NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers
Download the NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers PDF for free at AglaSem. Get accurate, step-by-step solutions to every question so you can check your answers, learn the correct method and see how to score full marks.
More Detail
Latest News
Finished viewing? Save it for later —
Download NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers (PDF · 7 pages)Downloaded 112 times
About NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers is available here for free download. Published by NCERT for Class 8, this solution can be viewed online or downloaded as a PDF (7 pages). Candidates preparing for Class 8 can use NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers to understand the exam pattern, the type of questions asked, and the overall difficulty level.
Frequently Asked Questions
How can I download NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers?
Open this page and click the Download button to save NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers as a PDF. It is completely free on AglaSem Docs.
Is NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers free to download?
Yes. NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers can be viewed online and downloaded as a PDF free of cost on AglaSem Docs.
How many pages does NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers have?
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers contains 7 pages, which you can read online or download together as a single PDF.
Where can I find more Class 8 study material?
You can find more Class 8 question papers, sample papers, syllabus, and answer keys on AglaSem Docs.
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers – Text
Read the full text of this solution below — useful to quickly search, copy and reference the content online without downloading the PDF.
📄 View text version (7 pages)
Page 1
NCERT
SOLUTIONS
CLASS - 8TH
aglase .co
SOLUTIONS
CLASS - 8TH
aglase .co
Page 2
Book : Mathematics Ncert Solutions | Chapter-1 Maths
Class : 8th
Subject : Maths
Chapter : 1
Chapter Name : Rational Numbers
Exercise 1.1
Q1 Using appropriate properties nd.
2 3 5 3 1 2 3 1 3 1 2
(i) − × + − × (ii) × (− ) − × + ×
3 5 2 5 6 5 7 6 2 14 5
Answer. (i)
2 3 5 3 1 2 3 3 1 5
− × + − × = − × − × +
3 5 2 5 6 3 5 5 6 2
(Using commutativity of rational numbers)
3 2 1 5
= (− ) × ( + ) + (Distributivity)
5 3 6 2
3 2×2+1 5 3 5 5
= (− ) × ( ) + = (− ) × ( ) +
5 6 2 5 6 2
3 5 −3+5×3 −3+15
= (− ) + = ( ) = ( )
6 2 6 6
12
= = 2
6
(ii) (By commutativity)
2 3 1 3 1 2 2 3 1 2 1 3
× (− ) − × + × = × (− ) + × − ×
5 7 6 2 14 5 5 7 14 5 6 2
(By distributivity)
2 3 1 1
= × (− + ) −
5 7 14 4
2 −3×2+1 1
= × ( ) −
5 14 4
2 −5 1
= × ( ) −
5 14 4
1 1
= − −
7 4
−4−7 −11
= =
28 28
Q2 Write the additive inverse of each of the following.
2 −5 −6 2 19
(i) (ii) (iii) (iv) (v)
8 9 −5 −9 −6
Answer (i)Additive inverse = − 2
8
(ii)Additive inverse =
5
9
Page 1 of 6 Aglasem Schools
Class : 8th
Subject : Maths
Chapter : 1
Chapter Name : Rational Numbers
Exercise 1.1
Q1 Using appropriate properties nd.
2 3 5 3 1 2 3 1 3 1 2
(i) − × + − × (ii) × (− ) − × + ×
3 5 2 5 6 5 7 6 2 14 5
Answer. (i)
2 3 5 3 1 2 3 3 1 5
− × + − × = − × − × +
3 5 2 5 6 3 5 5 6 2
(Using commutativity of rational numbers)
3 2 1 5
= (− ) × ( + ) + (Distributivity)
5 3 6 2
3 2×2+1 5 3 5 5
= (− ) × ( ) + = (− ) × ( ) +
5 6 2 5 6 2
3 5 −3+5×3 −3+15
= (− ) + = ( ) = ( )
6 2 6 6
12
= = 2
6
(ii) (By commutativity)
2 3 1 3 1 2 2 3 1 2 1 3
× (− ) − × + × = × (− ) + × − ×
5 7 6 2 14 5 5 7 14 5 6 2
(By distributivity)
2 3 1 1
= × (− + ) −
5 7 14 4
2 −3×2+1 1
= × ( ) −
5 14 4
2 −5 1
= × ( ) −
5 14 4
1 1
= − −
7 4
−4−7 −11
= =
28 28
Q2 Write the additive inverse of each of the following.
2 −5 −6 2 19
(i) (ii) (iii) (iv) (v)
8 9 −5 −9 −6
Answer (i)Additive inverse = − 2
8
(ii)Additive inverse =
5
9
Page 1 of 6 Aglasem Schools
Page 3
Book : Mathematics Ncert Solutions | Chapter-1 Maths
(iii)
−6 6
=
−5 5
Additive inverse = −
6
−5
(iv) 2 −2
=
−9 9
Additive inverse = 2
9
(v)
19 −19
=
−6 6
Additive inverse = 19
6
Q3 Verify that – (– x) = x for.
.
11 13
(i) x = (ii) x = −
15 17
Answer.
11
(i) x =
15
11
x=
The additive inverse of 15 11 11 11
− x = − as + (− ) = 0
is 15 15 15
This equality
11 11
+ (− ) = 0
15 15
11
−
represents that the additive inverse of 15
is 15 or it
11 11
can be said that − (− ) =
15 15 i.e., −(−x)=x
13
(ii)
x = −
17
The additive inverse of x = − 13
17
is − x =
13
17
as −
13
17
+
13
17
= 0
13 13 13 13
This equality − + = 0 represents that the additive inverse of is i.e.,
17 17 17 −17
−(−x) = x
Q4 Find the multiplicative inverse of the following.
−13 1 −5 −3 −2
(i) − 13 (ii) (iii) (iv) × (v) − 1 × ( vi) − 1
19 5 8 7 5
Answer. (i) 13
Multiplicative inverse =
1
−13
(ii) 13
−19
Multiplicative inverse =− 19
13
(iii)
1
5
Multiplicative inverse = 5
(iv)− × − = 5
8
3
7
15
56
Multiplicative inverse = 56
15
(v)−1 × − 2
5
=
2
5
Multiplicative inverse =
5
2
Page 2 of 6 Aglasem Schools
(iii)
−6 6
=
−5 5
Additive inverse = −
6
−5
(iv) 2 −2
=
−9 9
Additive inverse = 2
9
(v)
19 −19
=
−6 6
Additive inverse = 19
6
Q3 Verify that – (– x) = x for.
.
11 13
(i) x = (ii) x = −
15 17
Answer.
11
(i) x =
15
11
x=
The additive inverse of 15 11 11 11
− x = − as + (− ) = 0
is 15 15 15
This equality
11 11
+ (− ) = 0
15 15
11
−
represents that the additive inverse of 15
is 15 or it
11 11
can be said that − (− ) =
15 15 i.e., −(−x)=x
13
(ii)
x = −
17
The additive inverse of x = − 13
17
is − x =
13
17
as −
13
17
+
13
17
= 0
13 13 13 13
This equality − + = 0 represents that the additive inverse of is i.e.,
17 17 17 −17
−(−x) = x
Q4 Find the multiplicative inverse of the following.
−13 1 −5 −3 −2
(i) − 13 (ii) (iii) (iv) × (v) − 1 × ( vi) − 1
19 5 8 7 5
Answer. (i) 13
Multiplicative inverse =
1
−13
(ii) 13
−19
Multiplicative inverse =− 19
13
(iii)
1
5
Multiplicative inverse = 5
(iv)− × − = 5
8
3
7
15
56
Multiplicative inverse = 56
15
(v)−1 × − 2
5
=
2
5
Multiplicative inverse =
5
2
Page 2 of 6 Aglasem Schools
Page 4
Book : Mathematics Ncert Solutions | Chapter-1 Maths
(vi) -1
Multiplicative inverse = -1
Q5 Name the property under multiplication used in each of the following.
(i)
−4 −4 4 13 −2 −2 −13
× 1 = 1 × = − (ii) − × = ×
5 5 5 17 7 7 17
(iii)
−19 29
× = 1
29 −19
Answer. (i) 1 is the multiplicative identity.
(ii) Commutativity
(iii) Multiplicative inverse
Q6 Multiply by the reciprocal of .
6 −7
13 16
Answer. 6
13
× ( Reciprocal of −
7
16
) =
6
13
× −
16
7
= −
96
91
Q7 Tell what property allows you to compute 1
3
× (6 ×
4
3
) as (
1
3
× 6) ×
4
3
Answer. Associativity
Q8 Is 8
9
the multiplicative inverse of −1 1
8
? Why or why not?
Answer. If it is the multiplicative inverse, then the product should be 1.
However, here, the product is not 1 as
8 1 8 9
× (−1 ) = × (− ) = −1 ≠ 1
9 8 9 8
Q9 Is 0.3 the multiplicative inverse of 3 1
3
? Why or why not?
Answer. 3 1
3
=
10
3
1
0.3 ×
3
3 = 0.3 ×
10
3
=
3
10
×
10
3
= 1 Here, the product is 1. Hence, 0.3 is the multiplicative
inverse of 3 1
3
Page 3 of 6 Aglasem Schools
(vi) -1
Multiplicative inverse = -1
Q5 Name the property under multiplication used in each of the following.
(i)
−4 −4 4 13 −2 −2 −13
× 1 = 1 × = − (ii) − × = ×
5 5 5 17 7 7 17
(iii)
−19 29
× = 1
29 −19
Answer. (i) 1 is the multiplicative identity.
(ii) Commutativity
(iii) Multiplicative inverse
Q6 Multiply by the reciprocal of .
6 −7
13 16
Answer. 6
13
× ( Reciprocal of −
7
16
) =
6
13
× −
16
7
= −
96
91
Q7 Tell what property allows you to compute 1
3
× (6 ×
4
3
) as (
1
3
× 6) ×
4
3
Answer. Associativity
Q8 Is 8
9
the multiplicative inverse of −1 1
8
? Why or why not?
Answer. If it is the multiplicative inverse, then the product should be 1.
However, here, the product is not 1 as
8 1 8 9
× (−1 ) = × (− ) = −1 ≠ 1
9 8 9 8
Q9 Is 0.3 the multiplicative inverse of 3 1
3
? Why or why not?
Answer. 3 1
3
=
10
3
1
0.3 ×
3
3 = 0.3 ×
10
3
=
3
10
×
10
3
= 1 Here, the product is 1. Hence, 0.3 is the multiplicative
inverse of 3 1
3
Page 3 of 6 Aglasem Schools
Page 5
Book : Mathematics Ncert Solutions | Chapter-1 Maths
Q10 Write.
(i) The rational number that does not have a reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.
Answer. (i) 0 is a rational number but its reciprocal is not de ned.
(ii) 1 and —1 are the rational numbers that are equal to their reciprocals.
(iii) 0 is the rational number that is equal to its negative.
Page : 15 , Block Name : Exercise 1.1
Q11 Fill in the blanks.
(i) Zero has ________ reciprocal.
(ii) The numbers ________ and ________ are their own reciprocals
(iii) The reciprocal of – 5 is ________.
(iv) Reciprocal of 1 x , where x ≠ 0 is ________.
(v) The product of two rational numbers is always a _______.
(vi) The reciprocal of a positive rational number is ________.
Answer. (i) No
(ii) 1 , -1
(iii) − 1
5
(iv) x
(v) Rational number
(vi) Positive rational number
Page : 15 , Block Name : Exercise 1.1
Exercise 1.2
Q1 Represent these numbers on the number line. (i) 7
4
(ii) 5
6
Answer. (i) can be represented on the number line as follows.
7
4
Page 4 of 6 Aglasem Schools
Q10 Write.
(i) The rational number that does not have a reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.
Answer. (i) 0 is a rational number but its reciprocal is not de ned.
(ii) 1 and —1 are the rational numbers that are equal to their reciprocals.
(iii) 0 is the rational number that is equal to its negative.
Page : 15 , Block Name : Exercise 1.1
Q11 Fill in the blanks.
(i) Zero has ________ reciprocal.
(ii) The numbers ________ and ________ are their own reciprocals
(iii) The reciprocal of – 5 is ________.
(iv) Reciprocal of 1 x , where x ≠ 0 is ________.
(v) The product of two rational numbers is always a _______.
(vi) The reciprocal of a positive rational number is ________.
Answer. (i) No
(ii) 1 , -1
(iii) − 1
5
(iv) x
(v) Rational number
(vi) Positive rational number
Page : 15 , Block Name : Exercise 1.1
Exercise 1.2
Q1 Represent these numbers on the number line. (i) 7
4
(ii) 5
6
Answer. (i) can be represented on the number line as follows.
7
4
Page 4 of 6 Aglasem Schools
Page 6
Book : Mathematics Ncert Solutions | Chapter-1 Maths
Page : 20 , Block Name : Exercise 1.2
Q2 Represent on the number line.
−2 −5 −9
, ,
11 11 11
Answer.
Page : 20 , Block Name : Exercise 1.2
Q3 Write ve rational numbers which are smaller than 2.
Answer. 2 can be represented as 14
7
Therefore, ve rational numbers smaller than 2 are
13 12 11 10 9
, , , ,
7 7 7 7 7
Page : 20 , Block Name : Exercise 1.2
Q4 Find ten rational numbers between and
−2 1
5 2
Answer. and can be represented as − and respectively.
−2 1 8 10
5 2 20 20
Therefore, ten rational numbers between and are
−2 1
5 2
7 6 5 4 3 2 1 1 2
− ,− ,− ,− ,− ,− ,− , 0, ,
20 20 20 20 20 20 20 20 20
Page : 20 , Block Name : Exercise 1.2
Q5 Find ve rational numbers between.
(i) and
2
3
4
5
(ii)
−3 5
and
2 3
(iii) 1
4
and
1
2
Answer. (i) 2
3
and
4
5
can be represented as 30
45
and
36
45
respectively.
Page 5 of 6 Aglasem Schools
Page : 20 , Block Name : Exercise 1.2
Q2 Represent on the number line.
−2 −5 −9
, ,
11 11 11
Answer.
Page : 20 , Block Name : Exercise 1.2
Q3 Write ve rational numbers which are smaller than 2.
Answer. 2 can be represented as 14
7
Therefore, ve rational numbers smaller than 2 are
13 12 11 10 9
, , , ,
7 7 7 7 7
Page : 20 , Block Name : Exercise 1.2
Q4 Find ten rational numbers between and
−2 1
5 2
Answer. and can be represented as − and respectively.
−2 1 8 10
5 2 20 20
Therefore, ten rational numbers between and are
−2 1
5 2
7 6 5 4 3 2 1 1 2
− ,− ,− ,− ,− ,− ,− , 0, ,
20 20 20 20 20 20 20 20 20
Page : 20 , Block Name : Exercise 1.2
Q5 Find ve rational numbers between.
(i) and
2
3
4
5
(ii)
−3 5
and
2 3
(iii) 1
4
and
1
2
Answer. (i) 2
3
and
4
5
can be represented as 30
45
and
36
45
respectively.
Page 5 of 6 Aglasem Schools
Page 7
Book : Mathematics Ncert Solutions | Chapter-1 Maths
Therefore, ve rational numbers between are
2 4 31 32 33 34 35
and , , , ,
3 5 45 45 45 45 45
(ii) can be represented as − respectively
−3 5 9 10
and and
2 3 6 6
Therefore, ve rational numbers between are −
−3 5 8 7 5 4
and ,− , −1, − ,−
2 3 6 6 6 6
(iii) 1
4
and
1
2
can be represented as 8
32
and
16
32
Therefore, ve rational numbers between 1
4
and
1
2
are 9
32
,
10
32
,
11
32
,
12
32
,
13
32
Page : 20 , Block Name : Exercise 1.2
Q6 Write ve rational numbers greater than -2.
Answer. -2 can be represented as − 14
7
.
Therefore, ve rational numbers greater than —2 are
13 12 11 10 9
− ,− ,− ,− ,−
7 7 7 7 7
Page : 20 , Block Name : Exercise 1.2
Q7 Find ten rational numbers 3
5
and
3
4
.
Answer. can be represented as respectively.
3 3 48 60
and and
5 4 80 80
Therefore, ten rational numbers between 3
5
and
3
4
are
49 50 51 52 53 54 55 56 57 58
, , , , , , , , ,
80 80 80 80 80 80 80 80 80 80
Page : 20 , Block Name : Exercise 1.2
Page 6 of 6 Aglasem Schools
Therefore, ve rational numbers between are
2 4 31 32 33 34 35
and , , , ,
3 5 45 45 45 45 45
(ii) can be represented as − respectively
−3 5 9 10
and and
2 3 6 6
Therefore, ve rational numbers between are −
−3 5 8 7 5 4
and ,− , −1, − ,−
2 3 6 6 6 6
(iii) 1
4
and
1
2
can be represented as 8
32
and
16
32
Therefore, ve rational numbers between 1
4
and
1
2
are 9
32
,
10
32
,
11
32
,
12
32
,
13
32
Page : 20 , Block Name : Exercise 1.2
Q6 Write ve rational numbers greater than -2.
Answer. -2 can be represented as − 14
7
.
Therefore, ve rational numbers greater than —2 are
13 12 11 10 9
− ,− ,− ,− ,−
7 7 7 7 7
Page : 20 , Block Name : Exercise 1.2
Q7 Find ten rational numbers 3
5
and
3
4
.
Answer. can be represented as respectively.
3 3 48 60
and and
5 4 80 80
Therefore, ten rational numbers between 3
5
and
3
4
are
49 50 51 52 53 54 55 56 57 58
, , , , , , , , ,
80 80 80 80 80 80 80 80 80 80
Page : 20 , Block Name : Exercise 1.2
Page 6 of 6 Aglasem Schools
Document Details
| Board / Org | NCERT |
| Exam | Class 8 |
| Type | Solution |
| Pages | 7 |
| Language | english |
| Updated | 22 Jul 2026 |