# 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 –
(d) none of these

Question 2.
Rational numbers are not associative for –
(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

Question 11.
Additive inverse of rational number $$-\frac { 3 }{ 5 }$$ is
(a) 0
(b) 1
(c) $$\frac { 3 }{ 5 }$$
(d) $$-\frac { 5 }{ 3 }$$

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.

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.

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) $$\frac { 1 }{ 2 }$$

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

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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