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NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2

In Mathematics, a rational number can be described as a number that can be expressed as a fraction of two integers, where the denominator is not equal to zero. Put differently, any fraction where the numerator and denominator are integers falls under the category of rational numbers. To delve further, let's explore the NCERT Solutions of the chapter.

NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2

Let's have a look at NCERT Solutions of Rational Numbers!

Try These

Q1. Write the rational number for each point labelled with a letter.

NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2
NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2 

Ans: 
(i) Here, the rational number for the point A is 1/5
The rational number for the point B is 4/5
The rational number for the point C is 5/5 or 1
The rational number for the point D is 8/5
The rational number for the point E is 9/5

(ii) The rational number for:
The point is F -2/6 or 1/3
The point G is -5/6
The point H is -7/6
The point I is -8/6 or -43
The point J is -11/6

Exercise 1.2

Q.1. Represent these numbers on the number line.
(i) 7/4
(ii) - 5/6
Difficulty level: Medium

Reasoning: The positive numbers are on the right of 0 and negative numbers are represented on the left of 0 in the number line. The denominator of the rational number indicates the number of equal parts into which the first unit has to be divided whereas the numerator indicates as to how many of these parts are to be taken into consideration.

Solution:
7/4 The first unit has to be divided by 4 parts. We make 7 markings of distance
1/4 Each on the right of 0 and starting from 0. The seventh marking represents 7/4

Diagram

NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2

-5/6 The first unit has to be divided into 6 parts. We make 5 markings of distance 1/6 each on the left of 0 and starting from 0.
The fifth marking represents 5/6 left side of 0.

DiagramNCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2


Q2. Represent NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2on the number line.

Difficulty level: Medium

Reasoning: The negative numbers are represented on the left of 0 in the number line. The denominator of the rational number indicates the number of equal parts into which the first unit has to be divided whereas the numerator indicates as to how many of these parts are to be taken into consideration.

Solution:

We make 9 marking of distance 1/11 each on the left of 0 and starting from 0.

The second marking represent - 2/11 which is represented as A in the line.

The fifth marking represent -5/11 representations B in the line.

The ninth marking represent -9/11 represented as C in the number line.

Diagram

NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2


Q.3. Write five rational numbers which are smaller than 2.
Difficulty level: Easy
What is the known/given?

Rational numbers.

What is the unknown?

The rational numbers between given rational numbers.

Reasoning: We can write infinitely many rational numbers lesser than number 2.

Solution:

Five rational numbers which are smaller than 2 are NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2

Q.4.  Find ten rational numbers between -2/5 and 1/2
Difficulty level: Medium

What is the known/given?

Rational numbers.

What is the unknown?

The rational numbers between given rational numbers.

Reasoning:

We can find infinitely many rational numbers between any two given rational numbers by taking the mean of the two rational numbers. Another method: We can make the denominator same for the two given rational numbers.

Solution:

NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2[multiplying both numerator and denominator by 2]
NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2[multiplying both numerator and denominator by 5]

[Multiplying both numerators and denominators by the same number]
Now, there are 9 rational numbers between -4/10 and 5/10, but we need 10 numbers. So, we should again multiply both numerator and denominator by 2 in the two rational numbers -4/10 and 5/10
NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2

The ten rational numbers between -2/5 and 1/2 which can be taken as.
NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2
[There are many more such rational numbers.]


Q.5. Find five rational numbers between,

(i) 2/3 and 4/5
(ii) -3/2 and 5/3
(iii) 1/4 and 1/2
Difficulty level: Medium
What is the known/given?

Rational numbers.

What is the unknown?

The rational numbers between given rational numbers.

Reasoning: We can find infinitely many rational numbers between any two given rational numbers by taking the mean of the two rational numbers.
Another method: We can make the denominator same for the two given rational numbers.

Solution:

(i) 2/3 and 4/5

NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2[multiplying both numerator and denominator by 20]

NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2[multiplying both numerator and denominator by 12]

Answer: The five rational numbers between 2/3 and 4/5 that can be taken are:
NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2

Solution:
(ii) NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2

NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2[multiplying both numerator and denominator by 3]
NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2[multiplying both numerator denominator by 2]

Answer:

∴ The five rational numbers between -3/2 and 5/3 that can be taken are:
NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2
[There can be more such rational numbers]

(iii) Solution:

1/4 and 1/2
NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2[multiplying both numerator and denominator by 8]
NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2[multiplying both numerator and denominator by 16]

Answer:

Thus, five rational numbers between 1/2 and 1/4 that can be taken are:
NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2


Q.6. Write five rational numbers greater than –2.

Difficulty level: Medium

What is the known/given?

Rational numbers.

What is the unknown?

The rational numbers between given rational numbers.

Reasoning: We can find infinitely many rational numbers between any two given rational numbers by taking the mean of the two rational numbers. Another method: We can make the denominator same for the two given rational numbers.

Solution:

Some of the five rational numbers greater than – 2 are NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2

[There can be more such rational numbers]


Q.7. Find the rational numbers between 3/5 and 3/4
Difficulty level: Medium

What is the known/given?

Rational numbers.

What is the unknown?

The rational numbers between given rational numbers.

Reasoning: We can find infinitely many rational numbers between any two given rational numbers by taking the mean of the two rational numbers. Another method: We can make the denominator same for the two given rational numbers.

Solution:

NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2[multiplying both numerator and denominator by 32]
NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2[multiplying both numerator and denominator by 40]

Answer:

Thus, ten rational numbers between 3/5 and 3/4 that can be written are:
NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2
[There can be many more such rational numbers]

The document NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2 is a part of the Class 8 Course NCERT Textbooks & Solutions for Class 8.
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FAQs on NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers- 2

1. What are rational numbers?
Ans. Rational numbers are numbers that can be expressed in the form of p/q, where p and q are integers and q is not equal to zero.
2. What is the difference between a rational and an irrational number?
Ans. Rational numbers can be expressed in the form of p/q, whereas irrational numbers cannot be expressed in this form. Irrational numbers are decimal numbers that do not terminate or repeat.
3. How can we add and subtract rational numbers?
Ans. To add or subtract rational numbers, we need to have the same denominators. We can find the common denominator and then add or subtract the numerators accordingly.
4. How can we multiply and divide rational numbers?
Ans. To multiply rational numbers, we simply multiply the numerators and denominators separately. To divide rational numbers, we multiply the first number by the reciprocal of the second number.
5. How can we represent rational numbers on a number line?
Ans. We can represent rational numbers on a number line by marking the point that corresponds to the fraction p/q. The number line can be divided into equal parts and the fraction can be placed at the appropriate point.
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