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NCERT Solutions for Class 8 Maths Chapter 1: Rational Numbers - Exercise 1.1

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Class 8 Maths Chapter 1 NCERT Solutions - Ex 1.1

NCERT Solutions for Class 8 Maths Chapter 1 has always been the most preferred aid that helps in scoring satisfactory grades in the examination. Vedantu's NCERT Class 8 Maths Chapter 1 Solutions help students to hold a good grasp over the subject by allowing them a deep conceptual understanding of the same. When it comes to getting a helping hand for brainstorming subjects like mathematics, you can surely go for Vedantu’s NCERT Math Solution for Class 8 Chapter 1 PDF download option.


Class:

NCERT Solutions for Class 8

Subject:

Class 8 Maths

Chapter Name:

Chapter 1 - Rational Numbers

Exercise:

Exercise - 1.1

Content-Type:

Text, Videos, Images and PDF Format

Academic Year:

2023-24

Medium:

English and Hindi

Available Materials:

  • Chapter Wise

  • Exercise Wise

Other Materials

  • Important Questions

  • Revision Notes



Download NCERT Solutions for Class 8 Maths to help you to revise the complete syllabus and score more marks in your examinations.  NCERT Solutions for all classes and subjects are also available. Science students who are looking for NCERT Solutions for Class 8 Science will also find the solutions curated by our Master Teachers really helpful.

Access NCERT Solutions for class 8 Maths Chapter 1 – Rational Numbers

Exercise 1.1

1. Using appropriate properties find:

i. \[\text{-}\dfrac{\text{2}}{\text{3}}\text{ }\!\!\times\!\!\text{ }\dfrac{\text{3}}{\text{5}}\text{+}\dfrac{\text{5}}{\text{2}}\text{-}\dfrac{\text{3}}{\text{5}}\text{ }\!\!\times\!\!\text{ }\dfrac{\text{1}}{\text{6}}\]

Ans: Given \[\text{-}\dfrac{\text{2}}{\text{3}}\text{ }\!\!\times\!\!\text{ }\dfrac{\text{3}}{\text{5}}\text{+}\dfrac{\text{5}}{\text{2}}\text{-}\dfrac{\text{3}}{\text{5}}\text{ }\!\!\times\!\!\text{ }\dfrac{\text{1}}{\text{6}}\]  

By using commutative property of rational numbers i.e $\text{a+b=b+a}$

\[\text{=-}\dfrac{\text{2}}{\text{3}}\text{ }\!\!\times\!\!\text{ }\dfrac{\text{3}}{\text{5}}\text{-}\dfrac{\text{3}}{\text{5}}\text{ }\!\!\times\!\!\text{ }\dfrac{\text{1}}{\text{6}}\text{+}\dfrac{\text{5}}{\text{2}}\]                     

Now, by using distributive property of rational numbers i.e $\text{a }\!\!\times\!\!\text{ b+b }\!\!\times\!\!\text{ c=b }\!\!\times\!\!\text{ }\left( \text{a+c} \right)$

\[\text{=}\left( \text{-}\dfrac{\text{3}}{\text{5}} \right)\text{ }\!\!\times\!\!\text{ }\left( \dfrac{\text{2}}{\text{3}}\text{+}\dfrac{\text{1}}{\text{6}} \right)\text{+}\dfrac{\text{5}}{\text{2}}\]                  

\[\text{=}\left( \text{-}\dfrac{\text{3}}{\text{5}} \right)\text{ }\!\!\times\!\!\text{ }\left( \dfrac{\text{2 }\!\!\times\!\!\text{ 2+1}}{\text{6}} \right)\text{+}\dfrac{\text{5}}{\text{2}}\]

\[\text{=}\left( \text{-}\dfrac{\text{3}}{\text{5}} \right)\text{ }\!\!\times\!\!\text{ }\left( \dfrac{\text{5}}{\text{6}} \right)\text{+}\dfrac{\text{5}}{\text{2}}\]

\[\text{=}\left( \text{-}\dfrac{\text{3}}{\text{6}} \right)\text{+}\dfrac{\text{5}}{\text{2}}\]

\[\text{=}\left( \dfrac{\text{-3+5 }\!\!\times\!\!\text{ 3}}{\text{6}} \right)\]

\[\text{=}\left( \dfrac{\text{-3+15}}{\text{6}} \right)\]

\[\text{=}\dfrac{\text{12}}{\text{6}}\]

\[\text{=2}\]

ii. \[\dfrac{\text{2}}{\text{5}}\text{ }\!\!\times\!\!\text{ }\left( \text{-}\dfrac{\text{3}}{\text{7}} \right)\text{-}\dfrac{\text{1}}{\text{6}}\text{ }\!\!\times\!\!\text{ }\dfrac{\text{3}}{\text{2}}\text{+}\dfrac{\text{1}}{\text{14}}\text{ }\!\!\times\!\!\text{ }\dfrac{\text{2}}{\text{5}}\]

Ans: Given \[\dfrac{\text{2}}{\text{5}}\text{ }\!\!\times\!\!\text{ }\left( \text{-}\dfrac{\text{3}}{\text{7}} \right)\text{-}\dfrac{\text{1}}{\text{6}}\text{ }\!\!\times\!\!\text{ }\dfrac{\text{3}}{\text{2}}\text{+}\dfrac{\text{1}}{\text{14}}\text{ }\!\!\times\!\!\text{ }\dfrac{\text{2}}{\text{5}}\]

By using commutative property of rational numbers i.e $\text{a+b=b+a}$

\[\text{=}\dfrac{\text{2}}{\text{5}}\text{ }\!\!\times\!\!\text{ }\left( \text{-}\dfrac{\text{3}}{\text{7}} \right)\text{+}\dfrac{\text{1}}{\text{14}}\text{ }\!\!\times\!\!\text{ }\dfrac{\text{2}}{\text{5}}\text{-}\dfrac{\text{1}}{\text{6}}\text{ }\!\!\times\!\!\text{ }\dfrac{\text{3}}{\text{2}}\]

Now, by using distributive property of rational numbers i.e $\text{a }\!\!\times\!\!\text{ b+b }\!\!\times\!\!\text{ c=b }\!\!\times\!\!\text{ }\left( \text{a+c} \right)$

\[\text{=}\dfrac{\text{2}}{\text{5}}\text{ }\!\!\times\!\!\text{ }\left( \text{-}\dfrac{\text{3}}{\text{7}}\text{+}\dfrac{\text{1}}{\text{14}} \right)\text{-}\dfrac{\text{1}}{\text{4}}\]                          

\[\text{=}\dfrac{\text{2}}{\text{5}}\text{ }\!\!\times\!\!\text{ }\left( \dfrac{\text{-3 }\!\!\times\!\!\text{ 2+1}}{\text{14}} \right)\text{-}\dfrac{\text{1}}{\text{4}}\]

\[\text{=}\dfrac{\text{2}}{\text{5}}\text{ }\!\!\times\!\!\text{ }\left( \dfrac{\text{-5}}{\text{14}} \right)\text{-}\dfrac{\text{1}}{\text{4}}\]

\[\text{=-}\dfrac{\text{1}}{\text{7}}\text{-}\dfrac{\text{1}}{\text{4}}\]

\[\text{=}\dfrac{\text{-4-7}}{\text{28}}\]

  \[\text{=}\dfrac{\text{-11}}{\text{28}}\]

2. Write the additive inverse of each of the following:

i. \[\dfrac{\text{2}}{\text{8}}\]

Ans: Since, additive inverse of $\dfrac{\text{a}}{\text{b}}\text{=}\dfrac{\text{-a}}{\text{b}}$. We know that an additive inverse is a number which on adding in the given number gives zero. Since we add the \[\dfrac{\text{-2}}{\text{8}}\] with \[\dfrac{\text{2}}{\text{8}}\] as $\dfrac{2}{8}+\dfrac{-2}{8}=\dfrac{2-2}{8}$ gives zero.

Therefore, additive inverse of  \[\dfrac{\text{2}}{\text{8}}\]is \[\text{-}\dfrac{\text{2}}{\text{8}}\].

ii. \[\text{-}\dfrac{\text{5}}{\text{9}}\]

Ans: Since, additive inverse of $\text{-}\dfrac{\text{a}}{\text{b}}\text{=}\dfrac{\text{a}}{\text{b}}$. We know that an additive inverse is a number which on adding in the given number gives zero. Since we add the \[\dfrac{\text{5}}{\text{9}}\] with \[\dfrac{\text{-5}}{\text{9}}\] as $\dfrac{-5}{9}+\dfrac{5}{9}=\dfrac{5-5}{9}$ gives zero.

Therefore, additive inverse of  \[\text{-}\dfrac{\text{5}}{\text{9}}\]is \[\dfrac{\text{5}}{\text{9}}\].

iii. \[\dfrac{\text{-6}}{\text{-5}}\]

Ans: Since, additive inverse of $\dfrac{\text{-a}}{\text{-b}}\text{=-}\dfrac{\text{a}}{\text{b}}$. We know that an additive inverse is a number which on adding in the given number gives zero. Since we add the \[\dfrac{\text{-6}}{\text{-5}}\] with \[\dfrac{\text{-6}}{\text{5}}\] as $\dfrac{-6}{-5}+\dfrac{-6}{5}=\dfrac{6-6}{5}$ gives zero.

Therefore, additive inverse of \[\dfrac{\text{-6}}{\text{-5}}\]is \[\text{-}\dfrac{\text{6}}{\text{5}}\].

iv. \[\dfrac{\text{2}}{\text{-9}}\]

Ans: Since, additive inverse of $\dfrac{\text{a}}{\text{-b}}\text{=}\dfrac{\text{a}}{\text{b}}$. We know that an additive inverse is a number which on adding in the given number gives zero. Since we add the \[\dfrac{\text{2}}{\text{-9}}\] with \[\dfrac{\text{2}}{\text{9}}\] as $\dfrac{2}{9}+\dfrac{-2}{9}=\dfrac{2-2}{9}$ gives zero.

Therefore, additive inverse of  \[\dfrac{\text{2}}{\text{-9}}\] is  \[\dfrac{\text{2}}{\text{9}}\].

v. \[\dfrac{\text{19}}{\text{-6}}\]

Ans: Since, additive inverse of $\dfrac{\text{a}}{\text{-b}}\text{=}\dfrac{\text{a}}{\text{b}}$. We know that an additive inverse is a number which on adding in the given number gives zero. Since we add the \[\dfrac{\text{19}}{\text{-6}}\] with \[\dfrac{\text{19}}{\text{6}}\] as $-\dfrac{19}{6}+\dfrac{19}{6}=\dfrac{19-9}{6}$ gives zero.

Therefore, additive inverse of  \[\dfrac{\text{19}}{\text{-6}}\] is \[\dfrac{\text{19}}{\text{6}}\].

3. Verify that \[\text{-(-x)=x}\] for.

i. \[\text{x=}\dfrac{\text{11}}{\text{15}}\]

Ans: The additive inverse of  \[\text{x=}\dfrac{\text{11}}{\text{15}}\] is \[\text{-x=-}\dfrac{\text{11}}{\text{15}}\] 

Now,  \[\dfrac{\text{11}}{\text{15}}\text{+}\left( \text{-}\dfrac{\text{11}}{\text{15}} \right)\text{=0}\]

Thus , it represents that the additive inverse of \[\text{-}\dfrac{\text{11}}{\text{15}}\] is \[\dfrac{\text{11}}{\text{15}}\] i.e., \[\text{-}\left( \text{-}\dfrac{\text{11}}{\text{15}} \right)\text{=}\dfrac{\text{11}}{\text{15}}\] .

Hence, \[\text{-(-x)=x}\] holds for \[\text{x=}\dfrac{\text{11}}{\text{15}}\].

ii. \[\text{x=-}\dfrac{\text{13}}{\text{17}}\]

Ans: The additive inverse of \[\operatorname{x}=-\dfrac{13}{17}\] is \[\text{-x=}\dfrac{\text{13}}{\text{17}}\]

Now,  \[\text{-}\dfrac{\text{13}}{\text{17}}\text{+}\dfrac{\text{13}}{\text{17}}\text{=0}\]

Thus , it represents that the additive inverse of \[\dfrac{\text{13}}{\text{17}}\] is \[\text{-}\dfrac{\text{13}}{\text{17}}\] i.e., \[\text{-}\left( \text{-}\dfrac{\text{13}}{\text{17}} \right)\text{=}\dfrac{\text{13}}{\text{17}}\] .

Hence, \[\text{-(-x)=x}\] holds for \[\text{x=-}\dfrac{\text{13}}{\text{17}}\].

4. Find the multiplicative inverse of the following.

i. \[\text{-13}\]

Ans: Since, multiplicative inverse of $\text{-a=-}\dfrac{\text{1}}{\text{a}}$.

Therefore, the multiplicative inverse of  \[\text{-13}\] is \[\text{-}\dfrac{\text{1}}{\text{13}}\].

ii. \[\text{-}\dfrac{\text{13}}{\text{19}}\]

Ans: Since, multiplicative inverse of $\text{-}\dfrac{\text{a}}{\text{b}}\text{=-}\dfrac{\text{b}}{\text{a}}$.

Therefore, multiplicative inverse of  \[\text{-}\dfrac{\text{13}}{\text{19}}\] is \[\text{-}\dfrac{\text{19}}{\text{13}}\].

iii. \[\dfrac{\text{1}}{\text{5}}\]

Ans: Since, multiplicative inverse of $\dfrac{\text{a}}{\text{b}}\text{=}\dfrac{\text{b}}{\text{a}}$.

Therefore, the multiplicative inverse of  \[\dfrac{\text{1}}{\text{5}}\] is \[\text{5}\].

iv. \[\text{-}\dfrac{\text{5}}{\text{8}}\text{ }\!\!\times\!\!\text{ -}\dfrac{\text{3}}{\text{7}}\]

Ans: It can be written as \[\text{-}\dfrac{\text{5}}{\text{8}}\text{ }\!\!\times\!\!\text{ -}\dfrac{\text{3}}{\text{7}}\text{=}\dfrac{\text{15}}{\text{56}}\].

Since, multiplicative inverse of $\dfrac{\text{a}}{\text{b}}\text{=}\dfrac{\text{b}}{\text{a}}$.

Therefore, multiplicative inverse of  \[\text{-}\dfrac{\text{5}}{\text{8}}\text{ }\!\!\times\!\!\text{ -}\dfrac{\text{3}}{\text{7}}\] is \[\dfrac{\text{56}}{\text{15}}\].

v. \[\text{-1 }\!\!\times\!\!\text{ -}\dfrac{\text{2}}{\text{5}}\]

Ans: It can be written as\[\text{-1 }\!\!\times\!\!\text{ -}\dfrac{\text{2}}{\text{5}}\text{=}\dfrac{\text{2}}{\text{5}}\].

Since, multiplicative inverse of $\dfrac{\text{a}}{\text{b}}\text{=}\dfrac{\text{b}}{\text{a}}$.

Therefore, multiplicative inverse of  \[\text{-1 }\!\!\times\!\!\text{ -}\dfrac{\text{2}}{\text{5}}\] is \[\dfrac{\text{5}}{\text{2}}\].

vi. \[\text{-1}\]

Ans: Since, multiplicative inverse of $\text{-}\dfrac{\text{a}}{\text{b}}\text{=-}\dfrac{\text{b}}{\text{a}}$.

Therefore, the multiplicative inverse of  \[\text{-1}\] is \[\text{-1}\].

5. Name the property under multiplication used in each of the following:

i. \[\dfrac{\text{-4}}{\text{5}}\text{ }\!\!\times\!\!\text{ 1=1}\!\!\times\!\!\text{}\dfrac{\text{-4}}{\text{5}}\text{=}\dfrac{\text{-4}}{\text{5}}\]

Ans: Since, after multiplying by \[\text{1}\] , we are getting the same number.

Therefore, \[\text{1}\] is the multiplicative identity.

ii. \[\text{-}\dfrac{\text{13}}{\text{17}}\text{ }\!\!\times\!\!\text{ }\dfrac{\text{-2}}{\text{7}}\text{=}\dfrac{\text{-2}}{\text{7}}\text{ }\!\!\times\!\!\text{ }\dfrac{\text{-13}}{\text{17}}\]

Ans: Since, $\text{a }\!\!\times\!\!\text{ b=b }\!\!\times\!\!\text{ a}$.

Therefore, its Commutative property.


iii. \[\text{-}\dfrac{\text{19}}{\text{29}}\text{ }\!\!\times\!\!\text{ -}\dfrac{\text{29}}{\text{19}}\text{=1}\]

Ans: Since, \[\text{a }\!\!\times {\dfrac{1}{a}} \text{=1}\].

Therefore, the property is Multiplicative inverse.

6. Multiply \[\dfrac{\text{6}}{\text{13}}\] by the reciprocal of \[\text{-}\dfrac{\text{7}}{\text{16}}\]

Ans: Reciprocal of \[\text{-}\dfrac{\text{7}}{\text{16}}\]  is \[\text{-}\dfrac{\text{16}}{\text{7}}\].

Thus, \[\dfrac{\text{6}}{\text{13}}\text{ }\!\!\times\!\!\text{ -}\dfrac{\text{16}}{\text{7}}\]

 \[\text{=-}\dfrac{\text{96}}{\text{91}}\].

7. Tell what property allows you to compute \[\dfrac{\text{1}}{\text{3}}\text{ }\!\!\times\!\!\text{ }\left( \text{6 }\!\!\times\!\!\text{ }\dfrac{\text{4}}{\text{3}} \right)\] as \[\left( \dfrac{\text{1}}{\text{3}}\text{ }\!\!\times\!\!\text{ 6} \right)\text{ }\!\!\times\!\!\text{ }\dfrac{\text{4}}{\text{3}}\].

Ans: Since, $\text{a }\!\!\times\!\!\text{ }\left( \text{b }\!\!\times\!\!\text{ c} \right)\text{=}\left( \text{a }\!\!\times\!\!\text{ b} \right)\text{ }\!\!\times\!\!\text{ c}$ .

Therefore, its associative property.

8. Is \[\dfrac{\text{8}}{\text{9}}\] the multiplicative inverse of \[\text{-1}\dfrac{\text{1}}{\text{8}}\]? Why or why not?

Ans: We know, If it is the multiplicative inverse, then the product should be \[\text{1}\].

Now,

\[\dfrac{\text{8}}{\text{9}}\text{ }\!\!\times\!\!\text{ }\left( \text{-1}\dfrac{\text{1}}{\text{8}} \right)\text{=}\dfrac{\text{8}}{\text{9}}\text{ }\!\!\times\!\!\text{ }\left( \text{-}\dfrac{\text{9}}{\text{8}} \right)\]

\[\text{=-1}\] 

Since, the product is not \[\text{1}\].

Therefore, \[\dfrac{\text{8}}{\text{9}}\] is not the multiplicative inverse of \[\text{-1}\dfrac{\text{1}}{\text{8}}\].

9. Is \[\text{0}\text{.3}\] the multiplicative inverse of \[\text{3}\dfrac{\text{1}}{\text{3}}\]? Why or why not?

Ans: We know, If it is the multiplicative inverse, then the product should be \[\text{1}\].

Now,

\[\text{0}\text{.3 }\!\!\times\!\!\text{ 3}\dfrac{\text{1}}{\text{3}}\text{=0}\text{.3 }\!\!\times\!\!\text{ }\dfrac{\text{10}}{\text{3}}\]

\[\text{=}\dfrac{\text{3}}{\text{10}}\text{ }\!\!\times\!\!\text{ }\dfrac{\text{10}}{\text{3}}\]

\[\text{=1}\]

Since, the product is \[\text{1}\] .

Therefore, \[\text{0}\text{.3}\] is the multiplicative inverse of \[\text{3}\dfrac{\text{1}}{\text{3}}\] .

10. Write:

i. The rational number that does not have a reciprocal.

Ans: \[\text{0}\] is a rational number but its reciprocal is not defined.

ii. The rational numbers that are equal to their reciprocals.

Ans: \[\text{1}\] and \[\text{-1}\] are the rational numbers that are equal to their reciprocals.

iii. The rational number that is equal to its negative.

Ans: \[\text{0}\] is the rational number that is equal to its negative.

11. Fill in the blanks.

i. Zero has __________ reciprocal.

Ans: No

ii. The numbers __________ and __________ are their own reciprocals.

Ans: \[\text{1,-1}\]

iii. The reciprocal of \[\text{-5}\] is __________.

Ans: \[\text{-}\dfrac{\text{1}}{\text{5}}\]

iv. Reciprocal of \[\dfrac{\text{1}}{\text{x}}\], where \[\text{x}\ne \text{0}\] is __________.

Ans: \[\text{x}\]

v. The product of two rational numbers is always a __________.

Ans: Rational number

vi. The reciprocal of a positive rational number is __________.

Ans: Positive rational number 

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Important Topics

Here are the important topics of the chapter:


1. Rational numbers on a number line

We draw a line and mark a point O on it to symbolize the rational number zero in order to represent rational numbers on the number line. Positive rational numbers are shown on the right side of 0 and negative rational numbers are shown on the left side of 0.


2. Rational numbers between any two given rational numbers 

Any pair of rational numbers will have an infinite number of rational numbers in between them.


3. Natural number, whole number, integer and rational number 

  • Natural numbers include the numbers 1, 2, 3, 4, and so on. They are the numbers you normally count, and they will go on infinitely.

  • Whole numbers are all natural numbers, including 0. For example, 0, 1, 2, 3, 4,...

  • Integers include all whole integers and their negatives, such as...-4, -3, -2, -1, 0,1, 2, 3, 4,... The rational numbers include all integers.

  • A rational number is one that can be expressed as the quotient p/q of two integers where q ≠ 0.


4. Closure Property 

The closure property is true for whole number addition and multiplication. The sum of any two whole numbers will always be a whole number, i.e. if a and b are any two whole numbers, a + b will be a whole number.


5. Commutativity 

The commutative property states that the numbers on which we operate can be moved or swapped from their current position without affecting the answer. This property applies to addition and multiplication but not subtraction and division. 


6. Associativity 

The Associative property states that when three or more numbers are added or multiplied, the outcome (sum or product) remains the same regardless if the numbers are arranged differently. Brackets are used for grouping in this case. 

This is expressed as

  • a × (b × c) = (a × b) × c 

  • a + (b + c) = (a + b) + c


7. Additive identity 

The term additive implies that this identity is used while performing the operation of addition. According to additive identity, if a number is added to zero, the resultant is the number itself.


8. Multiplicative identity 

When executing a multiplication operation, the multiplicative identity is used. The concept of multiplicative identity implies that if a number is multiplied by one, the product is the number itself.


9. Distributive property 

According to the distributive property, an expression of the form A (B + C) can be solved as A (B + C) = AB + AC. This distributive law also applies to subtraction and is written as A (B - C) = AB - AC. This signifies that operand A is shared by the other two operands.


NCERT Maths Chapter 1 Is About Rational Numbers.

NCERT Chapter 1 for Class 8: Rational Numbers: 

A rational number is a number, which is a fraction of p where and q are integers, and q does not equal to 0. A rational number p/q is asserted to have numerator p and denominator q, respectively. Those numbers which are not rational are termed irrational numbers. The real line consists of all the rational and irrational numbers.

The collection of all rational numbers is correlated as the "rationals" and forms a field that is characterized by Q.The symbol derived from the German word called Quotient, which can be translated as "ratio.”

Some of the examples of rational numbers are-7, 0, 1, 1/2, 22/7, and so on. 

So we already discussed the basic operations relating to rational numbers. 

In the following chapter, you will explore some properties of operations on the different types of the number we have seen so far.

Different Variations Of Rational Numbers -

  1. The numeral which can be written in the form of p/q, and where p and q are integers and q does not equal to 0 is called a rational number. 

  2. For any rational number a, a/0 is not established.

The techniques for addition and multiplication are

  • Commutative

  • Associative

Study rational numbers include

  1. Addition

  2. Subtraction

  3. Multiplication

  4. Division

Vedantu has come up with solved examples for you to understand the topic. They have also provided you the role of 0 and the role of 1 with a quick description:- 

0 is an Additive individual for rational numbers, while 1 is Multiplicative individual for rational numbers.

Another topic that is included in is the Negative of several inverse additions. Additionally, in the following topic, reciprocal or multiplicative inverse, distributive of multiplication over addition for rational numbers are also elaborated.

Exercise 1.2 Is Based On -  

The manifestation of Rational Numbers on the Number Line and Rational Numbers between Two Rational Numbers

Properties:

  • Any rational number can be characterized by the number line

  • Between any two given rational numbers, there are infinite rational numbers

Rational numbers can easily be characterized on a number line by following some easy steps. Manifestation on number line depends upon the variety of rational fraction, which is to be characterized on the line. We should not forget to check the negative and positive aspects of the rational number before moving to the number line.

The right side of the zero on the number line is always represented by the positive rational numbers. But the left side of zero on the number line is always characterized as the negative aspect of rational numbers. 

Beneath are some of the categories of rational numbers and methods to characterize them on the number line:

I. Proper Fraction:

When the numerator is smaller than the denominator, such numbers are called proper fractions. Such portions only exist between zero and one. Proper fractions are smaller than one and bigger than zero. So, proper fractions always subsist between zero and one on a number line.

II. Improper Fractions:

When the numerator of the fraction is always greater than its denominator, those numbers are called Improper Fractions. Since the numerator is bigger than the denominator, the number will be greater than one. To know about such rational fractions on the number line, we modify the improper fraction with the mixed fractions to know between which integers the fraction will lie upon.

Finally, in Class 8 NCERT Maths Chapter 1, you will study the application of Closer properties of addition, subtraction, and Multiplication. You will also go through Commutative and Associative properties under the addition and multiplication. In the following operations, you need to check whether Individuality, Inverse exist or not just like additive individuality or multiplicative inverse. You should have an understanding of how should the rational numbers be characterized on a number line and find the rational number between any two given rational numbers as there are infinite rational numbers between two numbers.


NCERT Solutions for Class 8 Maths Chapter 1 Other Exercises

Chapter 1 - Rational Numbers Other Exercises in PDF Format

Exercise 1.2

7 Questions & Solutions

 

Along with this, students can also view additional study materials provided by Vedantu, for Class 8 Maths


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FAQs on NCERT Solutions for Class 8 Maths Chapter 1: Rational Numbers - Exercise 1.1

1. From where can I get the Class 8 Maths Chapter 1 NCERT Solutions?

NCERT solutions are available for all topics on Vedantu, India's top online learning platform, to assist students in getting ready for their math exams. These solutions were created by top topic specialists in accordance with the most recent CBSE curriculum. The solutions are presented step-by-step and are meticulously arranged and correct. You may receive the Class 8 Maths Chapter 1 NCERT Solutions for free by going to the Vedantu official website (Vedantu.com) or by downloading the Vedantu mobile application.

2. How many topics are there in Chapter 1 Rational number of NCERT Class 8 Maths?

There are many topics and subtopics in Chapter 1 of the rational number of NCERT Class 8,  and these are listed below:

  • Introduction

  • 1.2) Properties of Rational Numbers

  1. Closure

  2. Commutativity

  3. Associativity

  4. The role of zero

  5. The role of 1

  6. Negative of a number

  7. Reciprocal

  8. Distributivity of multiplication over addition for rational numbers.

  • Representation of Rational Numbers on the Number Line

  • Rational Numbers between Two Rational Numbers

3. How many questions are there in Class 8 Maths Chapter 1?

There are 18 questions in Chapter 1 of Class 8 Math on Rational Numbers. NCERT questions can be viewed as a helpful tool because they are filled with tactics that will enable pupils to get better outcomes. For the purpose of assisting students in their exam preparation, Vedantu offers NCERT Solutions for all the chapters of Class 8 math at no charge. You can download these solutions in PDF format from Vedantu's official website and mobile application.

4. What concepts are being discussed in chapter 1 Rational number of Class 8 Maths?

The types of rational numbers, their properties of addition and multiplication, their additive identities and inverses, and the last rational number on the number line were all covered in NCERT Class 8 Math. Because there are numerous questions in this chapter in both the board final exams and other competitive exams like the NTSE and other Class 8 level exams, students should thoroughly understand each concept covered in this chapter.

5. How can I revise Class 8 Maths Chapter 1 Maths?

For students taking any test or other competitive exam of class 8 level , constant review is crucial during the preparation phase. After finishing each chapter, move on to the corresponding exercises to practise solving the corresponding problems. Up until your final exam, frequently practise those problems. You can refer to the Class 8 Math revision notes created by the subject-matter specialists at Vedantu, which will assist you in remembering the equations and distinctive characteristics of each conic section.