# NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers (EX 1.1) Exercise 1.1

The NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 by Extramarks assists students to grasp the principles of rational numbers. Understanding the topics introduced in Class 8 is crucial since they are continued in Classes 9 and 10. It is advised to answer the questions given at the end of each chapter with the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 in order to do well on the Class 8 Mathematics exam. Students can understand all the concepts related to rational numbers thanks to the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1. Rational numbers are those that have a representation in the ratio p/q, where q is not equal to zero. One of the most important concepts in Mathematics class 8 is this one. A Rational Number is any fraction with a non-zero denominator. Readers must first simplify Rational Numbers in order to express them on a number line. As they work through the exercise questions, students can use the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 for any topic clarification or doubt clearing. The NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 should be practiced by students in order to more easily understand the key concepts.

The NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 also explains how to represent a rational number on a number line. To learn more about Rational Numbers and the concepts they encompass, students are suggested to read and practice the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1. They are encouraged to successfully practice with the help of the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 in order to perform well on the board exam. On the Extramarks website and mobile application, all the necessary study material, along with the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 with a thorough step-by-step explanation are available. Rational numbers and their uses are covered in NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1. A deep insight into the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 principles helps students not only achieve high grades but also lay the groundwork for learning new ideas presented in Class 8.

## Class 8 Maths Chapter 1 NCERT Solutions (Include PDF)

Before going through the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 to the significant problems, students should familiarise themselves with the following list of key concepts from NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 based on Rational Numbers. Here is the detailed analysis of Class 8 Maths Chapter 1 of which the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 are a part of:

• Introduction
• 1.2 Properties of Rational Numbers
• Closure\sCommutativity
• Associativity
• The role of zero
• 1’s function as a negative number
• For rational numbers, reciprocal distributivity of multiplication over addition.
• Rational Numbers between Two Rational Numbers
• Rational Numbers Represented on the Number Line

## Access NCERT Solutions for Class 8 Maths Chapter 1 – Rational Numbers

How Rational Numbers behave under various Arithmetic Operation qualities, such as Closure, Commutativity, Distributivity, and more is one of the important ideas taught in the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1. Solving every question in the NCERT coursebook is the only way to understand the principles described above. The greatest feature is that students may obtain a pdf version of all the solutions, organised exercise-wise. On the Extramarks website and mobile application, links to the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 are provided.

### NCERT Maths Chapter 1 is about Rational Numbers

Regular practice is the cornerstone to perfecting any skill. Students should therefore periodically check the aforesaid links and work through the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 on their own. Once they have tried a particular task, they can double-check their responses, add up their scores, and clear up any confusion. The following NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 based on Rational Numbers offer a step-by-step breakdown of all the sums.

The Closure Property, Commutativity, Associativity, Distributive Property, Additive Inverse, Multiplicative Inverse, and determining whether they hold true for different arithmetic operations such as Addition, Simple Arithmetic, Multiplication, and Division are the topics covered in the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1. The NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 also cover how to display a Rational Number on a number line and how to find a Rational Number between two specified values.

There are 18 questions in the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 based on Rational Numbers. They can be categorised as simple quick-response sums, six as more difficult sums, and four as difficult difficulties. The NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 contains formulas that are crucial for comprehending the workings of Rational Numbers in greater detail. The majority of the formulas in the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 have connections to other attributes. In addition, students can look at how to find the Mean of two Rational Numbers so that they can identify a third Rational Number that falls between the two supplied values. Below are a few significant equations and properties from NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1:

• Closure Property: a + b, a – b, a × b results in a rational number.
• Commutative property: a + b = b + a; a × b = b × a.
• Associative property: a + (b + c) = (a + b) + c; a × (b × c) = (a × b) × c.
• Distributive property: a × (b + c) = ab + ac; a × (b – c) = ab – ac.

### NCERT Chapter 1 for Class 8: Rational Numbers:

The NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 demonstrates to students that numbers are the basis of Mathematics. Numbers can be categorised as Real, Whole, Natural, Rational, Irrational, and Complex numbers based on their types. Students have been accustomed to using Whole Numbers and Natural Numbers to solve equations in earlier Mathematics lessons. The NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 enable students to provide a thorough response to the problems.  With the help of the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 students can understand that a rational number is a number that can be written as a fraction or as p/q. Such a number also has a decimal expansion that is either terminating or non-terminating and recurring. The NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 describes the many properties of Rational Numbers.

Students are taught more about Rational Numbers in-depth by using the exercise questions that are covered in these NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1. The properties of Whole and Natural Numbers are reviewed, and students learn how to apply these ideas to Rational Numbers. As a result, NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 is ideal for providing students with a comprehensive understanding of Rational Numbers and their varieties. In the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 there are 11 questions based on Rational Numbers that can be broken down into fill-in-the-blank, intuitive and commutative sums. The majority of the solutions in the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 revolve around confirming certain properties, such as determining a number’s additive or multiplicative inverse, determining the property given an operation, and resolving statements based on certain Mathematical properties.

The NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 teaches children the proper way to use a formula so they may quickly and simply solve problems. Children can sharpen their logical and analytical abilities by completing this practice. Students will discover that they need to have a solid understanding of ideas like the multiplicative inverse, which asserts that the outcome of multiplying a Rational Number by its reciprocal is 1. Another intriguing idea is the Commutative Property, which states that the order in which Rational Numbers are added to or multiplied does not affect the outcome. Children can read the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 based on Rational Numbers, which are accessible in PDF format, to understand more about these outstanding qualities.

Since students are more accustomed to dealing with Whole or Natural Numbers, NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 can help the students with thorough preparation. However, students will discover that they can master these NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 quickly with a little work and dedication. It is recommended to read through the examples that have been solved before trying the exercise problems. Additionally, students need to have a solid foundation for each property and a comprehensive awareness of how to use them. Students can use NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 as the ideal resource to advance their understanding of Rational Numbers. Students will be experts at using Rational Numbers and their properties once they have finished answering the questions in this practice.

### Different Variations of Rational Numbers -Exercise 1.2

Questions in the NCERT Solutions for Class 8 Mathematics Chapter 1 Exercise 1.2 on Rational Numbers are designed to help students learn about Rational Numbers visually. The foundation of the first two puzzles is the representation of a Rational Integer on a number line. Students will have a solid understanding of the placement of Rational Numbers and how to compare two or more numbers by completing these sums. Exercise 1.2 from Chapter 1 of Class 8 Maths in NCERT Solutions aids children in developing their mathematical and visual skills.

Finding Rational Numbers that fall between two specified numbers is the focus of the final five questions. Between any two Rational Numbers, there are an endless number of Rational Numbers. As a result, this exercise also describes the several methods that can be used to locate such Integers. Solutions for Chapter 1 exercise 1.2 from the Class 8 Mathematics NCERT Solutions Rational Numbers are accessible in PDF format, which works on mobile devices and laptop screens.

Children get a great opportunity to learn about the number line through the carefully crafted questions, as well as how to use various strategies to find rationales between any two numbers. The exercises do not involve any formulas; instead, students must use their intelligence and Mathematical abilities. The ideas discussed in NCERT solutions Class 8 maths Chapter 1 exercise 1.2 should not be overlooked. Children must therefore review this practice at least twice in order to ace their exams.

 Chapter 1 – Rational Numbers Exercises Exercise 1.1 Addition, Subtraction, Multiplication and Division Questions & Solutions Exercise 1.2 Representation of Rational Numbers on the Number Line Questions & Solutions

### NCERT Solutions for Class 8 Maths Chapter 1 Other Exercises

Here are a few points to remember related to the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1:

• Basic operations on Rational Numbers have already been covered.
• Students will attempt to investigate some properties of operations on the various types of numbers they have encountered in the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1.

Students will explore the following operations on rational numbers:

2. Subtraction
3. Compounding
4. Division
• Both the associativity and commutativity concepts will be covered using the same operations.
• To help the students comprehend the subject, solved examples are provided.
• The roles of zero (0) and one (1) is then made obvious by briefly describing each.
• 0 is the Additive identity for rational numbers
• 1 is Multiplicative identity for rational numbers

The negative of a number or additive inverse is the subject of Section 1.2.6. In a later section of this chapter, the distributivity of multiplication over addition for rational numbers is described. 11 questions make up Exercise 1.1. The subjects covered in the next exercise, 1.2, are Rational Numbers between Two Rational Numbers and Rational Numbers Representation on the Number Line. These NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 will cover the concepts of Independence, Associativity, and Closure as they relate to Real Numbers, Integers, Whole Numbers, Rational Numbers, and Natural Numbers. The NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 deals with the relationship between zero and one, addition over multiplication, the Representation of Rational Numbers on the Number Line, and the search for rational numbers that fall between two rational numbers.

The NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 also discusses additive identity (zero) and multiplicative identity (one). There are two exercises in this chapter, with questions covering every subject covered in the chapter. Rational numbers are those used in a wide variety of mathematical applications, such as addition, subtraction, and multiplication, and are inherently closed with a wide variety of mathematical operations. NCERT Solutions for Class 8 Mathematics will assist students in solving the issues in the CBSE-recommended math textbook. To help pupils do better on tests, the NCERT Solutions for Class 8 breaks down the solutions into specific steps. The team of highly competent, experienced, and professional faculty at Extramarks have prepared the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1.

Students may rapidly understand all of the mathematical ideas and formulas with the aid of the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1. Extramarks has a staff of teachers who are available at all times to answer questions if students have any while studying the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 that Extramarks experts are providing. The NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 is an extremely important learning tool for understanding Rational Numbers. It is a crucial chapter for students to learn since it will be tested in examinations and because it will help them develop a foundational understanding of numbers. The division of the unit numbers system deals with Rational Numbers.

Rational numbers are ones that may be expressed as a fraction or in the form of a numerator (p) upon a denominator (q) where the denominator can take on any value other than 0 or, alternatively, as a p/q form where q 0 and p & q are Integers. It follows that all Integers fall into the category of Rational Numbers according to this definition. Students will examine Rational, Real, Whole, Integer, and Natural Numbers and their properties, such as Closure, Commutativity, and Associativity, in these NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1. There are two exercises and a total of 24 questions in this chapter. The NCERT Class 8 Maths Syllabus must be finished as early as possible by the students. Additionally, students should use the NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1. All  24 questions in Chapter 1 of Class 8 Mathematics for Rational Numbers have all the NCERT solutions available.

### NCERT Solutions for Class 8

Students in Class 8 should be well-versed in solutions to the NCERT textbook’s questions. Students can refer to the Class 8 Mathematics and Science NCERT Solutions here. The answers offered at Extramarks are highly accurate and provide thorough answers to every problem found in each chapter of Mathematics and Science. The answers and in-depth explanations have been created by subject-matter experts after considerable research to provide students with a reliable and acceptable source of NCERT Solutions. Students will be able to swiftly and easily learn the ideas by using the solutions for Class 8 NCERT Science and Mathematics. If students carefully study NCERT Solutions, they can quickly clear up all of their doubts.

Science and Mathematics are two areas that should take priority in a student’s academic life Therefore, it is crucial to emphasise on practising the problems and solutions in order to fully grasp any topics from the relevant chapters if students want to earn good grades and advance in their chosen careers. Students can try practising the questions and answers based on the Class 8 CBSE Syllabus by referring to the NCERT Books for Class 8 for more practice.

The chapter-by-chapter solutions in the NCERT Class 8 Solutions give students the key to unlocking their problem-solving abilities. The academic career of students will be significantly impacted by their choice of learning approach. These answers will assist them in answering the questions and cross-checking their responses at the same time. To assist students in fully comprehending the themes and concepts is the main goal of offering the ideal NCERT Solutions. Students benefit from having a solid foundation for higher grades because of this understanding.

Here is how students can prepare easily for their examinations with the assistance of the NCERT Solutions provided by Extramarks:

• Early planning: The best method to prevent any last-minute hastle and trauma is to begin planning as soon as the school year begins. Students will benefit from doing this if they give themselves adequate time to complete each topic and the NCERT Solutions well in advance. They can get their questions answered as soon as possible if they solve the solution far in advance.
• Review the curriculum: The first step to studying well is to go through the entire syllabus and highlight the key areas to be learned and ensuring that the NCERT solutions for the subjects that students find challenging or significant are solved.
• Understand the exam pattern: It is critical to comprehend the exam pattern that has been approved by the board for the exam that students will take. They will gain an understanding of which chapter is more important and can then help students focus more intently on its solutions.
• Regular study: For the purpose of being very familiar with the approach to problem-solving, regularly study the solutions in addition to the NCERT books.
• Revision: As the exam date approaches, review all of the NCERT Solutions to refresh the memory and brush up on the material.

Q.1 Using appropriate properties find:

$\begin{array}{l}\left(\mathrm{i}\right)\frac{-2}{3}×\frac{3}{5}+\frac{5}{2}-\frac{3}{5}×\frac{1}{6}\\ \left(\mathrm{ii}\right)\frac{2}{5}×\left(-\frac{3}{7}\right)-\frac{1}{6}×\frac{3}{2}+\frac{1}{14}×\frac{2}{5}\end{array}$

Ans

$\begin{array}{l}\text{(i)}\frac{-2}{3}×\frac{3}{5}+\frac{5}{2}-\frac{3}{5}×\frac{1}{6}\\ =\frac{-2}{3}×\frac{3}{5}-\frac{3}{5}×\frac{1}{6}+\frac{5}{2}\text{}\left[\text{By using Commutative property}\right]\\ =\left(-\frac{3}{5}\right)×\left(\frac{2}{3}+\frac{1}{6}\right)+\frac{5}{2}\text{}\left[\text{By using Distributive property}\right]\\ =\left(-\frac{3}{5}\right)×\left(\frac{4+1}{6}\right)+\frac{5}{2}\end{array}$

$\begin{array}{l}=\left(-\frac{3}{5}\right)×\left(\frac{5}{6}\right)+\frac{5}{2}\\ =\left(-\frac{3}{6}\right)+\frac{5}{2}\\ =\left(\frac{-3+15}{6}\right)=\frac{12}{6}=2\end{array}$

$\begin{array}{l}\text{(ii)}\frac{2}{5}×\left(-\frac{3}{7}\right)-\frac{1}{6}×\frac{3}{2}+\frac{1}{14}×\frac{2}{5}\\ =\frac{2}{5}×\left(-\frac{3}{7}\right)+\frac{1}{14}×\frac{2}{5}-\frac{1}{6}×\frac{3}{2}\text{}\left[\text{By using Commutative property}\right]\\ =\frac{2}{5}×\left(-\frac{3}{7}+\frac{1}{14}\right)-\frac{1}{4}\\ =\frac{2}{5}×\left(\frac{-6+1}{14}\right)-\frac{1}{4}\\ =\frac{2}{5}×\left(\frac{-5}{14}\right)-\frac{1}{4}\\ =\left(\frac{-2}{14}\right)-\frac{1}{4}\\ =\frac{-1}{7}-\frac{1}{4}\\ =\frac{-4-7}{28}=\frac{-11}{28}\end{array}$

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

$\left(\mathrm{i-}\right)\frac{2}{8}\left(\mathrm{ii}\right)\frac{-5}{9}\left(\mathrm{iii}\right)\frac{-6}{-5}\left(\mathrm{iv}\right)\frac{2}{-9}\left(\mathrm{v}\right)\frac{19}{-6}$

Ans

$\begin{array}{l}\left(\text{i}\right)\text{Additive inverse of}\text{}\frac{2}{8}\text{}\text{=}-\frac{2}{8}\text{}\\ \left(\text{ii}\right)\text{Additive inverse of}\frac{-5}{9}\text{=}\frac{5}{9}\\ \left(\text{iii}\right)\text{Additive inverse of}\frac{-6}{-5}\text{}\text{=}\frac{-6}{5}\\ \left(\text{iv}\right)\text{Additive inverse of}\frac{2}{-9}\text{=}\frac{2}{9}\\ \left(\text{v}\right)\text{Additive inverse of}\frac{19}{-6}\text{=}\frac{19}{6}\end{array}$

Q.3 Verify that – (– x) = x for.

$\left(\mathrm{i}\right)\mathrm{x}=\frac{11}{15}\left(\mathrm{ii}\right)\mathrm{x}=-\frac{13}{17}$

Ans

$\begin{array}{l}\left(\text{i}\right)\text{x=}\frac{11}{15}\\ \text{L.H.S=}-\left(-\mathrm{x}\right)\\ =-\left(-\frac{11}{15}\right)\\ =\frac{11}{15}\left(\text{as two minus becomes plus}\right)\\ =\mathrm{x}\\ =\text{R.H.S}\\ \text{}\therefore \text{L.H.S=R.H.S}\\ \text{Hence proved.}\\ \\ \left(\text{ii}\right)\text{x=}-\frac{13}{17}\\ \text{L.H.S=}-\left(-\mathrm{x}\right)\\ =-\left(-\frac{13}{17}\right)\\ =\frac{13}{17}\text{}\left(\text{as two minus becomes plus}\right)\\ =\mathrm{x}\\ =\text{R.H.S}\\ \text{}\therefore \text{L.H.S=R.H.S}\\ \text{Hence proved.}\end{array}$

Q.4 Find the multiplicative inverse of the following.

$\begin{array}{l}\left(\mathrm{i}\right)-13\left(\mathrm{ii}\right)\frac{-13}{19}\left(\mathrm{iii}\right)\frac{1}{5}\left(\mathrm{iv}\right)\frac{-5}{8}×\frac{-3}{7}\\ \left(\mathrm{v}\right)-1×\frac{-2}{5}\left(\mathrm{vi}\right)-1\end{array}$

Ans

$\begin{array}{l}\left(\mathrm{i}\right)-13\\ \mathrm{The}\text{}\mathrm{multiplicative}\text{}\mathrm{inverse}\text{}\mathrm{of}-13=-\frac{1}{13}\\ \left(\mathrm{ii}\right)\frac{-13}{19}\\ \mathrm{The}\text{}\mathrm{multiplicative}\text{}\mathrm{inverse}\text{}\mathrm{of}\frac{-13}{19}=\frac{-19}{13}\\ \left(\mathrm{iii}\right)\frac{1}{5}\\ \mathrm{The}\text{}\mathrm{multiplicative}\text{}\mathrm{inverse}\text{}\mathrm{of}\frac{1}{5}=5\\ \left(\mathrm{iv}\right)\frac{-5}{8}×\frac{-3}{7}=\frac{15}{56}\\ \mathrm{The}\text{}\mathrm{multiplicative}\text{}\mathrm{inverse}\text{}\mathrm{of}\frac{15}{56}=\frac{56}{15}\\ \left(\mathrm{v}\right)-1×\frac{-2}{5}=\frac{2}{5}\\ \mathrm{The}\text{}\mathrm{multiplicative}\text{}\mathrm{inverse}\text{}\mathrm{of}\frac{2}{5}=\frac{5}{2}\\ \left(\mathrm{vi}\right)-1\\ \mathrm{The}\text{}\mathrm{multiplicative}\text{}\mathrm{inverse}\text{}\mathrm{of}-1=-1\end{array}$

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

$\begin{array}{l}\left(\mathrm{i}\right)\frac{-4}{5}×1=1×\frac{-4}{5}=\frac{-4}{5}\left(\mathrm{ii}\right)-\frac{13}{17}×\frac{-2}{7}=\frac{-2}{7}×\frac{-13}{17}\\ \left(\mathrm{iii}\right)\frac{-19}{29}×\frac{29}{-19}=1\end{array}$

Ans

$\begin{array}{l}\left(\mathrm{i}\right)\frac{-4}{5}×1=1×\frac{-4}{5}=\frac{-4}{5}\\ \text{Here, 1 is the multiplicative identity.}\\ \left(\mathrm{ii}\right)-\frac{13}{17}×\frac{-2}{7}=\frac{-2}{7}×\frac{-13}{17}\\ \text{Here, commutative property is used.}\\ \left(\mathrm{iii}\right)\frac{-19}{29}×\frac{29}{-19}=1\\ \text{Here,multiplicative inverse is being used.}\end{array}$

Q.6

$\mathrm{Multiply}\frac{6}{13}\mathrm{by}\mathrm{the}\mathrm{reciprocal}\mathrm{of}\frac{-7}{16}.$

Ans

$\begin{array}{l}\mathrm{The}\mathrm{reciprocal}\mathrm{of}\frac{-7}{16}\text{}\mathrm{is}\frac{-16}{7}.\\ \therefore \frac{6}{13}×\left(\frac{-16}{7}\right)=\frac{-96}{91}\end{array}$

Q.7

$\begin{array}{l}\mathrm{Tell}\mathrm{what}\mathrm{property}\mathrm{allows}\mathrm{you}\mathrm{to}\mathrm{compute}\\ \frac{1}{3}×\left(6×\frac{4}{3}\right)\mathrm{as}\left(\frac{1}{3}×6\right)×\frac{4}{3}.\end{array}$

Ans

$\begin{array}{l}\frac{1}{3}×\left(6×\frac{4}{3}\right)\mathrm{is}\mathrm{written}\mathrm{as}\left(\frac{1}{3}×6\right)×\frac{4}{3}\\ \text{Here, associative property is being used as the associative}\\ \text{property of multiplication is a × (b × c) = (a × b) × c}\end{array}$

Q.8

$\mathrm{Is}\frac{8}{9}\mathrm{the}\mathrm{multiplicative}\mathrm{inverse}\mathrm{of}-1\frac{1}{8}?\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{Why}\mathrm{or}\mathrm{why}\mathrm{not}?$

Ans

$\begin{array}{l}\mathrm{If}\frac{8}{9}\mathrm{is}\mathrm{the}\mathrm{multiplicative}\mathrm{inverse}\mathrm{of}-1\frac{1}{8},\mathrm{then}\mathrm{their}\\ \mathrm{product}\mathrm{should}\mathrm{b}\mathrm{eequal}\mathrm{to}1.\\ \\ \mathrm{However},\mathrm{their}\mathrm{product}\mathrm{is}\mathrm{not}\mathrm{equal}\mathrm{to}1\mathrm{as}\\ \frac{8}{9}×\left(-1\frac{1}{8}\right)=\frac{8}{9}×\frac{-9}{8}=-1\ne 1\\ \therefore \frac{8}{9}\mathrm{is}\text{}\mathrm{not}\mathrm{the}\mathrm{multiplicative}\mathrm{inverse}\mathrm{of}-1\frac{1}{8}.\end{array}$

Q.9

$\mathrm{Is}0.3\mathrm{the}\mathrm{multiplicative}\mathrm{inverse}\mathrm{of}3\frac{1}{3}?\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{Why}\mathrm{or}\mathrm{why}\mathrm{not}?$

Ans

$\begin{array}{l}\mathrm{If}0.3\mathrm{is}\mathrm{the}\mathrm{multiplicative}\mathrm{inverse}\mathrm{of}\text{}3\frac{1}{3},\mathrm{then}\mathrm{their}\\ \mathrm{product}\mathrm{should}\mathrm{be}\mathrm{equal}\mathrm{to}1.\\ \\ ⇒0.3×\left(3\frac{1}{3}\right)=0.3×\frac{10}{3}=\frac{3}{10}×\frac{10}{3}=1\\ \therefore 0.3\mathrm{is}\text{}\mathrm{the}\mathrm{multiplicative}\mathrm{inverse}\mathrm{of}\text{}3\frac{1}{3}.\end{array}$

Q.10 Write.
(i) The rational number that does not have a reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.

Ans

(i) The rational number that does not have a reciprocal is 0 because its reciprocal is not defined.
(ii) The rational numbers that are equal to their reciprocals are 1 and −1.
(iii) The rational number that is equal to its negative is 0.

Q.11 Fill in the blanks.

(i) Zero has ________ reciprocal.
(ii) The numbers ________ and ________ are their own reciprocals.
(iii) The reciprocal of – 5 is ________.

$\left(\mathrm{iv}\right)\mathrm{Reciprocal}\mathrm{of}\frac{1}{\mathrm{x}},\mathrm{where}\mathrm{x}\ne 0\mathrm{is}__________.$

(v) The product of two rational numbers is always a _______.
(vi) The reciprocal of a positive rational number is ________.

Ans

$\begin{array}{l}\left(\text{i}\right)\text{No}\\ \left(\text{ii}\right)\text{1},\text{}-\text{1}\\ \left(\text{iii}\right)\frac{-1}{5}\\ \left(\text{iv}\right)x\\ \left(\text{v}\right)\text{Rational number}\\ \left(\text{vi}\right)\text{Positive rational number}\end{array}$