RBSE Solutions for Class 8 Maths Chapter 1 Rational Numbers Additional Questions is part of RBSE Solutions for Class 8 Maths. Here we have given Rajasthan Board RBSE Class 8 Maths Chapter 1 Rational Numbers Additional Questions.

Board |
RBSE |

Textbook |
SIERT, Rajasthan |

Class |
Class 8 |

Subject |
Maths |

Chapter |
Chapter 1 |

Chapter Name |
Rational Numbers |

Exercise |
Additional Questions |

Number of Questions |
41 |

Category |
RBSE Solutions |

## Rajasthan Board RBSE Class 8 Maths Chapter 1 Rational Numbers Additional Questions

**I. Objective Type Questions**

Question 1.

Rational numbers are closed for –

(a) addition and multiplication

(b) addition and(RBSESolutions.com) subtraction

(c) addition, subtraction and multiplication

(d) none of these

Question 2.

Rational numbers are not associative for –

(a) addition

(b) multiplication

(c) both (a) and (b)

(d) division

Question 3.

Additive inverse of \(\frac { a }{ b }\) is –

(a) \(\frac { a }{ b }\)

(b) \(-\frac { a }{ b }\)

(c) \(\frac { b }{ a }\)

(d) a × b

Question 4.

Which property of multiplication is illustrated by –

(a) Commutative

(b) Inverse

(c) Associative

(d) None of these

Question 5.

What is the multiplicative inverse of \(\frac { 8 }{ 21 }\) ?

(a) \(-\frac { 8 }{ 21 }\)

(b) 1

(c) 0

(d) \(\frac { 21 }{ 8 }\)

Question 6.

Give one rational number between \(\frac { 1 }{ 4 }\) and \(\frac { 1 }{ 2 }\)

(a) \(\frac { 3 }{ 4 }\)

(b) 1

(c) \(\frac { 3 }{ 8 }\)

(d) \(\frac { 1 }{ 8 }\)

Question 7.

Rational number(RBSESolutions.com)between two rational numbers are –

(a) one

(b) four

(c) infinite

(d) zero

Question 8.

Multiplicative inverse of \(3\frac { 1 }{ 3 }\) is –

(a) 3

(b) \(-\frac { 1 }{ 3 }\)

(c) 0.3

(d) None of these

Question 9.

a x b = b x a follows which property?

(a) Associative

(b) Closed

(c) Inverse

(d) Commutative

Question 10.

a x (b x c) = (a x b) x c follows which property?

(a) Associative under multiplication

(b) Commutative under multiplication

(c) Associative(RBSESolutions.com)under Addition

(d) Commutative under Addition

Question 11.

Additive inverse of rational number \(-\frac { 3 }{ 5 }\) is

(a) 0

(b) 1

(c) \(\frac { 3 }{ 5 }\)

(d) \(-\frac { 5 }{ 3 }\)

Answers

1. (c)

2. (d)

3. (b)

4. (a)

5. (d)

6. (c)

7. (c)

8. (c)

9. (d)

10. (a)

11. (c).

**II. Fill in the blanks**

Question 1.

Rational numbers are____under subtraction.

Question 2.

The rational number___is the additive identity for rational numbers.

Question 3

\(\frac { 3 }{ 8 } \times \_ \_ =1\times \frac { 3 }{ 8 } =\frac { 3 }{ 8 } \)

Question 4

___can be represented on a number line.

Question 5.

Between any two(RBSESolutions.com)rational numbers there are ___ rational numbers.

Answers.

1. closed

2. zero

3. 1

4. rational numbers

5. infinite.

**III. True/False Type Questions**

Question 1.

Multiplicative Identity of \(-1\frac { 1 }{ 8 }\) is \(\frac { 8 }{ 9 }\).

Question 2.

Additive Inverse of \(\frac { -7 }{ 19 }\) is \(\frac { 7 }{ 19 }\)

Question 3.

Rational numbers are(RBSESolutions.com)represented on number line.

Question 4.

\(\left( \frac { a+b }{ 2 } \right) \) is the rational number between two rational numbers a and b.

Question 5.

Every natural number is a rational number.

Answers

1. False

2. True

3. True

4. True

5. True.

**IV. Matching Type Questions**

Match Section A to section B.

Section A |
Section B |

1. Rational number between 0 and 1 | (a) – 1 |

2. Additive inverse of rational number 1 | (b) undefined |

3. Multiplicative inverse of rational number 0 | (c) infinite |

4. How many rational number between two rational number | (d) \(\frac { 1 }{ 2 }\) |

Answers

1. (d)

2. (a)

3. (b)

4. (c)

**V. Very Short Answer Type Questions**

Question 1.

Define rational numbers.

Solution.

Rational number is(RBSESolutions.com)the quotient of two integers such that the denominator is a non-zero inter, i.e. Rational number = \(\frac { p }{ q }\), where p and q are integers and q ≠ 0

Question 2.

What is the multiplicative identity for rational numbers?

Solution.

1

Question 3.

Find \(\frac { -2 }{ 3 } \times \frac { 4 }{ 5 } \)

Solution.

\(\left( \frac { -2 }{ 3 } \right) \times \left( \frac { 4 }{ 5 } \right) =\frac { -8 }{ 15 } \)

Question 4.

Write the additive inverse of \(-\frac { 7 }{ 19 }\) and varify.

Solution.

\(-\frac { 7 }{ 19 }\) is the additive inverse of \(-\frac { 7 }{ 19 }\).

Verification:

Question 5.

Find the mean of \(\frac { 3 }{ 8 }\) and \(\frac { 1 }{ 2 }\)

Solution.

Question 6.

Is 0.6 is multiplicative inverse of \(1\frac { 2 }{ 3 }\)? Why or why not?

Solution.

Yes, 0.6 is multiplicative(RBSESolutions.com)of \(1\frac { 2 }{ 3 }\)

Because

**VI. Short Answer Type Questions**

Question 1.

Subtract a Rational number \(\frac { -3 }{ 8 }\) from \(\frac { -5 }{ 4 }\)

Solution.

\(\frac { -5 }{ 4 } -\left( \frac { -3 }{ 8 } \right) \)

We find out the LCM of denominator 4 and 8. LCM of 4 and 8 is 8

Question 2.

Find ten rational(RBSESolutions.com)number between \(\frac { -5 }{ 6 }\) and \(\frac { 5 }{ 8 }\).

Solution.

LCM of 6 and 8 is 24

So we can write ten rational number between \(\frac { -5 }{ 6 }\) and \(\frac { 5 }{ 8 }\) are

Question 3.

Find the value of

Solution.

LCM of 7, 11, 21, 22 = 462

Question 4.

Product of two(RBSESolutions.com)rational number is \(\frac { -28 }{ 81 }\). If one rational number is \(\frac { 14 }{ 27 }\) then find the other

Solution.

According to question,

\(\frac { 14 }{ 27 }\) x IInd number = \(\frac { -28 }{ 81 }\)

⇒ IInd number is

Hence, II nd number is \(\frac { -2 }{ 3 }\)

Question 5.

Find the value of

(x + y) ÷ (x – y)

If x = \(\frac { 5 }{ 4 }\), y = \(-\frac { 1 }{ 3 }\)

Solution

x + y = \(\frac { 5 }{ 4 } +\left( -\frac { 1 }{ 3 } \right) \)

Question 6.

By what number should we multiply \(\frac { 3 }{ -14 }\),so that the product may be \(\frac { 5 }{ 12 }\).

Solution

We have

Product of(RBSESolutions.com)two numbers = \(\frac { 5 }{ 12 }\)

One number is \(\frac { 3 }{ -14 }\)

∴ The other number = \(\frac { 5 }{ 12 } \div \frac { 3 }{ \left( -14 \right) } \)

Question 7.

Subtract the sum of \(\frac { 5 }{ 14 }\) and \(\frac { -4 }{ 7 }\) from the sum of \(\frac { 9 }{ 14 }\) and \(\frac { 23 }{ 14 }\)

Solution.

Question 8.

Solution.

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