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 [latex]\frac { a }{ b }[/latex] is –

(a) [latex]\frac { a }{ b }[/latex]

(b) [latex]-\frac { a }{ b }[/latex]

(c) [latex]\frac { b }{ a }[/latex]

(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 [latex]\frac { 8 }{ 21 }[/latex] ?

(a) [latex]-\frac { 8 }{ 21 }[/latex]

(b) 1

(c) 0

(d) [latex]\frac { 21 }{ 8 }[/latex]

Question 6.

Give one rational number between [latex]\frac { 1 }{ 4 }[/latex] and [latex]\frac { 1 }{ 2 }[/latex]

(a) [latex]\frac { 3 }{ 4 }[/latex]

(b) 1

(c) [latex]\frac { 3 }{ 8 }[/latex]

(d) [latex]\frac { 1 }{ 8 }[/latex]

Question 7.

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

(a) one

(b) four

(c) infinite

(d) zero

Question 8.

Multiplicative inverse of [latex]3\frac { 1 }{ 3 }[/latex] is –

(a) 3

(b) [latex]-\frac { 1 }{ 3 }[/latex]

(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 [latex]-\frac { 3 }{ 5 }[/latex] is

(a) 0

(b) 1

(c) [latex]\frac { 3 }{ 5 }[/latex]

(d) [latex]-\frac { 5 }{ 3 }[/latex]

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

[latex]\frac { 3 }{ 8 } \times \_ \_ =1\times \frac { 3 }{ 8 } =\frac { 3 }{ 8 } [/latex]

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 [latex]-1\frac { 1 }{ 8 }[/latex] is [latex]\frac { 8 }{ 9 }[/latex].

Question 2.

Additive Inverse of [latex]\frac { -7 }{ 19 }[/latex] is [latex]\frac { 7 }{ 19 }[/latex]

Question 3.

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

Question 4.

[latex]\left( \frac { a+b }{ 2 } \right) [/latex] 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) [latex]\frac { 1 }{ 2 }[/latex] |

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 = [latex]\frac { p }{ q }[/latex], where p and q are integers and q ≠ 0

Question 2.

What is the multiplicative identity for rational numbers?

Solution.

1

Question 3.

Find [latex]\frac { -2 }{ 3 } \times \frac { 4 }{ 5 } [/latex]

Solution.

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

Question 4.

Write the additive inverse of [latex]-\frac { 7 }{ 19 }[/latex] and varify.

Solution.

[latex]-\frac { 7 }{ 19 }[/latex] is the additive inverse of [latex]-\frac { 7 }{ 19 }[/latex].

Verification:

Question 5.

Find the mean of [latex]\frac { 3 }{ 8 }[/latex] and [latex]\frac { 1 }{ 2 }[/latex]

Solution.

Question 6.

Is 0.6 is multiplicative inverse of [latex]1\frac { 2 }{ 3 }[/latex]? Why or why not?

Solution.

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

Because

**VI. Short Answer Type Questions**

Question 1.

Subtract a Rational number [latex]\frac { -3 }{ 8 }[/latex] from [latex]\frac { -5 }{ 4 }[/latex]

Solution.

[latex]\frac { -5 }{ 4 } -\left( \frac { -3 }{ 8 } \right) [/latex]

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 [latex]\frac { -5 }{ 6 }[/latex] and [latex]\frac { 5 }{ 8 }[/latex].

Solution.

LCM of 6 and 8 is 24

So we can write ten rational number between [latex]\frac { -5 }{ 6 }[/latex] and [latex]\frac { 5 }{ 8 }[/latex] 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 [latex]\frac { -28 }{ 81 }[/latex]. If one rational number is [latex]\frac { 14 }{ 27 }[/latex] then find the other

Solution.

According to question,

[latex]\frac { 14 }{ 27 }[/latex] x IInd number = [latex]\frac { -28 }{ 81 }[/latex]

⇒ IInd number is

Hence, II nd number is [latex]\frac { -2 }{ 3 }[/latex]

Question 5.

Find the value of

(x + y) ÷ (x – y)

If x = [latex]\frac { 5 }{ 4 }[/latex], y = [latex]-\frac { 1 }{ 3 }[/latex]

Solution

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

Question 6.

By what number should we multiply [latex]\frac { 3 }{ -14 }[/latex],so that the product may be [latex]\frac { 5 }{ 12 }[/latex].

Solution

We have

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

One number is [latex]\frac { 3 }{ -14 }[/latex]

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

Question 7.

Subtract the sum of [latex]\frac { 5 }{ 14 }[/latex] and [latex]\frac { -4 }{ 7 }[/latex] from the sum of [latex]\frac { 9 }{ 14 }[/latex] and [latex]\frac { 23 }{ 14 }[/latex]

Solution.

Question 8.

Solution.

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