NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1
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| Textbook | NCERT |
| Board | CBSE |
| Category | NCERT Solutions |
| Class | Class 8 |
| Subject | Maths |
| Chapter | Chapter 1 |
| Exercise | Class 8 Chapter 1 Rational Numbers Exercise 1.1 |
| Number of Questions Solved | 11 |
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1
NCERT TEXTBOOK EXERCISES
Question 1. Using appropriate properties find:
(i) $-\frac { 2 }{ 5 } \times \frac { 3 }{ 5 } +\frac { 5 }{ 2 } -\frac { 3 }{ 5 } \times \frac { 1 }{ 6 }$
(ii) $\frac { 2 }{ 5 } \times \left( -\frac { 3 }{ 7 } \right) -\frac { 1 }{ 6 } \times \frac { 3 }{ 2 } +\frac { 1 }{ 14 } \times \frac { 2 }{ 5 }$
Solution.
Question 2. Write the additive inverse of each of the following:
Solution.
(i) 2/8
Additive inverse of 2/8 is 2/8
(ii) −5/9
−6/−5=6/5
Additive inverse of −6/−5 is −6/5
(iii) −6/−5
−6/−5=6/5
Additive inverse of −6/−5 is −6/5
(iv) 2/−9
Additive inverse of 2/−9 is 2/9
(v) 19/−6
Additive inverse of 19/−6 is 19/6
Question 3. Verify that – (-x) = x for :
(i) x=11/15
(ii) x=−13/17
Solution.
Question 4. Find the multiplicative inverse of the following:
Solution.
Question 5. Name the property under multiplication used in each of the following:
(i) $\frac { -4 }{ 5 } \times \left( 1 \right) =1\times \frac { -4 }{ 5 } =-\frac { 4 }{ 5 }$
(ii) $-\frac { 13 }{ 17 } \times \frac { -2 }{ 7 } =\frac { -2 }{ 7 } \times \frac { -13 }{ 17 }$
(iii) $\frac { -19 }{ 29 } \times \frac { 29 }{ -19 } =1$
Solution.
(i) 1 is the multiplicative identity
(ii) Commutativity of multiplication
(iii) Multiplicative inverse.
Question 6. Multiply 6/13 by the reciprocal of −7/16
Solution.
Reciprocal of −7/16 is −16/7
Now,
$\frac { 6 }{ 13 } \times \frac { -16 }{ 7 } =\frac { 6\times \left( -16 \right) }{ 13\times 7 } =\frac { -96 }{ 91 }$
Question 7. Tell what property allows you to compute : $\frac { 1 }{ 3 } \times \left( 6\times \frac { 4 }{ 3 } \right)$
Solution.
Associativity.
Question 8. Is the 8/9 multiplicative inverse of $-1\frac { 1 }{ 8 }$ ? Why or why not?
Solution.
$-1\frac { 1 }{ 8 } =-\frac { 9 }{ 8 }$
Now, $\frac { 8 }{ 9 } \times \frac { -9 }{ 8 } =-1\neq 1$
So, No ; 8/9 is not the multiplicative inverse of $-1\frac { 1 }{ 8 } \left( =-\frac { 9 }{ 8 } \right)$ because the product of 8/9 and -13(-) and $-1\frac { 1 }{ 8 } \left( =-\frac { 9 }{ 8 } \right)$ is not 1.
Question 9. Is 0.3 the multiplicative inverse of $3\frac { 1 }{ 3 }$ ? Why or why not?
Solution.
Yes ; 0.3 is the multiplicative inverse of 10/3 because
$\frac { 3 }{ 10 } \times \frac { 10 }{ 3 } =\frac { 3\times 10 }{ 10\times 3 } =\frac { 30 }{ 30 } =1$
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) The rational number ‘0′ does not have a reciprocal.
(ii) The rational numbers 1 and (-1) are equal to 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 1/x, where x≠0
(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.
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Exercise 1.1 PDF
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