RBSE Solutions for Class 8 Maths Chapter 1 Rational Numbers Additional Questions

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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