NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 8 |

Subject |
Maths |

Chapter |
Chapter 1 |

Chapter Name |
Rational Numbers |

Exercise |
Ex 1.1 |

Number of Questions Solved |
11 |

Category |
NCERT Solutions |

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

**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)** \(\frac { 2 }{ 8 } \)

Additive inverse of \(\frac { 2 }{ 8 } \) is \(\frac { 2 }{ 8 } \)

**(ii)** \(-\frac { 5 }{ 9 } \)

\(\frac { -6 }{ -5 } =\frac { 6 }{ 5 } \)

Additive inverse of \(\frac { -6 }{ -5 } \) is \(\frac { -6 }{ 5 } \)

**(iii) **\(\frac { -6 }{ -5 } \)

\(\frac { -6 }{ -5 } \)=\(\frac { 6 }{ 5 } \)

Additive inverse of \(\frac { -6 }{ -5 } \) is \(\frac { -6 }{ 5 } \)

**(iv)** \(\frac { 2 }{ -9 } \)

Additive inverse of \(\frac { 2 }{ -9 } \) is \(\frac { 2 }{ 9 }\)

**(v)** \(\frac { 19 }{ -6 } \)

Additive inverse of \(\frac { 19 }{ -6 } \) is \(\frac { 19 }{ 6 }\)

**Question 3.**

Verify that – (-x) = x for :

**(i)** \(x=\frac { 11 }{ 15 } \)

**(ii)** \(x=-\frac { 13 }{ 17 } \)

**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 \(\frac { 6 }{ 13 } \) by the reciprocal of \(\frac { -7 }{ 16 } \)

**Solution.**

Reciprocal of \(\frac { -7 }{ 16 } \) is \(\frac { -16 }{ 7 } \)

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 : \(\frac { 1 }{ 3 } \times \left( 6\times \frac { 4 }{ 3 } \right) \) as \(\left( \frac { 1 }{ 3 } \times 6 \right) \times \frac { 4 }{ 3 } \)

**Solution.**

Associativity.

**Question 8.**

Is the \(\frac { 8 }{ 9 } \) 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 ; \(\frac { 8 }{ 9 } \) is not the multiplicative inverse of \(-1\frac { 1 }{ 8 } \left( =-\frac { 9 }{ 8 } \right) \) because the product of \(\frac { 8 }{ 9 } \) 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 \(\frac { 10 }{ 3 } \) 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 \(\frac { 1 }{ x } \), where \(x\neq 0\)

**(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 \(-\frac { 1 }{ 5 } \)

**(iv)** Reciprocal of \(\frac { 1 }{ x } \), where \(x\neq 0\) is x.

**(v)** The product of two rational numbers is always a rational number.

**(vi)** The reciprocal of a positive rational number is positive.

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