NCERT Solutions for Class 7 Maths Chapter 8 Rational Numbers

NCERT
SOLUTIONS
CLASS - 7TH

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Book : Mathematics Ncert Solutions | Chapter-9 Maths

Class : 7th
Subject : Maths
Chapter : 9
Chapter Name : Rational Numbers

Exercise 9.1

Q1 List �ve rational numbers between:
(i) –1 and 0
(ii) –2 and –1
(iii) −4/5 and -2/3
(iv) – 1/2 and 2/3.

Answer. (i)
−1 and 0
−1 −1 −1 −1 −1
, , , ,
10 20 30 40 50

(ii)
−2 and − 1
−2 = −12
6
and − 1 = −6
6
Five rational numbers are
−11 −10 −9 −8 −7
6
, 6 , 6 , 6 , 6

(iii)
−4
5
and −2
3
−4 −4×9
5
= 5×9 = −36
45
and −2
3
= −2×15
3×15
= −30
45
Five rational numbers are
−35 −34 −33 −32 −31
45
, 45 , 45 , 45 , 45

(iv)
1
2
and 23
1
2
= 1×18
2×18
= 18
36
and 23 = 2×12
3×12
= 24
36
Five rational numbers are
19 20 21 22 23
, , , ,
36 36 36 36 36

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Book : Mathematics Ncert Solutions | Chapter-9 Maths

Page : 182 , Block Name : Exercise 9.1

Q2 Write four more rational numbers in each of the following patterns:
−3 −6 −9 −12
(i) 5
, 10 , 15 , 20 , …
−1 −2 −3
(ii) 4 , 8 , 12 , …
−1 2 3 4
(iii) 6 , −12 , −18 , −24 ,…
−2 2 4 6
(iv) 3 , −3 , −6 , −9 ,…

Answer. (i)
−3 −6 −9 −12
5
, 10 , 15 , 20 …
−3 −3×2 −3×3 −3×4
5
, 5×2 , 5×3 , 5×4 …
It can be observed that the numerator is a multiple of 3 while the denominator is a
multiple of 5 and as we increase them further, these multiples are increasing. Therefore,
the next four rational numbers in this pattern are
−3×5 −3×6 −3×7 −3×8
5×5
, 5×6 , 5×7 , 5×8 …
−15 −18 −21 −24
25
, 30 , 35 , 40 …

(ii)
−1 −2 −3
4
, 8 , 12 …
−1 −1×2 −1×3
4
, 4×2 , 4×3 …
The next four rational numbers in this pattern are
−1×4 −1×5 −1×6 −1×7
4×4
, 4×5 , 4×6 , 4×7 …
−4 −5 −6 −7
, , ,
16 20 24 28
…

(iii)
−1 2 3 4
6
, −12 , −18 , −24 …
−1 1×2 1×3 1×4
6
, −6×2 , −6×3 , −6×4 …
The next four rational numbers in this pattern are
1×5
, 1×6 , 1×7 , 1×8 …
−6×5 −6×6 −6×7 −6×8
5
, 6 , 7 , 8 …
−30 −36 −42 −48

(iv)
−2 2 4 6
3
, −3 , −6 , −9 …
−2 2 2×2 2×3
3
, −3 , −3×2 , −3×3 …
The next four rational numbers in this pattern are

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Book : Mathematics Ncert Solutions | Chapter-9 Maths

2×4
, 2×5 , 2×6 , 2×7 …
−3×4 −3×5 −3×6 −3×7
8
, 10 , 12 , 14 …
−12 −15 −18 −21

Page : 182 , Block Name : Exercise 9.1

Q3 Give four rational numbers equivalent to:
(i) -2/7
(ii) 5/-3
(iii) 4/9

Answer. (i) Four rational numbers are
−2×2 −2×3 −2×4 −2×5
7×2
, 7×3 , 7×4 , 7×5
−4 −6 −8 −10
, , , 35
14 21 28

(ii) Four rational numbers are
5×2
, 5×3 , 5×4 , 5×5
−3×2 −3×3 −3×4 −3×5
10 15
, , 20 , 25
−6 −9 −12 −15

(iii) Four rational numbers are
4×2 4×3 4×4 4×5
, , ,
9×2 9×3 9×4 9×5
8 12 16 20
, , ,
18 27 36 45

Page : 183 , Block Name : Exercise 9.1

Q4 Draw the number line and represent the following rational numbers on it:
(i) 3/4
(ii) -5/8
(iii) -7/4
(iv) 7/8

Answer. (i) 34
This fraction represents 3 parts out of 4 equal parts. Therefore, each space between two
integers on number line must be divided into 4 equal parts 34 can be represented as.

−5
(ii) 8
This fraction represents 5 parts out of 8 equal parts. Negative sign represents that it is on
the negative side of number line. Therefore, each space between two integers on number

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Book : Mathematics Ncert Solutions | Chapter-9 Maths

line must be divided into 8 equal parts.
−5
8
can be represented as

−7
(iii) 4
= −1 34
This fraction represents 1 full part and 3 parts out of 4 equal parts. Negative sign
represents that it is on the negative side of number line. Therefore, each space between
two integers on number line must be divided into 4 equal parts.
−7
4
can be represented as

7
(iv) 8
This fraction represents 7 parts out of 8 equal parts. Therefore, each space between two
integers on number line must be divided into 8 equal parts.
7
8
can be represented as

Page : 183 , Block Name : Exercise 9.1

Q5 The points P, Q, R, S, T, U, A and B on the number line are such that, TR = RS = SU and
AP = PQ = QB. Name the rational numbers represented by P, Q, R and S.

Answer. Distance between U and T = 1 unit
It is divided into 3 equal parts.
TR = RS = SU = 1/3
R= −1 − 13 = − 33 − 13 = −4
3
S= −1 − 3 = − 3 − 3 = − 53
2 3 2

Similarly,
AB = 1 unit
It is divided into 3 equal parts.
P = 2 + 13 = 63 + 13 = 73
2 6 2 8
Q= 2+ = + =
3 3 3 3

Page : 183 , Block Name : Exercise 9.1

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Book : Mathematics Ncert Solutions | Chapter-9 Maths

Q6 Which of the following pairs represent the same rational number?
−7
(i) 21 and 39
−16 20
(ii) 20
and −25
−2
(iii) −3 and 23
−3 −12
(iv) 5 and 20
8 −24
(v) −5 and 15
−1
(vi) 13 and 9
−5 5
(vii) −9 and −9

Answer. (i)
−7
21
and 39
−7
21
= −1
3
3 1
9
= 3
−1
As 3
≠ 13
Therefore, it does not represent same rational numbers.

(ii)
−16 20
20
and −25
−16
20
= −4
5
−20 −4
25
= 5
Therefore, it represents same rational numbers.

(iii)
−2
−3
and 23
−2
−3
= 23
Therefore, it represents same rational numbers.

(iv)
−3
5
and −12
20
−12
20
= −3
5
Therefore, it represents same rational numbers.

(v)

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Book : Mathematics Ncert Solutions | Chapter-9 Maths

8
−5
and −24
15
−24 −8
15
= 5
8
−5
= −8
5
Therefore, it represents same rational numbers.

(vi)
1
3
and −1
9

As 13 ≠ −1
9
Therefore, it does not represent same rational numbers.

(vii)
−5 5
−9
and −9
−5
−9
= 59
As 59 ≠ −5
9
Therefore, it does not represent same rational numbers.

Page : 183 , Block Name : Exercise 9.1

Q7 Rewrite the following rational numbers in the simplest form:
(i) -8/6
(ii) 25/45
(iii) -44/72
(iv) -8/10

Answer. (i)
−8
6
= −4×2
3×2
= −4
3

25 5×5 5
(ii) 45 = 9×5 = 9

−44
(iii) 72
= −11×4
18×4
= −11
18

−4×2
−8
(iv) 10 = 5×2
= −4
5

Page : 183 , Block Name : Exercise 9.1

Q8 Fill in the boxes with the correct symbol out of >, <, and =.

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Book : Mathematics Ncert Solutions | Chapter-9 Maths

Answer. (i)
−5
7
= −5×3
7×3
= −15
21
2
3
= 2×7
3×7
= 14
21
As − 15 < 14
−5
Therefore, 7 [<] 23

(ii)
−4
5
= −4×7
5×7
= −28
35
−5 −5×5 −25
7
= 7×5 = 35
As − 28 < −25
Therefore, −4
5
[≤ −5
7

(iii)
14
−16
7×2
= −8×2 7
= −8 = −7
8
−7 14
Therefore, 8 □ −16

(iv)
−8
5
= −8×4
5×4
= −32
20
−7 −7×5 −35
4
= 4×5 = 20
As − 32 > −35
Therefore, −8
5
[≥ −7
4
Therefore,
−8
5
[>] −7
4

(v)
−1
3
= −1×4
3×4
= −4
12
−1 −1×3 −3
4
= 4×3 = 12
As − 4 < −3

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Book : Mathematics Ncert Solutions | Chapter-9 Maths

−1
Therefore, 3
[≤] −1
4

5 −5
(vi) −11 = 11

−7
(vii) 0[>] 6

Page : 183 , Block Name : Exercise 9.1

Q9 Which is greater in each of the following:
5
(i) 23 , 2
−5 −4
(ii) 6
, 3
−3 2
(iii) 4 , −3
−1
(iv) 4 , 14
(v) −3 27 , −3 45

5
Answer. (i) 23 , 2
By converting these into like fractions,
2
3
= 2×2
3×2
= 46
5
2
= 5×3
2×3
= 156
5
As 15 > 4, therefore, 2 is greater.

(ii)
−5 −4
6
, 3
−4
3
= −4×2
3×2
= −8
6
As -5 > -8,
−5
Therefore, 6
is greater.

(iii)
−3 2
4
, −3
Or, −3 4
, −2
3
By converting these into like fractions,
−3
4
= −3×3
4×3
= −9
12
−2 −2×4 −8
3
= 3×4 = 12
As -8 > -9 ,
−2
Therefore, 3
is greater.

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(iv)
−1 1
4
,4
1
4
> −1
4

(v)
−3 27 , −3 45
−23 −19
7
, 5
By converting these into like fractions,
−23
7
= −23×5
7×5
= −115
35
−19
5
= −19×7
5×7
= −133
35
As − 115 > −133, therefore, − 3 27 is greater.

Page : 184 , Block Name : Exercise 9.1

Q10 Write the following rational numbers in ascending order:

−3 −2 −1
(i) 5
, 5 , 5
−1 −2 −4
(ii) 3 , 9 , 3
−3 −3 −3
(iii) 7 , 2 , 4

Answer. (i) As −3 < −2 < −1
∴ −3
5
< −2
5
< −1
5

(ii) By converting these into like fractions,
−1×3 −2 −4×3
3×3
, 9 , 3×3
−3 −2 −12
9
, 9 , 9
As −12 < −3 < −2
∴ −4
3
< −1
3
< −2
9

(iii) By converting these into like fractions,
−3×4 −3×14 −3×7
7×4
, 2×14 , 4×7
−12 −42 −21
28
, 28 , 28
As −42 < −21 < −12
∴ −3
2
< −3
4
< −3
7

Page : 184 , Block Name : Exercise 9.1

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