RS Aggarwal Solutions: Rational Numbers | Mathematics (Maths) Class 7 PDF Download

 Page 1


Question:1
What are rational numbers? Give examples of five positive and five negative rational numbers. Is there any rational number which is neither positive nor negative? Name it.
Solution:
The numbers that are in the form of  
p
q
, where p and q are integers and q ?0, are called rational numbers.
For example: 
Five positive rational numbers:
5
7
,
-3
-4
,
7
8
,
-14
-15
,
5
9
Five negative rational numbers:
 
-3
7
,
-3
8
,
8
-9
,
-19
25
,
8
-25
Yes, there is a rational number that is neither positive nor negative, i.e. zero 0.   
Question:2
Which of the following are rational numbers?
i 
5
-8
ii 
-6
11
iii 
7
15
iv 
-8
-12
v 6
vi -3
vii 0
viii 
0
1
ix 
1
0
x 
0
0
Solution:
i) 
5
-8
 is a rational number because it is in the form of   
p
q
, where p and q are integers and q?0. 
ii)
-6
11
 is a rational number because it is in the form of   
p
q
, where p and q are integers and q?0. 
iii)
-13
15
is a rational number because it is in the form of   
p
q
, w here p and q are integers and q?0. 
iv)
-8
-12
is a rational number because it is in the form of   
p
q
, w here p and q are integers and q ? 0. 
v) 6  is a rational number because it is in the form of  
p
q
, w here p and q are integers and q ? 0. 
vi) -3 is a rational number because it is in the form of  
p
q
, w here p and q are integers and q ? 0. 
vii) 0 = 
0
1
is a rational number because it is in the form of 
p
q
, w here p and q are integers and q ? 0. 
viii)
0 
1 
 is a rational number because it is in the form of   
p
q
, w here p and q are integers and q ? 0. 
ix)
1
0
is not a rational number because, here, q = 0.
x)
0 
0 
 is not a rational number because, here, q = 0.
 
 
 
   
Question:3
Write down the numerator and the denominator of each of the following rational numbers:
i 
8
19
ii 
5
-8
iii 
-13
15
iv 
-8
-11
v 9
Solution:
i 
8
19
Numerator = 8
Denominator =19
ii
5
-8
Numerator  = 5
Denominator = -8
iii 
-13
5
Numerator = -13
Denominator =15
Page 2


Question:1
What are rational numbers? Give examples of five positive and five negative rational numbers. Is there any rational number which is neither positive nor negative? Name it.
Solution:
The numbers that are in the form of  
p
q
, where p and q are integers and q ?0, are called rational numbers.
For example: 
Five positive rational numbers:
5
7
,
-3
-4
,
7
8
,
-14
-15
,
5
9
Five negative rational numbers:
 
-3
7
,
-3
8
,
8
-9
,
-19
25
,
8
-25
Yes, there is a rational number that is neither positive nor negative, i.e. zero 0.   
Question:2
Which of the following are rational numbers?
i 
5
-8
ii 
-6
11
iii 
7
15
iv 
-8
-12
v 6
vi -3
vii 0
viii 
0
1
ix 
1
0
x 
0
0
Solution:
i) 
5
-8
 is a rational number because it is in the form of   
p
q
, where p and q are integers and q?0. 
ii)
-6
11
 is a rational number because it is in the form of   
p
q
, where p and q are integers and q?0. 
iii)
-13
15
is a rational number because it is in the form of   
p
q
, w here p and q are integers and q?0. 
iv)
-8
-12
is a rational number because it is in the form of   
p
q
, w here p and q are integers and q ? 0. 
v) 6  is a rational number because it is in the form of  
p
q
, w here p and q are integers and q ? 0. 
vi) -3 is a rational number because it is in the form of  
p
q
, w here p and q are integers and q ? 0. 
vii) 0 = 
0
1
is a rational number because it is in the form of 
p
q
, w here p and q are integers and q ? 0. 
viii)
0 
1 
 is a rational number because it is in the form of   
p
q
, w here p and q are integers and q ? 0. 
ix)
1
0
is not a rational number because, here, q = 0.
x)
0 
0 
 is not a rational number because, here, q = 0.
 
 
 
   
Question:3
Write down the numerator and the denominator of each of the following rational numbers:
i 
8
19
ii 
5
-8
iii 
-13
15
iv 
-8
-11
v 9
Solution:
i 
8
19
Numerator = 8
Denominator =19
ii
5
-8
Numerator  = 5
Denominator = -8
iii 
-13
5
Numerator = -13
Denominator =15
iv
-8
-11
Numerator = -8
Denominator = -11
v 9
i.e 
9
1
Numerator = 9
Denominator = 1
Question:4
Write each of the following integers as a rational number. Write the numerator and the denominator in each case.
i 5
ii -3
iii 1
iv 0
v -23
Solution:
i 5
The rational number will be 
5
1
.
Numerator = 5
Denominator = 1
 
ii -3
The rational number will be 
-3
1
.
Numerator   = -3
Denominator = 1
ii i 1
The rational number will be 
1
1
.
Numerator = 1
Denominator = 1
iv 0
The rational number will be 
0
1
.
Numerator =0
Denominator = 1
v -23
The rational number will be 
-23
1
.
Numerator = -23
Denominator = 1
Question:5
Which of the following are positive rational numbers?
i 
3
-5
ii 
-11
15
iii 
-5
-8
iv 
37
53
v 
0
3
Solution:
Positive rational numbers:
iii 
-5
-8
iv 
37
53
vi 8 because 8 can be written as 
8
1
, where 1 ? 0.
0 is neither positive nor negative.
Question:6
Which of the following are negative rational numbers?
i 
-15
-14
ii 0
iii 
-5
7
iv 
4
-9
v -6
vi 
1
-2
Solution:
Negative rational numbers:
Page 3


Question:1
What are rational numbers? Give examples of five positive and five negative rational numbers. Is there any rational number which is neither positive nor negative? Name it.
Solution:
The numbers that are in the form of  
p
q
, where p and q are integers and q ?0, are called rational numbers.
For example: 
Five positive rational numbers:
5
7
,
-3
-4
,
7
8
,
-14
-15
,
5
9
Five negative rational numbers:
 
-3
7
,
-3
8
,
8
-9
,
-19
25
,
8
-25
Yes, there is a rational number that is neither positive nor negative, i.e. zero 0.   
Question:2
Which of the following are rational numbers?
i 
5
-8
ii 
-6
11
iii 
7
15
iv 
-8
-12
v 6
vi -3
vii 0
viii 
0
1
ix 
1
0
x 
0
0
Solution:
i) 
5
-8
 is a rational number because it is in the form of   
p
q
, where p and q are integers and q?0. 
ii)
-6
11
 is a rational number because it is in the form of   
p
q
, where p and q are integers and q?0. 
iii)
-13
15
is a rational number because it is in the form of   
p
q
, w here p and q are integers and q?0. 
iv)
-8
-12
is a rational number because it is in the form of   
p
q
, w here p and q are integers and q ? 0. 
v) 6  is a rational number because it is in the form of  
p
q
, w here p and q are integers and q ? 0. 
vi) -3 is a rational number because it is in the form of  
p
q
, w here p and q are integers and q ? 0. 
vii) 0 = 
0
1
is a rational number because it is in the form of 
p
q
, w here p and q are integers and q ? 0. 
viii)
0 
1 
 is a rational number because it is in the form of   
p
q
, w here p and q are integers and q ? 0. 
ix)
1
0
is not a rational number because, here, q = 0.
x)
0 
0 
 is not a rational number because, here, q = 0.
 
 
 
   
Question:3
Write down the numerator and the denominator of each of the following rational numbers:
i 
8
19
ii 
5
-8
iii 
-13
15
iv 
-8
-11
v 9
Solution:
i 
8
19
Numerator = 8
Denominator =19
ii
5
-8
Numerator  = 5
Denominator = -8
iii 
-13
5
Numerator = -13
Denominator =15
iv
-8
-11
Numerator = -8
Denominator = -11
v 9
i.e 
9
1
Numerator = 9
Denominator = 1
Question:4
Write each of the following integers as a rational number. Write the numerator and the denominator in each case.
i 5
ii -3
iii 1
iv 0
v -23
Solution:
i 5
The rational number will be 
5
1
.
Numerator = 5
Denominator = 1
 
ii -3
The rational number will be 
-3
1
.
Numerator   = -3
Denominator = 1
ii i 1
The rational number will be 
1
1
.
Numerator = 1
Denominator = 1
iv 0
The rational number will be 
0
1
.
Numerator =0
Denominator = 1
v -23
The rational number will be 
-23
1
.
Numerator = -23
Denominator = 1
Question:5
Which of the following are positive rational numbers?
i 
3
-5
ii 
-11
15
iii 
-5
-8
iv 
37
53
v 
0
3
Solution:
Positive rational numbers:
iii 
-5
-8
iv 
37
53
vi 8 because 8 can be written as 
8
1
, where 1 ? 0.
0 is neither positive nor negative.
Question:6
Which of the following are negative rational numbers?
i 
-15
-14
ii 0
iii 
-5
7
iv 
4
-9
v -6
vi 
1
-2
Solution:
Negative rational numbers:
iii 
-5
7
iv 
4
-9
v  -6
vi 
1
-2
Question:7
Find four rational numbers equivalent to each of the following.
i 
6
11
ii 
-3
8
iii 
7
-15
iv 8
v 1
vi -1
Solution:
i Following are the four rational numbers that are equivalent to 
6
11
.
6×2
11×2
,
6×3
11×3
,
6×4
11×4
 and 
6×5
11×5
i.e. 
12
22
,
18
33
,
24
44
 and 
30
55
ii Following are the four rational numbers that are equivalent to 
-3
8
.
-3×2
8×2
,
-3×3
8×3
, 
-3×4
8×4
 and 
-3×5
8×5
 
  i.e. 
-6
16
, 
-9
24
, 
-12
32
 and 
-15
40
iii Following are the four rational numbers that are equivalent to 
7
-15
.
7×2
-15×2
, 
7×3
-15×3
, 
7×4
-15×4
 and 
7×5
-15×5
i.e. 
14
-30
, 
21
-45
, 
28
-60
 and 
35
-75
iv Following are the four rational numbers that are equivalent to 8, i.e. 
8
1
.
8×2
1×2
, 
8×3
1×3
, 
8×4
1×4
 and 
8×5
1×5
i. e. 
16
2
, 
24
3
, 
32
4
 and  
40
5
v Following are the four rational numbers that are equivalent to ??-1, i.e. 
1
1
.
1×2
1×2
, 
1×3
1×3
, 
1×4
1×4
 and  
1×5
1×5
i.e. 
2
2
,
3
3
, 
4
4
 and 
5
5
vi Following are the four rational numbers that are equivalent to ??-1, i.e. 
-1
1
.
-1×2
1×2
, 
-1×3
1×3
, 
-1×4
1×4
 and 
-1×5
1×5
i.e. 
-2
2
,
-3
3
, 
-4
4
 and 
-5
5
 
Question:8
Write each of the following as a rational number with positive denominator.
i 
12
-17
ii 
1
-2
iii 
-8
-19
iv 
11
-6
Solution:
i 
12×(-1)
(-17)×(-1)
=
-12
17
ii 
1×(-1)
(-2)×(-1)
=
-1
2
iii 
-8
-19
=
-8×(-1)
(-19)×(-1)
=
8
19
iv 
11×(-1)
-6×(-1)
=
-11
6
Page 4


Question:1
What are rational numbers? Give examples of five positive and five negative rational numbers. Is there any rational number which is neither positive nor negative? Name it.
Solution:
The numbers that are in the form of  
p
q
, where p and q are integers and q ?0, are called rational numbers.
For example: 
Five positive rational numbers:
5
7
,
-3
-4
,
7
8
,
-14
-15
,
5
9
Five negative rational numbers:
 
-3
7
,
-3
8
,
8
-9
,
-19
25
,
8
-25
Yes, there is a rational number that is neither positive nor negative, i.e. zero 0.   
Question:2
Which of the following are rational numbers?
i 
5
-8
ii 
-6
11
iii 
7
15
iv 
-8
-12
v 6
vi -3
vii 0
viii 
0
1
ix 
1
0
x 
0
0
Solution:
i) 
5
-8
 is a rational number because it is in the form of   
p
q
, where p and q are integers and q?0. 
ii)
-6
11
 is a rational number because it is in the form of   
p
q
, where p and q are integers and q?0. 
iii)
-13
15
is a rational number because it is in the form of   
p
q
, w here p and q are integers and q?0. 
iv)
-8
-12
is a rational number because it is in the form of   
p
q
, w here p and q are integers and q ? 0. 
v) 6  is a rational number because it is in the form of  
p
q
, w here p and q are integers and q ? 0. 
vi) -3 is a rational number because it is in the form of  
p
q
, w here p and q are integers and q ? 0. 
vii) 0 = 
0
1
is a rational number because it is in the form of 
p
q
, w here p and q are integers and q ? 0. 
viii)
0 
1 
 is a rational number because it is in the form of   
p
q
, w here p and q are integers and q ? 0. 
ix)
1
0
is not a rational number because, here, q = 0.
x)
0 
0 
 is not a rational number because, here, q = 0.
 
 
 
   
Question:3
Write down the numerator and the denominator of each of the following rational numbers:
i 
8
19
ii 
5
-8
iii 
-13
15
iv 
-8
-11
v 9
Solution:
i 
8
19
Numerator = 8
Denominator =19
ii
5
-8
Numerator  = 5
Denominator = -8
iii 
-13
5
Numerator = -13
Denominator =15
iv
-8
-11
Numerator = -8
Denominator = -11
v 9
i.e 
9
1
Numerator = 9
Denominator = 1
Question:4
Write each of the following integers as a rational number. Write the numerator and the denominator in each case.
i 5
ii -3
iii 1
iv 0
v -23
Solution:
i 5
The rational number will be 
5
1
.
Numerator = 5
Denominator = 1
 
ii -3
The rational number will be 
-3
1
.
Numerator   = -3
Denominator = 1
ii i 1
The rational number will be 
1
1
.
Numerator = 1
Denominator = 1
iv 0
The rational number will be 
0
1
.
Numerator =0
Denominator = 1
v -23
The rational number will be 
-23
1
.
Numerator = -23
Denominator = 1
Question:5
Which of the following are positive rational numbers?
i 
3
-5
ii 
-11
15
iii 
-5
-8
iv 
37
53
v 
0
3
Solution:
Positive rational numbers:
iii 
-5
-8
iv 
37
53
vi 8 because 8 can be written as 
8
1
, where 1 ? 0.
0 is neither positive nor negative.
Question:6
Which of the following are negative rational numbers?
i 
-15
-14
ii 0
iii 
-5
7
iv 
4
-9
v -6
vi 
1
-2
Solution:
Negative rational numbers:
iii 
-5
7
iv 
4
-9
v  -6
vi 
1
-2
Question:7
Find four rational numbers equivalent to each of the following.
i 
6
11
ii 
-3
8
iii 
7
-15
iv 8
v 1
vi -1
Solution:
i Following are the four rational numbers that are equivalent to 
6
11
.
6×2
11×2
,
6×3
11×3
,
6×4
11×4
 and 
6×5
11×5
i.e. 
12
22
,
18
33
,
24
44
 and 
30
55
ii Following are the four rational numbers that are equivalent to 
-3
8
.
-3×2
8×2
,
-3×3
8×3
, 
-3×4
8×4
 and 
-3×5
8×5
 
  i.e. 
-6
16
, 
-9
24
, 
-12
32
 and 
-15
40
iii Following are the four rational numbers that are equivalent to 
7
-15
.
7×2
-15×2
, 
7×3
-15×3
, 
7×4
-15×4
 and 
7×5
-15×5
i.e. 
14
-30
, 
21
-45
, 
28
-60
 and 
35
-75
iv Following are the four rational numbers that are equivalent to 8, i.e. 
8
1
.
8×2
1×2
, 
8×3
1×3
, 
8×4
1×4
 and 
8×5
1×5
i. e. 
16
2
, 
24
3
, 
32
4
 and  
40
5
v Following are the four rational numbers that are equivalent to ??-1, i.e. 
1
1
.
1×2
1×2
, 
1×3
1×3
, 
1×4
1×4
 and  
1×5
1×5
i.e. 
2
2
,
3
3
, 
4
4
 and 
5
5
vi Following are the four rational numbers that are equivalent to ??-1, i.e. 
-1
1
.
-1×2
1×2
, 
-1×3
1×3
, 
-1×4
1×4
 and 
-1×5
1×5
i.e. 
-2
2
,
-3
3
, 
-4
4
 and 
-5
5
 
Question:8
Write each of the following as a rational number with positive denominator.
i 
12
-17
ii 
1
-2
iii 
-8
-19
iv 
11
-6
Solution:
i 
12×(-1)
(-17)×(-1)
=
-12
17
ii 
1×(-1)
(-2)×(-1)
=
-1
2
iii 
-8
-19
=
-8×(-1)
(-19)×(-1)
=
8
19
iv 
11×(-1)
-6×(-1)
=
-11
6
Question:9
Express 
5
8
 as a rational number with numerator
i 15
ii -10
Solution:
i Numerator of  
5
8
  is 5.
5 should be multiplied by 3 to get 15.
Multiplying both the numerator and the denominator by 3:
5×3
8×3
=
15
24
 
5
8
=
15
24
ii  Numerator of  
5
8
  is 5.
5 should be multiplied by -2 to get -10.
Multiplying both the numerator and the denominator by -2:
5×(-2)
8×(-2)
=
-10
-16
 
5
8
=
-10
-16
Question:10
Express 
4
7
 as a rational number with denominator
i 21
ii -35
Solution:
i Denominator of 
4
7
 is 7.
7 should be multiplied by 3 to get 21.
Multiplying both the numerator and the denominator by 3:
4×3
7×3
= 
12
21
4×3
7×3
= 
4
7
 
ii 
Denominator of 
4
7
 is 7. 
7 should be multiplied by -5 to get -35. 
Multiplying both the numerator and the denominator by -5:
4×(-5)
7×(-5)
=
-20
-35
 
4
7
=
-20
-35
Question:11
Express 
-12
13
 as a rational number with numerator
i -48
ii 60
Solution:
i Numerator of 
-12
13
 is -12.
-12 should be multiplied by 4 to get 48.
Multiplying both the numerator and the denominator by 4:
-12×4
13×4
=
-48
52
-12
13
=
-48
52
ii Numerator of 
-12
13
 is -12. ? -12 should be multiplied by -5 to get 60
 Multiplying its numerator and denominator by -5:
-12×(-5)
13×(-5)
=
60
-65
-12
13
=
60
-65
Question:12
Express 
-8
11
 as a rational number with denominator
i 22
ii -55
Solution:
i Denominator of
-8
11
  is 11.
Clearly, 11×2= ?22
Multiplying both the numerator and the denominator by 2:
Page 5


Question:1
What are rational numbers? Give examples of five positive and five negative rational numbers. Is there any rational number which is neither positive nor negative? Name it.
Solution:
The numbers that are in the form of  
p
q
, where p and q are integers and q ?0, are called rational numbers.
For example: 
Five positive rational numbers:
5
7
,
-3
-4
,
7
8
,
-14
-15
,
5
9
Five negative rational numbers:
 
-3
7
,
-3
8
,
8
-9
,
-19
25
,
8
-25
Yes, there is a rational number that is neither positive nor negative, i.e. zero 0.   
Question:2
Which of the following are rational numbers?
i 
5
-8
ii 
-6
11
iii 
7
15
iv 
-8
-12
v 6
vi -3
vii 0
viii 
0
1
ix 
1
0
x 
0
0
Solution:
i) 
5
-8
 is a rational number because it is in the form of   
p
q
, where p and q are integers and q?0. 
ii)
-6
11
 is a rational number because it is in the form of   
p
q
, where p and q are integers and q?0. 
iii)
-13
15
is a rational number because it is in the form of   
p
q
, w here p and q are integers and q?0. 
iv)
-8
-12
is a rational number because it is in the form of   
p
q
, w here p and q are integers and q ? 0. 
v) 6  is a rational number because it is in the form of  
p
q
, w here p and q are integers and q ? 0. 
vi) -3 is a rational number because it is in the form of  
p
q
, w here p and q are integers and q ? 0. 
vii) 0 = 
0
1
is a rational number because it is in the form of 
p
q
, w here p and q are integers and q ? 0. 
viii)
0 
1 
 is a rational number because it is in the form of   
p
q
, w here p and q are integers and q ? 0. 
ix)
1
0
is not a rational number because, here, q = 0.
x)
0 
0 
 is not a rational number because, here, q = 0.
 
 
 
   
Question:3
Write down the numerator and the denominator of each of the following rational numbers:
i 
8
19
ii 
5
-8
iii 
-13
15
iv 
-8
-11
v 9
Solution:
i 
8
19
Numerator = 8
Denominator =19
ii
5
-8
Numerator  = 5
Denominator = -8
iii 
-13
5
Numerator = -13
Denominator =15
iv
-8
-11
Numerator = -8
Denominator = -11
v 9
i.e 
9
1
Numerator = 9
Denominator = 1
Question:4
Write each of the following integers as a rational number. Write the numerator and the denominator in each case.
i 5
ii -3
iii 1
iv 0
v -23
Solution:
i 5
The rational number will be 
5
1
.
Numerator = 5
Denominator = 1
 
ii -3
The rational number will be 
-3
1
.
Numerator   = -3
Denominator = 1
ii i 1
The rational number will be 
1
1
.
Numerator = 1
Denominator = 1
iv 0
The rational number will be 
0
1
.
Numerator =0
Denominator = 1
v -23
The rational number will be 
-23
1
.
Numerator = -23
Denominator = 1
Question:5
Which of the following are positive rational numbers?
i 
3
-5
ii 
-11
15
iii 
-5
-8
iv 
37
53
v 
0
3
Solution:
Positive rational numbers:
iii 
-5
-8
iv 
37
53
vi 8 because 8 can be written as 
8
1
, where 1 ? 0.
0 is neither positive nor negative.
Question:6
Which of the following are negative rational numbers?
i 
-15
-14
ii 0
iii 
-5
7
iv 
4
-9
v -6
vi 
1
-2
Solution:
Negative rational numbers:
iii 
-5
7
iv 
4
-9
v  -6
vi 
1
-2
Question:7
Find four rational numbers equivalent to each of the following.
i 
6
11
ii 
-3
8
iii 
7
-15
iv 8
v 1
vi -1
Solution:
i Following are the four rational numbers that are equivalent to 
6
11
.
6×2
11×2
,
6×3
11×3
,
6×4
11×4
 and 
6×5
11×5
i.e. 
12
22
,
18
33
,
24
44
 and 
30
55
ii Following are the four rational numbers that are equivalent to 
-3
8
.
-3×2
8×2
,
-3×3
8×3
, 
-3×4
8×4
 and 
-3×5
8×5
 
  i.e. 
-6
16
, 
-9
24
, 
-12
32
 and 
-15
40
iii Following are the four rational numbers that are equivalent to 
7
-15
.
7×2
-15×2
, 
7×3
-15×3
, 
7×4
-15×4
 and 
7×5
-15×5
i.e. 
14
-30
, 
21
-45
, 
28
-60
 and 
35
-75
iv Following are the four rational numbers that are equivalent to 8, i.e. 
8
1
.
8×2
1×2
, 
8×3
1×3
, 
8×4
1×4
 and 
8×5
1×5
i. e. 
16
2
, 
24
3
, 
32
4
 and  
40
5
v Following are the four rational numbers that are equivalent to ??-1, i.e. 
1
1
.
1×2
1×2
, 
1×3
1×3
, 
1×4
1×4
 and  
1×5
1×5
i.e. 
2
2
,
3
3
, 
4
4
 and 
5
5
vi Following are the four rational numbers that are equivalent to ??-1, i.e. 
-1
1
.
-1×2
1×2
, 
-1×3
1×3
, 
-1×4
1×4
 and 
-1×5
1×5
i.e. 
-2
2
,
-3
3
, 
-4
4
 and 
-5
5
 
Question:8
Write each of the following as a rational number with positive denominator.
i 
12
-17
ii 
1
-2
iii 
-8
-19
iv 
11
-6
Solution:
i 
12×(-1)
(-17)×(-1)
=
-12
17
ii 
1×(-1)
(-2)×(-1)
=
-1
2
iii 
-8
-19
=
-8×(-1)
(-19)×(-1)
=
8
19
iv 
11×(-1)
-6×(-1)
=
-11
6
Question:9
Express 
5
8
 as a rational number with numerator
i 15
ii -10
Solution:
i Numerator of  
5
8
  is 5.
5 should be multiplied by 3 to get 15.
Multiplying both the numerator and the denominator by 3:
5×3
8×3
=
15
24
 
5
8
=
15
24
ii  Numerator of  
5
8
  is 5.
5 should be multiplied by -2 to get -10.
Multiplying both the numerator and the denominator by -2:
5×(-2)
8×(-2)
=
-10
-16
 
5
8
=
-10
-16
Question:10
Express 
4
7
 as a rational number with denominator
i 21
ii -35
Solution:
i Denominator of 
4
7
 is 7.
7 should be multiplied by 3 to get 21.
Multiplying both the numerator and the denominator by 3:
4×3
7×3
= 
12
21
4×3
7×3
= 
4
7
 
ii 
Denominator of 
4
7
 is 7. 
7 should be multiplied by -5 to get -35. 
Multiplying both the numerator and the denominator by -5:
4×(-5)
7×(-5)
=
-20
-35
 
4
7
=
-20
-35
Question:11
Express 
-12
13
 as a rational number with numerator
i -48
ii 60
Solution:
i Numerator of 
-12
13
 is -12.
-12 should be multiplied by 4 to get 48.
Multiplying both the numerator and the denominator by 4:
-12×4
13×4
=
-48
52
-12
13
=
-48
52
ii Numerator of 
-12
13
 is -12. ? -12 should be multiplied by -5 to get 60
 Multiplying its numerator and denominator by -5:
-12×(-5)
13×(-5)
=
60
-65
-12
13
=
60
-65
Question:12
Express 
-8
11
 as a rational number with denominator
i 22
ii -55
Solution:
i Denominator of
-8
11
  is 11.
Clearly, 11×2= ?22
Multiplying both the numerator and the denominator by 2:
-8×2
11×2
=
-16
22
-8
11
=
-16
22
ii Denominator of
-8
11
  is 11.
Clearly, 11×5=55
Multiplying both the numerator and the denominator by 5:
-8×5
11×5
=
-40
55
 
-8
11
=
-40
55
Question:13
Express 
14
-5
 as a rational number with numerator
i 56
ii -70
Solution:
i Numerator of 
14
-5
 is 14.
Clearly, 1 4 × 4 =56
Multiplying both the numerator and the denominator by 4:
14×4
-5×4
=
56
-20
14
-5
=
56
-20
ii -70
Numerator of 
14
-5
 is 14. ? Clearly, 14×-5=-70
Multiplying both the numerator and the denominator by -5:
14×(-5)
(-5)×(-5)
=
-70
25
14
-5
= ? -70
25
Question:14
Express 
13
-8
 as a rational number with denominator
i -40
ii 32
Solution:
i Denominator of 
13
-8
 is -8.
Clearly, (-8)×5= -40
Multiplying both the numerator and the denominator by 5:
13×5
-8×5
=
65
-40
13
-8
=
65
-40
ii Denominator of 
13
-8
 is -8.
Clearly, -8×(-4)= 32
Multiplying both the numerator and the denominator by -4:
13×(-4)
-8×(-4)
=
-52
32
 
13
-8
=
-52
32
Question:15
Express 
-36
24
 as a rational number with numerator
i -9
ii 6
Solution:
i Numerator of  
-36
24
 is -36.
Clearly, -36 ÷ 4= -9
Dividing both the numerator and the denominator by 4:
 
-36÷4
24÷4
=
-9
6
ii Numerator of  
-36
24
 is -36. ? Clearly, -36 ÷ -6 = 6
Dividing both the numerator and the denominator by -6: