 equal parts in different 
ways, we get 
1
6
 chikki pieces of different shapes. Are they of 
the same size?
A whole chikki cut 
into 6 equal pieces.
A whole chikki cut into 6 equal 
pieces in a different way.
Math 
Talk
A whole chikki
Below, a picture of the chikki broken 
into  2  pieces  is  shown.  How  much  of
the original chikki is each piece?
We can see that the bigger piece has 3 pieces of 
1
4
 chikki in it. So, we 
can measure the bigger piece using the fractional unit 
1
4
. We see that 
the bigger piece is 
3
4
 chikki.
3
4
1
6
1
6
Chapter 7_Fractions.indd   154 10-08-2024   17:52:18
Page 5


Recall that when some whole number of things are shared 
equally among some number of people, fractions tell us how 
much each share is.
Shabnam:  Do you remember, if one roti is divided equally 
between two children, how much 
roti will each child get?
Mukta: Each child will get half a roti.
Shabnam:  The fraction ‘one half’ is written as 
1
2
 . We also sometimes read this as 
‘one upon two.’
Mukta:  If one roti is equally shared among 
4 children, how much roti will one child get?
Shabnam: Each child’s share is 
1
4
 roti. 
Mukta: And which is more 
1
2
 roti or 
1
4
 roti? 
Shabnam: When 2 children share 1 roti 
equally, each child gets 
1
2
 roti. When 
4 children share 1 roti equally, each 
child gets 
1
4
 roti. Since, in the second 
group more children share the 
Fractions
7
Chapter 7_Fractions.indd   151 10-08-2024   17:52:17
Ganita Prakash | Grade 6
152
same one roti, each child gets a smaller share. So, 
1
2
 roti is 
more than 
1
4
 roti.
7.1 Fractional Units and Equal Shares 
Beni: Which fraction is greater? 
1
5
 or 
1
9
?
Arvin: 9 is bigger than 5. So I would guess that 
1
9
 is greater 
than 
1
5
. Am I right?
Beni: No! That is a common mistake. Think of these fractions 
as shares.
Arvin: If one roti is shared among 5 children, each one gets a 
share of 
1
5
 roti. If one roti is shared among 9 children, 
each one gets a share of 
1
9
 roti?
Beni: Exactly! Now think again - which share is higher?
Arvin: If I share with more people, I will get less. So 
1
9
 < 
1
5
.
Beni: You got it!
Oh, so 
1
100
 is bigger than 
1
200
!
When one unit is divided into several equal parts, each part is 
called a fractional unit. These are all fractional units: 
1
2
, 
1
3
, 
1
4
, 
1
5
, 
1
6
, …, 
1
10
, …, 
1
50
, …, 
1
100
, etc.
We also sometimes refer to fractional units as ‘unit fractions.’
 Figure it Out 
 Fill in the blanks with fractions.
1.   Three guavas together weigh 1 kg. If they are roughly of the same 
size, each guava will roughly weigh ____kg.
2.  A wholesale merchant packed 1 kg of rice in four packets 
of equal weight. The weight of each packet is ___ kg.
3.  Four friends ordered 3 glasses of sugarcane juice and 
shared it equally among themselves. Each one drank ____ 
glass of sugarcane juice
1
2
 > 
1
4
 
Math 
Talk
Math 
Talk
Chapter 7_Fractions.indd   152 10-08-2024   17:52:17
Fractions
153
same one roti, each child gets a smaller share. So, 
1
2
 roti is 
more than 
1
4
 roti.
7.1 Fractional Units and Equal Shares 
Beni: Which fraction is greater? 
1
5
 or 
1
9
?
Arvin: 9 is bigger than 5. So I would guess that 
1
9
 is greater 
than 
1
5
. Am I right?
Beni: No! That is a common mistake. Think of these fractions 
as shares.
Arvin: If one roti is shared among 5 children, each one gets a 
share of 
1
5
 roti. If one roti is shared among 9 children, 
each one gets a share of 
1
9
 roti?
Beni: Exactly! Now think again - which share is higher?
Arvin: If I share with more people, I will get less. So 
1
9
 < 
1
5
.
Beni: You got it!
Oh, so 
1
100
 is bigger than 
1
200
!
When one unit is divided into several equal parts, each part is 
called a fractional unit. These are all fractional units: 
1
2
, 
1
3
, 
1
4
, 
1
5
, 
1
6
, …, 
1
10
, …, 
1
50
, …, 
1
100
, etc.
We also sometimes refer to fractional units as ‘unit fractions.’
 Figure it Out 
 Fill in the blanks with fractions.
1.   Three guavas together weigh 1 kg. If they are roughly of the same 
size, each guava will roughly weigh ____kg.
2.  A wholesale merchant packed 1 kg of rice in four packets 
of equal weight. The weight of each packet is ___ kg.
3.  Four friends ordered 3 glasses of sugarcane juice and 
shared it equally among themselves. Each one drank ____ 
glass of sugarcane juice
1
2
 > 
1
4
 
Math 
Talk
Math 
Talk
4.  The  big  fish  weighs 
1
2
 kg. The small one weighs 
1
4
 kg. 
Together they weigh ____ kg.
Knowledge from the past!
Fractions have been used and named in India since ancient 
times. In the Rig Veda, the fraction 
3
4
 is referred to as tri-
pada. This has the same meaning as the words for 
3
4
 in many 
Indian  languages  toda y ,  e.g.,  ?teen paav '  in  colloquial  Hindi  and
‘mukkaal’ in Tamil. Indeed, words for fractions used today in 
many Indian languages go back to ancient times. 
 Find out and discuss the words for fractions that are used in the 
different languages spoken in your home, city, or state. Ask your 
grandparents, parents, teachers, and classmates what words they use 
for different fractions, such as for one and a half, three quarters, one 
and a quarter, half, quarter, and two and a half, and write them here:
___________ ___________ ___________ ___________ ___________ ___________
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.
Write your answer here.
Chapter 7_Fractions.indd   153 10-08-2024   17:52:17
Ganita Prakash | Grade 6
154
7.2 Fractional Units as Parts of a Whole 
The picture shows a whole chikki.
 By dividing the whole chikki into 6 equal parts in different 
ways, we get 
1
6
 chikki pieces of different shapes. Are they of 
the same size?
A whole chikki cut 
into 6 equal pieces.
A whole chikki cut into 6 equal 
pieces in a different way.
Math 
Talk
A whole chikki
Below, a picture of the chikki broken 
into  2  pieces  is  shown.  How  much  of
the original chikki is each piece?
We can see that the bigger piece has 3 pieces of 
1
4
 chikki in it. So, we 
can measure the bigger piece using the fractional unit 
1
4
. We see that 
the bigger piece is 
3
4
 chikki.
3
4
1
6
1
6
Chapter 7_Fractions.indd   154 10-08-2024   17:52:18
Fractions
155
What is the fractional unit of chikki shown below?
We get this piece 
by breaking the 
chikki into 3 
equal pieces. So 
this is 
1
3
 chikki.
 Figure it Out
The  figures  below  show  different  fr actional  units  of  a  whole  chikki. 
How  much  of  a  whole  chikki  is  each  piece?
a.
e. f. g. h.
b. c. d.
A whole chikki
1
3
Chapter 7_Fractions.indd   155 10-08-2024   17:52:18