NCERT Textbook - Fractions and Decimals Class 7 Notes | EduRev

Mathematics (Maths) Class 7

Created by: Praveen Kumar

Class 7 : NCERT Textbook - Fractions and Decimals Class 7 Notes | EduRev

 Page 1


FRACTIONS AND DECIMALS 29 29 29 29 29
2.1  INTRODUCTION
Y ou have learnt fractions and decimals in earlier classes. The study of fractions included
proper, improper and mixed fractions as well as their addition and subtraction. We also
studied comparison of fractions, equivalent fractions, representation of fractions on the
number line and ordering of fractions.
Our study of decimals included, their comparison, their representation on the number
line and their addition and subtraction.
W e shall now learn multiplication and division of fractions as well as of decimals.
2.2  HOW WELL HAVE YOU LEARNT ABOUT FRACTIONS?
A proper fraction is a fraction that represents a part of a whole. Is 
7
4
a proper fraction?
Which is bigger, the numerator or the denominator?
An improper fraction is a combination of whole and a proper fraction. Is 
7
4
 an
improper fraction? Which is bigger here, the numerator or the denominator?
The improper fraction 
7
4
can be written as 
3
1
4
.  This is a mixed fraction.
Can you write five examples each of proper, improper and mixed fractions?
EXAMPLE 1 Write five equivalent fractions of 
3
5
 .
SOLUTION One of the equivalent fractions of 
3
5
 is
33 2 6
55 2 10
×
==
×
.  Find the other four.
Chapter  2
Fractions and
Decimals
Page 2


FRACTIONS AND DECIMALS 29 29 29 29 29
2.1  INTRODUCTION
Y ou have learnt fractions and decimals in earlier classes. The study of fractions included
proper, improper and mixed fractions as well as their addition and subtraction. We also
studied comparison of fractions, equivalent fractions, representation of fractions on the
number line and ordering of fractions.
Our study of decimals included, their comparison, their representation on the number
line and their addition and subtraction.
W e shall now learn multiplication and division of fractions as well as of decimals.
2.2  HOW WELL HAVE YOU LEARNT ABOUT FRACTIONS?
A proper fraction is a fraction that represents a part of a whole. Is 
7
4
a proper fraction?
Which is bigger, the numerator or the denominator?
An improper fraction is a combination of whole and a proper fraction. Is 
7
4
 an
improper fraction? Which is bigger here, the numerator or the denominator?
The improper fraction 
7
4
can be written as 
3
1
4
.  This is a mixed fraction.
Can you write five examples each of proper, improper and mixed fractions?
EXAMPLE 1 Write five equivalent fractions of 
3
5
 .
SOLUTION One of the equivalent fractions of 
3
5
 is
33 2 6
55 2 10
×
==
×
.  Find the other four.
Chapter  2
Fractions and
Decimals
MATHEMATICS 30 30 30 30 30
EXAMPLE 2 Ramesh solved 
2
7
part of an exercise while Seema solved 
4
5
 of it. Who
solved lesser part?
SOLUTION In order to find who solved lesser part of the exercise, let us compare
2
7
 and 
4
5
.
Converting them to like fractions we have, 
210
735
=
 , 
428
535
= .
Since10 < 28 , so 
10 28
35 35
<
.
Thus,
24
<
75
 .
Ramesh solved lesser part than Seema.
EXAMPLE 3 Sameera purchased 
1
3
2
 kg apples and 
3
4
4
 kg oranges. What is the
total weight of fruits purchased by her?
SOLUTION The total weight of the fruits 
13
34 kg
24
??
=+
??
??
= 
719 14 19
kg kg
24 4 4
?? ? ?
+= +
?? ? ?
?? ? ?
= 
33 1
kg 8 kg
44
=
EXAMPLE 4 Suman studies for 
2
5
3
 hours daily. She devotes 
4
2
5
 hours of her time
for Science and Mathematics. How much time does she devote for
other subjects?
SOLUTION Total time of Suman’s study  =  
2
5
3
 h =  
17
3
 h
Time devoted by her for Science and Mathematics = 
4
2
5
 =  
14
5
  h
Page 3


FRACTIONS AND DECIMALS 29 29 29 29 29
2.1  INTRODUCTION
Y ou have learnt fractions and decimals in earlier classes. The study of fractions included
proper, improper and mixed fractions as well as their addition and subtraction. We also
studied comparison of fractions, equivalent fractions, representation of fractions on the
number line and ordering of fractions.
Our study of decimals included, their comparison, their representation on the number
line and their addition and subtraction.
W e shall now learn multiplication and division of fractions as well as of decimals.
2.2  HOW WELL HAVE YOU LEARNT ABOUT FRACTIONS?
A proper fraction is a fraction that represents a part of a whole. Is 
7
4
a proper fraction?
Which is bigger, the numerator or the denominator?
An improper fraction is a combination of whole and a proper fraction. Is 
7
4
 an
improper fraction? Which is bigger here, the numerator or the denominator?
The improper fraction 
7
4
can be written as 
3
1
4
.  This is a mixed fraction.
Can you write five examples each of proper, improper and mixed fractions?
EXAMPLE 1 Write five equivalent fractions of 
3
5
 .
SOLUTION One of the equivalent fractions of 
3
5
 is
33 2 6
55 2 10
×
==
×
.  Find the other four.
Chapter  2
Fractions and
Decimals
MATHEMATICS 30 30 30 30 30
EXAMPLE 2 Ramesh solved 
2
7
part of an exercise while Seema solved 
4
5
 of it. Who
solved lesser part?
SOLUTION In order to find who solved lesser part of the exercise, let us compare
2
7
 and 
4
5
.
Converting them to like fractions we have, 
210
735
=
 , 
428
535
= .
Since10 < 28 , so 
10 28
35 35
<
.
Thus,
24
<
75
 .
Ramesh solved lesser part than Seema.
EXAMPLE 3 Sameera purchased 
1
3
2
 kg apples and 
3
4
4
 kg oranges. What is the
total weight of fruits purchased by her?
SOLUTION The total weight of the fruits 
13
34 kg
24
??
=+
??
??
= 
719 14 19
kg kg
24 4 4
?? ? ?
+= +
?? ? ?
?? ? ?
= 
33 1
kg 8 kg
44
=
EXAMPLE 4 Suman studies for 
2
5
3
 hours daily. She devotes 
4
2
5
 hours of her time
for Science and Mathematics. How much time does she devote for
other subjects?
SOLUTION Total time of Suman’s study  =  
2
5
3
 h =  
17
3
 h
Time devoted by her for Science and Mathematics = 
4
2
5
 =  
14
5
  h
FRACTIONS AND DECIMALS 31 31 31 31 31
Thus, time devoted by her for other subjects = 
17 14
35
??
-
??
??
 h
 = 
17 × 5 14 × 3
–h
15 15
??
??
??
 = 
85 – 42
h
15
??
??
??
 = 
43
15
 h = 
13
2
15
 h
EXERCISE 2.1
1. Solve:
(i)
3
2
5
-
(ii)
7
4
8
+
(iii)
32
57
+
(iv)
94
11 15
-
(v)
72 3
10 5 2
++
(vi)
21
23
32
+
(vii)
15
83
28
-
2. Arrange the following in descending order:
(i)
2
9
2
3
8
21
,,
(ii)
1
5
3
7
7
10
,,
.
3. In a “magic square”, the sum of the numbers in each row, in each column and along
the diagonals is the same. Is this a magic square?
4
11
3
11
8
11
9
11
5
11
1
11
2
11
7
11
6
11
4. A rectangular sheet of paper is 
1
12
2
cm long and 
2
10
3
 cm wide.
Find its perimeter.
5. Find the perimeters of (i) ? ABE (ii) the rectangle  BCDE in this
figure. Whose perimeter is greater?
6. Salil wants to put a picture in a frame. The picture is  
7
3
5
 cm wide.
T o fit in the frame the picture cannot be more than 
7
3
10
 cm wide. How much should
the picture be trimmed?
(Along the first row 
49 2 15
11 11 11 11
++ = ).
5
cm
2 3
2cm
4
3
3cm
5
7
cm
6
Page 4


FRACTIONS AND DECIMALS 29 29 29 29 29
2.1  INTRODUCTION
Y ou have learnt fractions and decimals in earlier classes. The study of fractions included
proper, improper and mixed fractions as well as their addition and subtraction. We also
studied comparison of fractions, equivalent fractions, representation of fractions on the
number line and ordering of fractions.
Our study of decimals included, their comparison, their representation on the number
line and their addition and subtraction.
W e shall now learn multiplication and division of fractions as well as of decimals.
2.2  HOW WELL HAVE YOU LEARNT ABOUT FRACTIONS?
A proper fraction is a fraction that represents a part of a whole. Is 
7
4
a proper fraction?
Which is bigger, the numerator or the denominator?
An improper fraction is a combination of whole and a proper fraction. Is 
7
4
 an
improper fraction? Which is bigger here, the numerator or the denominator?
The improper fraction 
7
4
can be written as 
3
1
4
.  This is a mixed fraction.
Can you write five examples each of proper, improper and mixed fractions?
EXAMPLE 1 Write five equivalent fractions of 
3
5
 .
SOLUTION One of the equivalent fractions of 
3
5
 is
33 2 6
55 2 10
×
==
×
.  Find the other four.
Chapter  2
Fractions and
Decimals
MATHEMATICS 30 30 30 30 30
EXAMPLE 2 Ramesh solved 
2
7
part of an exercise while Seema solved 
4
5
 of it. Who
solved lesser part?
SOLUTION In order to find who solved lesser part of the exercise, let us compare
2
7
 and 
4
5
.
Converting them to like fractions we have, 
210
735
=
 , 
428
535
= .
Since10 < 28 , so 
10 28
35 35
<
.
Thus,
24
<
75
 .
Ramesh solved lesser part than Seema.
EXAMPLE 3 Sameera purchased 
1
3
2
 kg apples and 
3
4
4
 kg oranges. What is the
total weight of fruits purchased by her?
SOLUTION The total weight of the fruits 
13
34 kg
24
??
=+
??
??
= 
719 14 19
kg kg
24 4 4
?? ? ?
+= +
?? ? ?
?? ? ?
= 
33 1
kg 8 kg
44
=
EXAMPLE 4 Suman studies for 
2
5
3
 hours daily. She devotes 
4
2
5
 hours of her time
for Science and Mathematics. How much time does she devote for
other subjects?
SOLUTION Total time of Suman’s study  =  
2
5
3
 h =  
17
3
 h
Time devoted by her for Science and Mathematics = 
4
2
5
 =  
14
5
  h
FRACTIONS AND DECIMALS 31 31 31 31 31
Thus, time devoted by her for other subjects = 
17 14
35
??
-
??
??
 h
 = 
17 × 5 14 × 3
–h
15 15
??
??
??
 = 
85 – 42
h
15
??
??
??
 = 
43
15
 h = 
13
2
15
 h
EXERCISE 2.1
1. Solve:
(i)
3
2
5
-
(ii)
7
4
8
+
(iii)
32
57
+
(iv)
94
11 15
-
(v)
72 3
10 5 2
++
(vi)
21
23
32
+
(vii)
15
83
28
-
2. Arrange the following in descending order:
(i)
2
9
2
3
8
21
,,
(ii)
1
5
3
7
7
10
,,
.
3. In a “magic square”, the sum of the numbers in each row, in each column and along
the diagonals is the same. Is this a magic square?
4
11
3
11
8
11
9
11
5
11
1
11
2
11
7
11
6
11
4. A rectangular sheet of paper is 
1
12
2
cm long and 
2
10
3
 cm wide.
Find its perimeter.
5. Find the perimeters of (i) ? ABE (ii) the rectangle  BCDE in this
figure. Whose perimeter is greater?
6. Salil wants to put a picture in a frame. The picture is  
7
3
5
 cm wide.
T o fit in the frame the picture cannot be more than 
7
3
10
 cm wide. How much should
the picture be trimmed?
(Along the first row 
49 2 15
11 11 11 11
++ = ).
5
cm
2 3
2cm
4
3
3cm
5
7
cm
6
MATHEMATICS 32 32 32 32 32
7. Ritu ate 
3
5
 part of an apple and the remaining apple was eaten by her brother Somu.
How much part of the apple did Somu eat? Who had the larger share? By how
much?
8. Michael finished colouring a picture in  
7
12
  hour . V aibhav finished colouring the same
picture in 
3
4
 hour. Who worked longer? By what fraction was it longer?
2.3  MULTIPLICATION OF FRACTIONS
Y ou know how to find the area of a rectangle. It is equal to length × breadth. If the length
and breadth of a rectangle are 7 cm and 4 cm respectively, then what will be its area? Its
area would be 7 × 4 = 28 cm
2
.
What will be the area of the rectangle if its length and breadth are 
7
1
2
 cm and
3
1
2
 cm respectively? Y ou will say it will be 
7
1
2
 × 
3
1
2
 = 
15
2
 × 
7
2
 cm
2
. The numbers 
15
2
and 
7
2
 are fractions. T o calculate the area of the given rectangle, we need to know how to
multiply fractions. W e shall learn that now .
2.3.1  Multiplication of a Fraction by a Whole Number
Observe the pictures at the left (Fig 2.1). Each shaded part is 
1
4
  part of
a circle. How much will the two shaded parts represent together? They
will represent 
11
44
+
 = 
1
2×
4
.
Combining the two shaded parts, we get  Fig 2.2 . What part of a circle does the
shaded part in Fig 2.2 represent? It represents 
2
4
 part of a circle .
Fig 2.1
Fig 2.2
or
Page 5


FRACTIONS AND DECIMALS 29 29 29 29 29
2.1  INTRODUCTION
Y ou have learnt fractions and decimals in earlier classes. The study of fractions included
proper, improper and mixed fractions as well as their addition and subtraction. We also
studied comparison of fractions, equivalent fractions, representation of fractions on the
number line and ordering of fractions.
Our study of decimals included, their comparison, their representation on the number
line and their addition and subtraction.
W e shall now learn multiplication and division of fractions as well as of decimals.
2.2  HOW WELL HAVE YOU LEARNT ABOUT FRACTIONS?
A proper fraction is a fraction that represents a part of a whole. Is 
7
4
a proper fraction?
Which is bigger, the numerator or the denominator?
An improper fraction is a combination of whole and a proper fraction. Is 
7
4
 an
improper fraction? Which is bigger here, the numerator or the denominator?
The improper fraction 
7
4
can be written as 
3
1
4
.  This is a mixed fraction.
Can you write five examples each of proper, improper and mixed fractions?
EXAMPLE 1 Write five equivalent fractions of 
3
5
 .
SOLUTION One of the equivalent fractions of 
3
5
 is
33 2 6
55 2 10
×
==
×
.  Find the other four.
Chapter  2
Fractions and
Decimals
MATHEMATICS 30 30 30 30 30
EXAMPLE 2 Ramesh solved 
2
7
part of an exercise while Seema solved 
4
5
 of it. Who
solved lesser part?
SOLUTION In order to find who solved lesser part of the exercise, let us compare
2
7
 and 
4
5
.
Converting them to like fractions we have, 
210
735
=
 , 
428
535
= .
Since10 < 28 , so 
10 28
35 35
<
.
Thus,
24
<
75
 .
Ramesh solved lesser part than Seema.
EXAMPLE 3 Sameera purchased 
1
3
2
 kg apples and 
3
4
4
 kg oranges. What is the
total weight of fruits purchased by her?
SOLUTION The total weight of the fruits 
13
34 kg
24
??
=+
??
??
= 
719 14 19
kg kg
24 4 4
?? ? ?
+= +
?? ? ?
?? ? ?
= 
33 1
kg 8 kg
44
=
EXAMPLE 4 Suman studies for 
2
5
3
 hours daily. She devotes 
4
2
5
 hours of her time
for Science and Mathematics. How much time does she devote for
other subjects?
SOLUTION Total time of Suman’s study  =  
2
5
3
 h =  
17
3
 h
Time devoted by her for Science and Mathematics = 
4
2
5
 =  
14
5
  h
FRACTIONS AND DECIMALS 31 31 31 31 31
Thus, time devoted by her for other subjects = 
17 14
35
??
-
??
??
 h
 = 
17 × 5 14 × 3
–h
15 15
??
??
??
 = 
85 – 42
h
15
??
??
??
 = 
43
15
 h = 
13
2
15
 h
EXERCISE 2.1
1. Solve:
(i)
3
2
5
-
(ii)
7
4
8
+
(iii)
32
57
+
(iv)
94
11 15
-
(v)
72 3
10 5 2
++
(vi)
21
23
32
+
(vii)
15
83
28
-
2. Arrange the following in descending order:
(i)
2
9
2
3
8
21
,,
(ii)
1
5
3
7
7
10
,,
.
3. In a “magic square”, the sum of the numbers in each row, in each column and along
the diagonals is the same. Is this a magic square?
4
11
3
11
8
11
9
11
5
11
1
11
2
11
7
11
6
11
4. A rectangular sheet of paper is 
1
12
2
cm long and 
2
10
3
 cm wide.
Find its perimeter.
5. Find the perimeters of (i) ? ABE (ii) the rectangle  BCDE in this
figure. Whose perimeter is greater?
6. Salil wants to put a picture in a frame. The picture is  
7
3
5
 cm wide.
T o fit in the frame the picture cannot be more than 
7
3
10
 cm wide. How much should
the picture be trimmed?
(Along the first row 
49 2 15
11 11 11 11
++ = ).
5
cm
2 3
2cm
4
3
3cm
5
7
cm
6
MATHEMATICS 32 32 32 32 32
7. Ritu ate 
3
5
 part of an apple and the remaining apple was eaten by her brother Somu.
How much part of the apple did Somu eat? Who had the larger share? By how
much?
8. Michael finished colouring a picture in  
7
12
  hour . V aibhav finished colouring the same
picture in 
3
4
 hour. Who worked longer? By what fraction was it longer?
2.3  MULTIPLICATION OF FRACTIONS
Y ou know how to find the area of a rectangle. It is equal to length × breadth. If the length
and breadth of a rectangle are 7 cm and 4 cm respectively, then what will be its area? Its
area would be 7 × 4 = 28 cm
2
.
What will be the area of the rectangle if its length and breadth are 
7
1
2
 cm and
3
1
2
 cm respectively? Y ou will say it will be 
7
1
2
 × 
3
1
2
 = 
15
2
 × 
7
2
 cm
2
. The numbers 
15
2
and 
7
2
 are fractions. T o calculate the area of the given rectangle, we need to know how to
multiply fractions. W e shall learn that now .
2.3.1  Multiplication of a Fraction by a Whole Number
Observe the pictures at the left (Fig 2.1). Each shaded part is 
1
4
  part of
a circle. How much will the two shaded parts represent together? They
will represent 
11
44
+
 = 
1
2×
4
.
Combining the two shaded parts, we get  Fig 2.2 . What part of a circle does the
shaded part in Fig 2.2 represent? It represents 
2
4
 part of a circle .
Fig 2.1
Fig 2.2
or
FRACTIONS AND DECIMALS 33 33 33 33 33
The shaded portions in Fig 2.1 taken together are the same as the shaded portion in
Fig 2.2, i.e., we get Fig 2.3.
Fig 2.3
or
1
2×
4
 =
2
4
 .
Can you now tell what this picture will represent? (Fig 2.4)
             Fig 2.4
And this? (Fig 2.5)
Fig 2.5
Let us now find 
1
3×
2
.
W e have
1
3×
2
 =
11 1 3
222 2
++ =
We also have                       
1 1 1 1+1+1 3×1 3
++ = = =
22 2 2 2 2
So
1
3×
2
 =
3×1
2
 = 
3
2
Similarly
2
×5
3
 =
2×5
3
 = ?
Can you tell
2
3×
7
 =?
3
4× ?
5
=
The fractions that we considered till now, i.e., 
12 2
,,
23 7
 and 
3
5
 were proper fractions.
=
=
=
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