Rational Numbers Class 8 Extra Questions Maths Chapter 1

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Rational Numbers Class 8 Extra Questions Maths Chapter 1

Extra Questions for Class 8 Maths Chapter 1 Rational Numbers

Rational Numbers Class 8 Extra Questions Very Short Answer Type

Rational Numbers Class 8 Worksheet Question 1.
Pick up the rational numbers from the following numbers.
\(\frac { 6 }{ 7 }\), \(\frac { -1 }{ 2 }\), 0, \(\frac { 1 }{ 0 }\), \(\frac { 100 }{ 0 }\)
Solution:
Since rational numbers are in the form of \(\frac { a }{ b }\) where b ≠ 0.
Only \(\frac { 6 }{ 7 }\), \(\frac { -1 }{ 2 }\) and 0 are the rational numbers.

Rational Numbers Class 8 Worksheet With Answers Pdf Question 2.
Find the reciprocal of the following rational numbers:
(a) \(\frac { -3 }{ 4 }\)
(b) 0
(c) \(\frac { 6 }{ 11 }\)
(d) \(\frac { 5 }{ -9 }\)
Solution:
(a) Reciprocal of \(\frac { -3 }{ 4 }\) is \(\frac { -4 }{ 3 }\)
(b) Reciprocal of 0, i.e. \(\frac { 1 }{ 0 }\) is not defined.
(c) Reciprocal of \(\frac { 6 }{ 11 }\) is \(\frac { 11 }{ 6 }\)
(d) Reciprocal of \(\frac { 5 }{ -9 }\) = \(\frac { -9 }{ 5 }\)

Rational Numbers Class 8 Extra Questions Question 3.
Write two such rational numbers whose multiplicative inverse is same as they are.
Solution:
Reciprocal of 1 = \(\frac { 1 }{ 1 }\) = 1
Reciprocal of -1 = \(\frac { 1 }{ -1 }\) = -1
Hence, the required rational numbers are -1 and 1.

Class 8 Maths Chapter 1 Extra Questions Question 4.
What properties, the following expressions show?
(i) \(\frac { 2 }{ 3 } +\frac { 4 }{ 5 } =\frac { 4 }{ 5 } +\frac { 2 }{ 3 }\)
(ii) \(\frac { 1 }{ 3 } \times \frac { 2 }{ 3 } =\frac { 2 }{ 3 } \times \frac { 1 }{ 3 }\)
Solution:
(i) \(\frac { 2 }{ 3 } +\frac { 4 }{ 5 } =\frac { 4 }{ 5 } +\frac { 2 }{ 3 }\) shows the commutative property of addition of rational numbers.
(ii) \(\frac { 1 }{ 3 } \times \frac { 2 }{ 3 } =\frac { 2 }{ 3 } \times \frac { 1 }{ 3 }\) shows the commutative property of multiplication of rational numbers.

Class 8 Rational Numbers Worksheet Question 5.
What is the multiplicative identity of rational numbers?
Solution:
1 is the multiplicating identity of rational numbers.

Rational Numbers Questions For Class 8 Question 6.
What is the additive identity of rational numbers?
Solution:
0 is the additive identity of rational numbers.

Rational Numbers Class 8 Worksheets Ncert Question 7.
If a = \(\frac { 1 }{ 2 }\), b = \(\frac { 3 }{ 4 }\), verify the following:
(i) a × b = b × a
(ii) a + b = b + a
Solution:
Rational Numbers Worksheet Class 8
Rational Numbers Class 8 Questions

Questions On Rational Numbers For Class 8 With Answers Question 8.
Multiply \(\frac { 5 }{ 8 }\) by the reciprocal of \(\frac { -3 }{ 8 }\)
Solution:
Class 8 Maths Ch 1 Extra Questions

Class 8 Maths Chapter 1 Worksheet With Answers Question 9.
Find a rational number between \(\frac { 1 }{ 2 }\) and \(\frac { 1 }{ 3 }\).
Solution:
Rational number between
Worksheet On Rational Numbers For Class 8

Class 8 Rational Numbers Extra Questions Question 10.
Write the additive inverse of the following:
(a) \(\frac { -6 }{ 7 }\)
(b) \(\frac { 101 }{ 213 }\)
Solution:
Rational Numbers Class 8 Worksheet 1

Class 8 Maths Chapter 1 Worksheet Question 11.
Write any 5 rational numbers between \(\frac { -5 }{ 6 }\) and \(\frac { 7 }{ 8 }\). (NCERT Exemplar)
Solution:
Class 8 Chapter 1 Extra Questions

Extra Questions For Class 8 Maths Chapter 1 Question 12.
Identify the rational number which is different from the other three : \(\frac { 2 }{ 3 }\), \(\frac { -4 }{ 5 }\), \(\frac { 1 }{ 2 }\), \(\frac { 1 }{ 3 }\). Explain your reasoning.
Solution:
\(\frac { -4 }{ 5 }\) is the rational number which is different from the other three, as it lies on the left side of zero while others lie on the right side of zero on the number line.

Rational Numbers Class 8 Extra Questions Short Answer Type

Rational Numbers Extra Questions Class 8 Question 13.
Calculate the following:
Ncert Class 8 Maths Chapter 1 Extra Questions
Solution:
Extra Questions On Rational Numbers Class 8
Rational Numbers Class 8 Extra Questions With Answers

Question 14.
Represent the following rational numbers on number lines.
(a) \(\frac { -2 }{ 3 }\)
(b) \(\frac { 3 }{ 4 }\)
(c) \(\frac { 3 }{ 2 }\)
Solution:
Worksheet For Class 8 Maths Chapter 1

Question 15.
Find 7 rational numbers between \(\frac { 1 }{ 3 }\) and \(\frac { 1 }{ 2 }\).
Solution:
Rational Numbers Class 8 Worksheet With Solutions

Question 16.
Show that:
Extra Questions for Class 8 Maths Rational Numbers Q16
Solution:
Extra Questions for Class 8 Maths Rational Numbers Q16.1

Question 17.
If x = \(\frac { 1 }{ 2 }\), y = \(\frac { -2 }{ 3 }\) and z = \(\frac { 1 }{ 4 }\), verify that x × (y × z) = (x × y) × z.
Solution:
We have x = \(\frac { 1 }{ 2 }\), y = \(\frac { -2 }{ 3 }\) and z = \(\frac { 1 }{ 4 }\)
LHS = x × (y × z)
Extra Questions for Class 8 Maths Rational Numbers Q17

Question 18.
If the cost of 4\(\frac { 1 }{ 2 }\) litres of milk is ₹89\(\frac { 1 }{ 2 }\), find the cost of 1 litre of milk.
Solution:
Extra Questions for Class 8 Maths Rational Numbers Q18

Question 19.
The product of two rational numbers is \(\frac { 15 }{ 56 }\). If one of the numbers is \(\frac { -5 }{ 48 }\), find the other.
Solution:
Product of two rational numbers = \(\frac { 15 }{ 56 }\)
One number = \(\frac { -5 }{ 48 }\)
Other number = Product ÷ First number
Extra Questions for Class 8 Maths Rational Numbers Q19
Hence, the other number = \(\frac { -18 }{ 7 }\)

Question 20.
Let O, P and Z represent the numbers 0, 3 and -5 respectively on the number line. Points Q, R and S are between O and P such that OQ = QR = RS = SP. (NCERT Exemplar)
What are the rational numbers represented by the points Q, R and S. Next choose a point T between Z and 0 so that ZT = TO. Which rational number does T represent?
Solution:
Extra Questions for Class 8 Maths Rational Numbers Q20
As OQ = QR = RS = SP and OQ + QR + RS + SP = OP
therefore Q, R and S divide OP into four equal parts.
Extra Questions for Class 8 Maths Rational Numbers Q20.1

Question 21.
Let a, b, c be the three rational numbers where a = \(\frac { 2 }{ 3 }\), b = \(\frac { 4 }{ 5 }\) and c = \(\frac { -5 }{ 6 }\) (NCERT Exemplar)
Verify:
(i) a + (b + c) = (a + b) + c (Associative property of addition)
(ii) a × (b × c) – (a × b) × c (Associative property of multiplication)
Solution:
Extra Questions for Class 8 Maths Rational Numbers Q21
Extra Questions for Class 8 Maths Rational Numbers Q21.1

Rational Numbers Class 8 Extra Questions Higher Order Thinking Skills (HOTS)

Question 22.
Rajni had a certain amount of money in her purse. She spent ₹ 10\(\frac { 1 }{ 4 }\) in the school canteen, bought a gift worth ₹ 25\(\frac { 3 }{ 4 }\) and gave ₹ 16\(\frac { 1 }{ 2 }\) to her friend. How much she have to begin with?
Solution:
Amount given to school canteen = ₹ 10\(\frac { 1 }{ 4 }\)
Amount given to buy gift = ₹ 25\(\frac { 3 }{ 4 }\)
Amount given to her friend = ₹ 16\(\frac { 1 }{ 2 }\)
To begin with Rajni had
Extra Questions for Class 8 Maths Rational Numbers Q22

Question 23.
One-third of a group of people are men. If the number of women is 200 more than the men, find the total number of people.
Solution:
Number of men in the group = \(\frac { 1 }{ 3 }\) of the group
Number of women = 1 – \(\frac { 1 }{ 3 }\) = \(\frac { 2 }{ 3 }\)
Difference between the number of men and women = \(\frac { 2 }{ 3 }\) – \(\frac { 1 }{ 3 }\) = \(\frac { 1 }{ 3 }\)
If difference is \(\frac { 1 }{ 3 }\), then total number of people = 1
If difference is 200, then total number of people
= 200 ÷ \(\frac { 1 }{ 3 }\)
= 200 × 3 = 600
Hence, the total number of people = 600

Question 24.
Fill in the blanks:
(a) Numbers of rational numbers between two rational numbers is ……….
Extra Questions for Class 8 Maths Rational Numbers Q24
Solution:
(a) Countless
(b) \(\frac { 6 }{ 11 }\)
(c) \(\frac { -3 }{ 2 }\)
(d) \(\frac { 3 }{ 5 }\)
(e) Commutative
(f) associative
(g) equivalent
(h) \(\frac { 3 }{ 11 }\)

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Extra Questions for Class 8 Maths

NCERT Solutions for Class 8 Maths