Class 8 Maths NCERT Solutions for Chapter – 1 Rational Numbers Ex – 1.1

Rational Numbers

Question 1.
Using appropriate properties find.
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 1
Solution:
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 2
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 3

Question 2.
Write the additive inverse of each of the following:
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 4
Solution:
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 5
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 6

Question 3.
Verify that – (-x) = x for:
(i) x=\frac { 11 }{ 15 }
(ii) x=-\frac { 13 }{ 17 } .

Solution:
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 7

Question 4.
Find the multiplicative inverse of the following:
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 8
Solution:
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 9
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 10

Question 5.
Name the property under multiplication used in each of the following:
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 11
Solution:
(i) Existence of multiplicative identity.
(ii) Commutative property of multiplication.
(iii) Existence of multiplicative inverse.

Question 6.
Multiply \frac { 6 }{ 13 }  by the reciprocal of \frac { -7 }{ 16 } .

Solution:
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 12

Question 7.
Tell what property allows you to compute.
\frac { 1 }{ 3 } \times \left( 6\times \frac { 4 }{ 3 } \right) as\left( \frac { 1 }{ 3 } \times 6 \right) \times \frac { 4 }{ 3 }
Solution:
Associative property of multiplication over rational numbers allows us to compute :
\frac { 1 }{ 3 } \times \left( 6\times \frac { 4 }{ 3 } \right) as\left( \frac { 1 }{ 3 } \times 6 \right) \times \frac { 4 }{ 3 }

Question 8.
Is \frac { 9 }{ 8 }  the multiplicative inverse of – 1 \frac { 1 }{ 8 } ? Why or why not?

Solution:
No, \frac { 9 }{ 8 }  is not the multiplicative inverse of -1 \frac { 1 }{ 8 } .
Because \frac { 8 }{ 9 } \times -1\frac { 1 }{ 8 } =\frac { 8 }{ 9 } \times \frac { -9 }{ 8 } =-1\neq 1.

Question 9.
Is 0.3 the multiplicative inverse of 3\frac { 1 }{ 3 } ? Why or why not?

Solution:
Yes, 0.3 is multiplicative inverse of 3\frac { 1 }{ 3 } .
Because 0.3\times 3\frac { 1 }{ 3 } =\frac { 3 }{ 10 } \times \frac { 10 }{ 3 } =1.

Question 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) We know that there is no rational number which when multiplied with 0, gives 1. Therefore, the rational number 0 has no reciprocal.
(ii) We know that the reciprocal of 1 is 1 and the reciprocal of -1 is -1. 1 and -1 are the only rational numbers which are their own reciprocals.
(iii) The rational number 0 is equal to its negative.

Question 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 \frac { 1 }{ x } , where ≠0 is ………
(v) The product of two rational numbers is always a ………….
(vi) The reciprocal of a positive rational number is ………..

Solution:
(i) No,
(ii) 1, -1,
(iii) \frac { -1 }{ 5 }
(iv) x,
(v) rational number,
(vi) positive.

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