NCERT Textbook: Fractions Notes | Study Mathematics (Maths) Class 6 - Class 6

 Page 1


Subhash had learnt about fractions in
Classes IV and V , so whenever possible
he would try to use fractions. One
occasion was when he forgot his lunch
at home. His friend Farida invited him
to share her lunch. She had five pooris
in her lunch box. So, Subhash and
Farida took two pooris each. Then
Farida made two equal halves of the
fifth poori and gave one-half to Subhash
and took the other half herself. Thus,
both Subhash and Farida had 2 full
pooris  and one-half poori.
Where do you come across situations with fractions in
your life?
Subhash knew that one-half is written as 
1
2
. While
eating he further divided his half poori into two equal
parts and asked Farida what fraction of the whole poori
was that piece? (Fig 7.1)
Without answering, Farida also divided her portion of the
half puri into two equal parts and kept them beside Subhash’s
shares. She said that these four equal parts together make
Fig 7.2
Fig 7.1
7.1 Introduction
Chapter 7 Chapter 7 Chapter 7 Chapter 7 Chapter 7
Fractions Fractions
Fractions Fractions Fractions
2 pooris + half-poori–Subhash
2 pooris + half-poori–Farida
2020-21
Page 2


Subhash had learnt about fractions in
Classes IV and V , so whenever possible
he would try to use fractions. One
occasion was when he forgot his lunch
at home. His friend Farida invited him
to share her lunch. She had five pooris
in her lunch box. So, Subhash and
Farida took two pooris each. Then
Farida made two equal halves of the
fifth poori and gave one-half to Subhash
and took the other half herself. Thus,
both Subhash and Farida had 2 full
pooris  and one-half poori.
Where do you come across situations with fractions in
your life?
Subhash knew that one-half is written as 
1
2
. While
eating he further divided his half poori into two equal
parts and asked Farida what fraction of the whole poori
was that piece? (Fig 7.1)
Without answering, Farida also divided her portion of the
half puri into two equal parts and kept them beside Subhash’s
shares. She said that these four equal parts together make
Fig 7.2
Fig 7.1
7.1 Introduction
Chapter 7 Chapter 7 Chapter 7 Chapter 7 Chapter 7
Fractions Fractions
Fractions Fractions Fractions
2 pooris + half-poori–Subhash
2 pooris + half-poori–Farida
2020-21
MATHEMATICS
134
one whole (Fig 7.2). So, each equal part is one-fourth of one whole poori and
4 parts together will be 
4
4
 or 1 whole poori.
When they ate, they discussed
what they had learnt earlier. Three
parts out of 4 equal parts is 
3
4
.
Similarly, 
3
7
 is obtained when we
divide a whole into seven equal parts
and take three parts (Fig 7.3). For 
1
8
, we divide a whole into eight equal parts
and take one part out of it (Fig 7.4).
Farida said that we have learnt that a fraction is a number representing
part of a whole. The whole may be a single object or a group of objects.
Subhash observed that the parts have to be equal.
7.2  A Fraction
Let us recapitulate the discussion.
A fraction means a part of a group or of a region.
5
12
 is a fraction. We read it as “five-twelfths”.
What does “12” stand for? It is the number of equal parts
into which the whole has been divided.
What does “5” stand for? It is the number of equal parts which have been
taken out.
Here 5 is called the numerator and 12 is called the denominator.
Name the numerator of 
3
7
 and the denominator of 
4
15
.
2
3
 Play this Game
You can play this game with your friends.
Take many copies of the grid as shown here.
Consider any fraction, say 
1
2
.
Each one of you should shade 
1
2
 of the grid.
Fig 7.4 Fig 7.3
2020-21
Page 3


Subhash had learnt about fractions in
Classes IV and V , so whenever possible
he would try to use fractions. One
occasion was when he forgot his lunch
at home. His friend Farida invited him
to share her lunch. She had five pooris
in her lunch box. So, Subhash and
Farida took two pooris each. Then
Farida made two equal halves of the
fifth poori and gave one-half to Subhash
and took the other half herself. Thus,
both Subhash and Farida had 2 full
pooris  and one-half poori.
Where do you come across situations with fractions in
your life?
Subhash knew that one-half is written as 
1
2
. While
eating he further divided his half poori into two equal
parts and asked Farida what fraction of the whole poori
was that piece? (Fig 7.1)
Without answering, Farida also divided her portion of the
half puri into two equal parts and kept them beside Subhash’s
shares. She said that these four equal parts together make
Fig 7.2
Fig 7.1
7.1 Introduction
Chapter 7 Chapter 7 Chapter 7 Chapter 7 Chapter 7
Fractions Fractions
Fractions Fractions Fractions
2 pooris + half-poori–Subhash
2 pooris + half-poori–Farida
2020-21
MATHEMATICS
134
one whole (Fig 7.2). So, each equal part is one-fourth of one whole poori and
4 parts together will be 
4
4
 or 1 whole poori.
When they ate, they discussed
what they had learnt earlier. Three
parts out of 4 equal parts is 
3
4
.
Similarly, 
3
7
 is obtained when we
divide a whole into seven equal parts
and take three parts (Fig 7.3). For 
1
8
, we divide a whole into eight equal parts
and take one part out of it (Fig 7.4).
Farida said that we have learnt that a fraction is a number representing
part of a whole. The whole may be a single object or a group of objects.
Subhash observed that the parts have to be equal.
7.2  A Fraction
Let us recapitulate the discussion.
A fraction means a part of a group or of a region.
5
12
 is a fraction. We read it as “five-twelfths”.
What does “12” stand for? It is the number of equal parts
into which the whole has been divided.
What does “5” stand for? It is the number of equal parts which have been
taken out.
Here 5 is called the numerator and 12 is called the denominator.
Name the numerator of 
3
7
 and the denominator of 
4
15
.
2
3
 Play this Game
You can play this game with your friends.
Take many copies of the grid as shown here.
Consider any fraction, say 
1
2
.
Each one of you should shade 
1
2
 of the grid.
Fig 7.4 Fig 7.3
2020-21
Fractions and Fractions and
Fractions and Fractions and Fractions and
Integers Integers
Integers Integers Integers
Fractions and Fractions and
Fractions and Fractions and Fractions and
Integers Integers
Integers Integers Integers
FRACTIONS
135
1
6
1
3
3
4
EXERCISE 7.1
1. Write the fraction representing the shaded portion.
2. Colour the part according to the given fraction.
1
4
(v) (vi) (vii) (viii)
(i) (ii) (iii) (iv)
(ix) (x)
4
9
2020-21
Page 4


Subhash had learnt about fractions in
Classes IV and V , so whenever possible
he would try to use fractions. One
occasion was when he forgot his lunch
at home. His friend Farida invited him
to share her lunch. She had five pooris
in her lunch box. So, Subhash and
Farida took two pooris each. Then
Farida made two equal halves of the
fifth poori and gave one-half to Subhash
and took the other half herself. Thus,
both Subhash and Farida had 2 full
pooris  and one-half poori.
Where do you come across situations with fractions in
your life?
Subhash knew that one-half is written as 
1
2
. While
eating he further divided his half poori into two equal
parts and asked Farida what fraction of the whole poori
was that piece? (Fig 7.1)
Without answering, Farida also divided her portion of the
half puri into two equal parts and kept them beside Subhash’s
shares. She said that these four equal parts together make
Fig 7.2
Fig 7.1
7.1 Introduction
Chapter 7 Chapter 7 Chapter 7 Chapter 7 Chapter 7
Fractions Fractions
Fractions Fractions Fractions
2 pooris + half-poori–Subhash
2 pooris + half-poori–Farida
2020-21
MATHEMATICS
134
one whole (Fig 7.2). So, each equal part is one-fourth of one whole poori and
4 parts together will be 
4
4
 or 1 whole poori.
When they ate, they discussed
what they had learnt earlier. Three
parts out of 4 equal parts is 
3
4
.
Similarly, 
3
7
 is obtained when we
divide a whole into seven equal parts
and take three parts (Fig 7.3). For 
1
8
, we divide a whole into eight equal parts
and take one part out of it (Fig 7.4).
Farida said that we have learnt that a fraction is a number representing
part of a whole. The whole may be a single object or a group of objects.
Subhash observed that the parts have to be equal.
7.2  A Fraction
Let us recapitulate the discussion.
A fraction means a part of a group or of a region.
5
12
 is a fraction. We read it as “five-twelfths”.
What does “12” stand for? It is the number of equal parts
into which the whole has been divided.
What does “5” stand for? It is the number of equal parts which have been
taken out.
Here 5 is called the numerator and 12 is called the denominator.
Name the numerator of 
3
7
 and the denominator of 
4
15
.
2
3
 Play this Game
You can play this game with your friends.
Take many copies of the grid as shown here.
Consider any fraction, say 
1
2
.
Each one of you should shade 
1
2
 of the grid.
Fig 7.4 Fig 7.3
2020-21
Fractions and Fractions and
Fractions and Fractions and Fractions and
Integers Integers
Integers Integers Integers
Fractions and Fractions and
Fractions and Fractions and Fractions and
Integers Integers
Integers Integers Integers
FRACTIONS
135
1
6
1
3
3
4
EXERCISE 7.1
1. Write the fraction representing the shaded portion.
2. Colour the part according to the given fraction.
1
4
(v) (vi) (vii) (viii)
(i) (ii) (iii) (iv)
(ix) (x)
4
9
2020-21
MATHEMATICS
136
 3. Identify the error, if any .
This is 
1
2
This is 
1
4
This is 
3
4
4. What fraction of a day is 8 hours?
5. What fraction of an hour is 40 minutes?
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?
7. Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses.
What fraction of dresses has she finished?
8. Write the natural numbers from 2 to 12. What fraction of them are prime numbers?
9. Write the natural numbers from 102 to 1 13. What fraction of them are prime numbers?
10. What fraction of these circles have X’s in them?
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?
7.3 Fraction on the Number Line
Y ou have learnt to show whole numbers like 0,1,2... on a number line.
W e can also show fractions on a number line. Let us draw a number line and
try to mark 
1
2
 on it.
We know that 
1
2
 is greater than 0 and less than 1, so it should lie between 0
and 1.
Since we have to show 
1
2
, we divide the gap between 0 and 1 into two equal
parts and show 1 part as 
1
2
 (as shown in the Fig 7.5).
2020-21
Page 5


Subhash had learnt about fractions in
Classes IV and V , so whenever possible
he would try to use fractions. One
occasion was when he forgot his lunch
at home. His friend Farida invited him
to share her lunch. She had five pooris
in her lunch box. So, Subhash and
Farida took two pooris each. Then
Farida made two equal halves of the
fifth poori and gave one-half to Subhash
and took the other half herself. Thus,
both Subhash and Farida had 2 full
pooris  and one-half poori.
Where do you come across situations with fractions in
your life?
Subhash knew that one-half is written as 
1
2
. While
eating he further divided his half poori into two equal
parts and asked Farida what fraction of the whole poori
was that piece? (Fig 7.1)
Without answering, Farida also divided her portion of the
half puri into two equal parts and kept them beside Subhash’s
shares. She said that these four equal parts together make
Fig 7.2
Fig 7.1
7.1 Introduction
Chapter 7 Chapter 7 Chapter 7 Chapter 7 Chapter 7
Fractions Fractions
Fractions Fractions Fractions
2 pooris + half-poori–Subhash
2 pooris + half-poori–Farida
2020-21
MATHEMATICS
134
one whole (Fig 7.2). So, each equal part is one-fourth of one whole poori and
4 parts together will be 
4
4
 or 1 whole poori.
When they ate, they discussed
what they had learnt earlier. Three
parts out of 4 equal parts is 
3
4
.
Similarly, 
3
7
 is obtained when we
divide a whole into seven equal parts
and take three parts (Fig 7.3). For 
1
8
, we divide a whole into eight equal parts
and take one part out of it (Fig 7.4).
Farida said that we have learnt that a fraction is a number representing
part of a whole. The whole may be a single object or a group of objects.
Subhash observed that the parts have to be equal.
7.2  A Fraction
Let us recapitulate the discussion.
A fraction means a part of a group or of a region.
5
12
 is a fraction. We read it as “five-twelfths”.
What does “12” stand for? It is the number of equal parts
into which the whole has been divided.
What does “5” stand for? It is the number of equal parts which have been
taken out.
Here 5 is called the numerator and 12 is called the denominator.
Name the numerator of 
3
7
 and the denominator of 
4
15
.
2
3
 Play this Game
You can play this game with your friends.
Take many copies of the grid as shown here.
Consider any fraction, say 
1
2
.
Each one of you should shade 
1
2
 of the grid.
Fig 7.4 Fig 7.3
2020-21
Fractions and Fractions and
Fractions and Fractions and Fractions and
Integers Integers
Integers Integers Integers
Fractions and Fractions and
Fractions and Fractions and Fractions and
Integers Integers
Integers Integers Integers
FRACTIONS
135
1
6
1
3
3
4
EXERCISE 7.1
1. Write the fraction representing the shaded portion.
2. Colour the part according to the given fraction.
1
4
(v) (vi) (vii) (viii)
(i) (ii) (iii) (iv)
(ix) (x)
4
9
2020-21
MATHEMATICS
136
 3. Identify the error, if any .
This is 
1
2
This is 
1
4
This is 
3
4
4. What fraction of a day is 8 hours?
5. What fraction of an hour is 40 minutes?
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?
7. Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses.
What fraction of dresses has she finished?
8. Write the natural numbers from 2 to 12. What fraction of them are prime numbers?
9. Write the natural numbers from 102 to 1 13. What fraction of them are prime numbers?
10. What fraction of these circles have X’s in them?
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?
7.3 Fraction on the Number Line
Y ou have learnt to show whole numbers like 0,1,2... on a number line.
W e can also show fractions on a number line. Let us draw a number line and
try to mark 
1
2
 on it.
We know that 
1
2
 is greater than 0 and less than 1, so it should lie between 0
and 1.
Since we have to show 
1
2
, we divide the gap between 0 and 1 into two equal
parts and show 1 part as 
1
2
 (as shown in the Fig 7.5).
2020-21
Fractions and Fractions and
Fractions and Fractions and Fractions and
Integers Integers
Integers Integers Integers
Fractions and Fractions and
Fractions and Fractions and Fractions and
Integers Integers
Integers Integers Integers
FRACTIONS
137
Suppose we want to show 
1
3
 on a number line. Into how many equal parts
should the length between 0 and 1 be divided? We divide the length between
0 and 1 into 3 equal parts and show one part as 
1
3
 (as shown in the Fig 7.6)
Can we show 
2
3
 on this number line? 
2
3
 means 2 parts out of 3 parts as
shown (Fig 7.7).
Similarly, how would you show 
0
3
and 
3
3
 on this number line?
0
3
 is the point zero whereas since 
3
3
 is
1 whole, it can be shown by the point 1
(as shown in Fig 7.7)
So if we have to show 
3
7
 on a
number line, then, into how many
equal parts should the length between
0 and 1 be divided? If P shows 
3
7
 then
how many equal divisions lie between
0 and P? Where do 
0
7
 and 
7
7
 lie?
Fig 7.7
×
1
3
0 1
Fig 7.6
1. Show 
3
5
 on a number line.
2. Show 
1
10
0
10
5
10
, ,
 and 
10
10
 on
a number line.
3. Can you show any other fraction
between 0 and 1?
Write five more fractions that
you can show and depict them
on the number line.
4. How many fractions lie between
0 and 1? Think, discuss and
write your answer?
×
1
2
0 1
Fig 7.5
2020-21