NCERT Class 8 Maths Chapter 1 Rational Numbers Exercise 1.1

Chapter 1 Rational Numbers Exercise 1.1

Question 1: Using appropriate properties find.
(i) -2/3 × 3/5 + 5/2 - 3/5 × 1/6
Answer:

= (-2/3 × 3/5) + 5/2 - (3/5 × 1/6)
= -6/15 + 5/2 - 3/30
= -2/5 + 5/2 - 1/10
LCM of 2, 5 = 10
= -2/5 × 2/2 = -4/10, 5/2 × 5/5 = 25/10
= -4/10 + 25/10 = -4 + 25/10 = 21/10
= 21/10 - 1/10 = 21 - 1/10 = 20/10 = 2

(ii) 2/5 × (-3/7) - 1/6 × 3/2 + 1/14 × 2/5
Answer:

= [2/5 × (-3/7)] - [1/6 × 3/2] + [1/14 × 2/5]
= -6/35 - 3/12 + 2/70
= -6/35 - 1/4 + 1/35
LCM of 4, 35, 35 = 120
= -6/35 × 4/4 = -24/120, 1/4 × 35/35 = 35/120, 1/35 × 4/4 = 4/120
= -24/120 - 35/120 + 4/120 = -24 - 35 + 4/120 = -55/120 = -11/28

Question 2: Write the additive inverse of each of the following
(i) 2/8
Answer:
Additive inverse of 2/8 is – 2/8

(ii) -5/9
Answer:
Additive inverse of -5/9 is 5/9

(iii) -6/-5 = 6/5
Answer:
Additive inverse of 6/5 is -6/5

(iv) 2/-9 = -2/9
Answer:
Additive inverse of -2/9 is 2/9

(v) 19/-16 = -19/16
Answer:
Additive inverse of -19/16 is 19/16

Question 3: Verify that: -(-x) = x for.
(i) x = 11/15
Answer:

x = 11/15, -x = -11/15
= 11/15 + (-11/15) = 0
-x = -(-11/15), x = 11/15
= -(-11/15) + 11/15 = 0
Therefore, -(-x) = x.

(ii) x = -13/17
Answer:

x = -13/17, -x = 13/17
= (-13/17) + 13/17 = 0
-x = 13/17, x = -13/17
= 13/17 + (-13/17) = 0
Therefore, -(-x) = x.

Question 4: Find the multiplicative inverse of the
(i) -13
Answer:
-1/13

(ii) -13/19
Answer:
-19/13

(iii) 1/5
Answer:
5

(iv) -5/8 × (-3/7)
Answer:
56/15

(v) -1 × (-2/5)
Answer:
5/2

(vi) -1
Answer:
-1

Question 5: Name the property under multiplication used in each of the following.
(i) -4/5 × 1 = 1 × (-4/5) = -4/5
Answer:
1 is multiplicative identity.

(ii) -13/17 × (-2/7) = -2/7 × (-13/17)
Answer:
Commutativity

(iii) -19/29 × 29/-19 = 1
Answer:
Multiplicative inverse

Question 6: Multiply 6/13 by the reciprocal of -7/16
Answer:

Reciprocal of -7/16 = 16/-7 = -16/7
= 6/13 × (-16/7) = -96/91

Question 7: Tell what property allows you to compute 1/3 × (6 × 4/3) as (1/3 × 6) × 4/3
Answer:
Associativity

Question 8: Is 8/9 the multiplication inverse of 1 1/8? Why or why not?
Answer:
No, 8/9 is no the multiplicative inverse of -1 1/8 because 8/9 × -7/8 ≠ 1

Question 9: If 0.3 the multiplicative inverse of 3 1/3? Why or why not?
Answer:
Yes, 0.3 is the multiplicative inverse of 3 1/3 because 3/10 × 10/3 = 30/30

Question 10: Write
(i) The rational number that does not have a reciprocal.
Answer:
0

(ii) The rational numbers that are equal to their reciprocals.
Answer:
1 and (-1)

(iii) The rational number that is equal to its negative.
Answer:
0

Question 11: Fill in the blanks.
(i) Zero has
no reciprocal.
(ii) The numbers
1 and -1 are their own reciprocals
(iii) The reciprocal of -5 is
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.

No comments:

Post a Comment

Also read!

Class 6 Solutions

• Class 7

Class 7 Computer Kips Solutions
Class 7 Gul Mohar English Solutions
English Grammar Class 7
English Writing Skills Class 7
Class 7 Map Pointing Solutions
Class 7 NCERT Civics Solutions
Class 7 NCERT Civics Notes
Class 7 NCERT Civics Extra Questions
Class 7 NCERT Geography Solutions
Class 7 NCERT Geography Notes
Class 7 NCERT Geography Extra Questions
Class 7 NCERT History Solutions
Class 7 NCERT History Notes
Class 7 NCERT History Extra Questions
Class 7 NCERT Maths Solutions
Class 7 NCERT Science Solutions
Class 7 NCERT Science Notes
Class 7 NCERT Science Extra Questions

• Class 8

Class 8 Kips Artificial Intelligence Solutions
Class 8 Gul Mohar English Solutions
English Grammar Class 8
English Writing Skills Class 8
Class 8 Map Pointing Solutions
Class 8 NCERT Civics Solutions
Class 8 NCERT Civics Notes
Class 8 NCERT Civics Extra Questions
Class 8 NCERT Geography Solutions
Class 8 NCERT Geography Notes
Class 8 NCERT Geography Extra Questions
Class 8 NCERT History Solutions
Class 8 NCERT History Notes
Class 8 NCERT History Extra Questions
Class 8 NCERT Maths Solutions
Class 8 NCERT Science Solutions
Class 8 NCERT Science Notes
Class 8 NCERT Science Extra Questions
Class 8 NCERT Science Exemplar
Class 8 NCERT Science MCQs

Class 9 Solutions

• Class 10

Class 10 Kips Artificial Intelligence Solutions
Class 10 NCERT English Solutions
→ Class 10 Map Pointing Solutions
Class 10 NCERT Civics Solutions
Class 10 NCERT Civics Notes
Class 10 NCERT Civics Extra Questions
Class 10 NCERT Geography Solutions
Class 10 NCERT Geography Notes
Class 10 NCERT Geography Extra Questions
Class 10 NCERT History Solutions
→ Class 10 NCERT History Notes
Class 10 NCERT History Extra Questions
Class 10 NCERT Maths Solutions
Class 10 NCERT Science Solutions
Class 10 NCERT Science Notes
Class 10 NCERT Science Extra Questions

• Computer languages
Python Basics

• Extra Activities
Extra Activities

• Extra Knowledge
Extra Information
General Knowledge
Historical Places in India
Latest technology
Physical Sciences
Facts

• Mathematics quick links
Mathematical Terms
Maths Tricks

CONTACT US