NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Exercise 1.1 can be referred to and downloaded from the link available below. The questions presented in Exercise 1.1 have been solved by our experts in Maths with utmost care. Exercise 1.1 of Class 8 Maths takes the students through the basic concepts of Rational Numbers, as well as the different properties of the same. The solutions for the questions in the NCERT textbook are prepared according to the NCERT syllabus and guidelines so that the students can enhance their confidence by repeatedly solving these questions. Hence, students who aim to score high in the examination of Maths should practise these NCERT Solutions for Class 8 Maths without fail.
NCERT Solutions for Class 8 Maths Chapter 1 – Rational Numbers Exercise 1.1
Access other exercise solutions of Class 8 Maths Chapter 1 – Rational Numbers
Exercise 1.2 Solutions 7 Questions (7 Short Answer Questions)
Access Answers of Maths NCERT Class 8 Chapter 1 – Rational Numbers Exercise 1.1 Page Number 14
1. Using appropriate properties, find:
(i) -2/3 × 3/5 + 5/2 – 3/5 × 1/6
Solution:
-2/3 × 3/5 + 5/2 – 3/5 × 1/6
= -2/3 × 3/5– 3/5 × 1/6+ 5/2 (by commutativity)
= 3/5 (-2/3 – 1/6)+ 5/2
= 3/5 ((- 4 – 1)/6)+ 5/2
= 3/5 ((–5)/6)+ 5/2 (by distributivity)
= – 15 /30 + 5/2
= – 1 /2 + 5/2
= 4/2
= 2
(ii) 2/5 × (- 3/7) – 1/6 × 3/2 + 1/14 × 2/5
Solution:
2/5 × (- 3/7) – 1/6 × 3/2 + 1/14 × 2/5
= 2/5 × (- 3/7) + 1/14 × 2/5 – (1/6 × 3/2) (by commutativity)
= 2/5 × (- 3/7 + 1/14) – 3/12
= 2/5 × ((- 6 + 1)/14) – 3/12
= 2/5 × ((- 5)/14)) – 1/4
= (-10/70) – 1/4
= – 1/7 – 1/4
= (– 4– 7)/28
= – 11/28
2. Write the additive inverse of each of the following:
Solution:
(i) 2/8
The additive inverse of 2/8 is –2/8.
(ii) -5/9
The additive inverse of -5/9 is 5/9.
(iii) -6/-5 = 6/5
The additive inverse of 6/5 is -6/5.
(iv) 2/-9 = -2/9
The additive inverse of -2/9 is 2/9.
(v) 19/-16 = -19/16
The additive inverse of -19/16 is 19/16.
3. Verify that: -(-x) = x for:
(i) x = 11/15
(ii) x = -13/17
Solution:
(i) x = 11/15
We have, x = 11/15
The additive inverse of x is –x (as x + (-x) = 0)
Then, the additive inverse of 11/15 is – 11/15 (as 11/15 + (-11/15) = 0)
The same equality, 11/15 + (-11/15) = 0, shows that the additive inverse of -11/15 is 11/15.
Or – (-11/15) = 11/15
i.e., -(-x) = x
(ii) -13/17
We have, x = -13/17
The additive inverse of x is – x (as x + (-x) = 0)
Then, the additive inverse of -13/17 is 13/17 (as 11/15 + (-11/15) = 0)
The same equality (-13/17 + 13/17) = 0, shows that the additive inverse of 13/17 is -13/17.
Or – (13/17) = -13/17,
i.e., -(-x) = x
4. Find the multiplicative inverse of the following:
(i) -13 (ii) -13/19 (iii) 1/5 (iv) -5/8 × (-3/7) (v) -1 × (-2/5) (vi) -1
Solution:
(i) -13
Multiplicative inverse of -13 is -1/13.
(ii) -13/19
Multiplicative inverse of -13/19 is -19/13.
(iii) 1/5
Multiplicative inverse of 1/5 is 5.
(iv) -5/8 × (-3/7) = 15/56
Multiplicative inverse of 15/56 is 56/15.
(v) -1 × (-2/5) = 2/5
Multiplicative inverse of 2/5 is 5/2.
(vi) -1
Multiplicative inverse of -1 is -1.
5. Name the property under multiplication used in each of the following:
(i) -4/5 × 1 = 1 × (-4/5) = -4/5
(ii) -13/17 × (-2/7) = -2/7 × (-13/17)
(iii) -19/29 × 29/-19 = 1
Solution:
(i) -4/5 × 1 = 1 × (-4/5) = -4/5
Here 1 is the multiplicative identity.
(ii) -13/17 × (-2/7) = -2/7 × (-13/17)
The property of commutativity is used in the equation
(iii) -19/29 × 29/-19 = 1
The multiplicative inverse is the property used in this equation.
6. Multiply 6/13 by the reciprocal of -7/16
Solution:
Reciprocal of -7/16 = 16/-7 = -16/7
According to the question,
6/13 × (Reciprocal of -7/16)
6/13 × (-16/7) = -96/91
7. Tell what property allows you to compute 1/3 × (6 × 4/3) as (1/3 × 6) × 4/3
Solution:
1/3 × (6 × 4/3) = (1/3 × 6) × 4/3
Here, the way in which factors are grouped in a multiplication problem supposedly does not change the product. Hence, the Associativity Property is used here.
8. Is 8/9 the multiplication inverse of – 
? Why or why not?
Solution:
–
= -9/8
According to the question,
8/9 × (-9/8) = -1 ≠1
Therefore, 8/9 is not the multiplicative inverse of –
.
9. If 0.3 is the multiplicative inverse of
? Why or why not?
Solution:
= 10/3
0.3 = 3/10
[Multiplicative inverse ⟹ product should be 1]According to the question,
3/10 × 10/3 = 1
Therefore, 0.3 is the multiplicative inverse of
.
10. 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.
Solution:
(i) The rational number that does not have a reciprocal is 0.
Reason:
0 = 0/1
Reciprocal of 0 = 1/0, which is not defined.
(ii) The rational numbers that are equal to their reciprocals are 1 and -1.
Reason:
1 = 1/1
Reciprocal of 1 = 1/1 = 1 Similarly, Reciprocal of -1 = – 1
(iii) The rational number that is equal to its negative is 0.
Reason:
Negative of 0=-0=0
11. 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 _____.
Solution:
(i) Zero has no reciprocal.
(ii) The numbers -1 and 1 are their own reciprocals
(iii) The reciprocal of –5 is -1/5.
(iv) Reciprocal of 1/x, where x ≠0 is x.
(v) The product of two rational numbers is always a rational number.
(vi) The reciprocal of a positive rational number is positive.
Exercise 1.1 of NCERT Class 8 Maths Chapter 1, Rational Numbers, deals with the basic concepts related to rational numbers. We can say that the exercise mainly deals with brushing up on the properties the students have learnt in the chapter. The first exercise of the chapter primarily deals with the fundamental explanations of properties. Some of the topics that are focused on prior to Exercise 1.1 include the following.
- Properties of Rational Numbers
- Closure
- Commutativity
- Associativity
- The Role of Zero
- The Role of 1
- Negative of a Number
- Reciprocal
- Distributivity of Multiplication over Addition for Rational Numbers.
The NCERT Solutions can help the students to practise and learn each and every concept, as it provides the answers to all the questions asked in the NCERT textbook. Students who aim to score high in their Class 8 Maths annual examination should practise all the questions present in the NCERT as many times as possible.
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