NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5

Students can be well-prepared for their future endeavours by using NCERT books, which are the basic textbooks for CBSE students. NCERT books are very beneficial for students and provide several advantages for boosting their fundamental knowledge. The full comprehension of fundamental ideas in all areas is supported by NCERT texts. Students may thoroughly understand the concepts by reading the NCERT textbooks carefully. Long-term benefits come from this, since students will be able to tackle issues if they have the requisite conceptual clarity. If a student could comprehend a concept, it would not be necessary for them to memorise it. CBSE seldom asks questions that go beyond these NCERT textbooks since NCERT books are comprehensive and inclusive in their own right. The students have to read and study these books in depth. While there is nothing wrong with studying non-NCERT books, students should make sure they have studied every single topic from the NCERT books. Before reading any other book, it is important to properly understand the NCERT texts.

Once students follow NCERT and carefully study from these books, they will discover that they can immediately provide solutions to all of the questions from past years’ papers. All of the questions in the annual CBSE Class 9 examination were sourced from NCERT books. To assess students’ knowledge, only a few questions and phrases are altered. If a student needs help, they can consult the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5. The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5, can be used by students who plan to sit for competitive examinations.

NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5 (Ex 1.5) (Include PDF)

CBSE students of Class 10 can easily download the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5. They can download the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5 from Extramarks’ website or mobile application in PDF format so that they can study NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5 even in offline mode.

For students to score well in the Class 9 examination, they must become familiar with the NCERT solutions. Experts in Mathematics from Extramarks have answered these NCERT problems. Students will be able to comprehend and solve a range of Number System problems with the aid of NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5. Students should focus on Class 9 Mathematics from the perspective of the board examinations. They can use the NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.5 to clarify their understanding. Students in Class 9 must adhere to the most recent CBSE curriculum to gain a comprehensive understanding of all the topics and subtopics covered in Mathematics. The vast amount of information covered in Class 9 necessitates frequent study and practice. Maths Class 9 Ex 1.5 is an important exercise in Chapter : Number System. It is recommended that students use the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5 to solve the exercises. Students are required to respond to each exercise question. They must utilise the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5, as much as possible.

Access NCERT Solutions for Class 9 Maths Chapter 1 – Number System

The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5, are available to students on the Extramarks website and mobile application. Students who want to take examinations like the Joint Entrance Exam (JEE) will find this tool very simple to use. This provides help to students who want to get admitted to institutes like the Indian Institute of Technology (IIT) and the National Institute of Technology (NITs). Students can apply for competitive examinations like the Central Universities Entrance Tests (CUET). As the questions would be multiple choice questions (MCQs), NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5 will be beneficial for them. Students may simply go through the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5, since it follows the Extramarks’ format. Extramarks is a learning portal where students can quickly obtain Class 9 solutions in PDF format, making it useful even when they are offline. Students must access NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5, for thorough preparation. The majority of students find Class 9 tough since the material becomes more extensive after Class 8. However, when a learner is moving from a basic to an advanced level, they sometimes find it challenging to select what to do.

Class 9 Maths Chapter 1 – Number System

The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5 which provide solutions to the first chapter of Mathematics for Class 9 is titled Number System. In this chapter, the Number System is covered in great detail. The number systems and their uses are covered in this chapter. Whole, Rational, and Integers are all included in the chapter’s introduction.

The chapter begins with an overview of number systems in section 1.1, followed by sections 1.2, 1.3, 1.4, and 1.5 on crucial topics. Irrational numbers are those that cannot be expressed as p/q.

Real Numbers and their Decimal Expansions: In this section, students examine Real Number Decimal Expansions to determine if they may be used to discern between logical and irrational behaviour. The NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.5 cover everything.  Every topic has been discussed in the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5, which is designed by Extramarks’ experts. Representing Real Numbers on the Number Line – This section contains answers to the first exercise’s two issues.

Real Number Operations: Here, students can find various Irrational Numbers and operations including Addition, Subtraction, Multiplication, and Division.

Exponentiation Laws for Real Numbers: To answer the problems, students must use the exponentiation Laws. Only on NCERT Solutions For Class 9 Maths can students learn more about Number Systems and how to resolve all types of issues. One of the greatest academic tools for studying for their CBSE exams is the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5.

Rational Numbers And Irrational Numbers

Both Rational and Irrational Numbers are Real, yet they differ in terms of some properties. A Rational Number can be written as P/Q, where P and Q are both integers and Q ≠ 0. However, an Irrational Number cannot be expressed using straightforward fractions. An illustration of a Rational Number is ⅔, whereas an Irrational Number is √2. Every detail with short notes and tables is available on the website of Extramarks, and students can easily access the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5. They must know that NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5 are solved in lucid language for the ease of students with plenty of examples and illustrations.

Simplify Of Expression

To simplify an expression, the creation of an equivalent expression without any identical terms is required. The expression will be rewritten using the fewest terms feasible. Students will understand the concepts better when they will solve questions based on the Simplifying of Expression. Students can learn more from the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5. Therefore, students must know the importance of these concepts as questions are asked about them in the examinations as well. It is advised that students practice the mathematical questions daily and understand them properly.

Word Problem 

The NCERT answers for Class 9 Mathematics include all the fundamentals of the Number System, which is important for laying the groundwork for Mathematics. Number systems in Chapter 1 of Class 9 Mathematics will help students understand the difference between rational and irrational numbers, the latter of which cannot be stated as a ratio, as well as Real Numbers. Word problems can be complicated at times for students. Therefore, they must seek help from NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5, which has been solved and explained in the most understandable way.

Representation Of Numbers On Number Line

A number line, which is a straight line that displays integers at equal intervals, can be used to represent Real Numbers. On a Number Line, both Positive and Negative numbers can be shown in succession. The endpoints of this line go on forever. Number lines serve as a point of comparison and ordering for Real Numbers, such as Natural Numbers, Whole Numbers, Integers, Rational Numbers, and Irrational Numbers. The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5, will help students in every possible way to clear their confusion. Hence, students must not feel overwhelmed by the different questions and solve them confidently.

Questions On Rationalization

In elementary algebra, the procedure of rationalization is performed to get rid of the irrational number in the denominator. Its use in Mathematics entails simplifying and reducing the equations to their more useful form. Hence, questions on rationalization are always asked in examinations. Therefore, students should have an understanding of concepts to answer every question. The understanding of basic concepts will get clear with the use of NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5.

Class 9 Maths Chapter 1

The analysis and explanation of each question from the Class 9 NCERT textbook are included in the NCERT answers for Class 9 Mathematics. To help students comprehend the ideas as they go through the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5, the answers are given in depth. Some of the most qualified professionals in the field of mathematics developed these NCERT Class 9 answers. For students getting ready for Olympiads, state or national competitive examinations, and CBSE examinations, NCERT answers for Class 9 Mathematics are a huge assistance. The NCERT textbooks’ organizational scheme is used for the CBSE examinations. In addition, the NCERT answers for Class 9 mathematics aid in preparing students for Class 10 and the associated board examinations.

Students must solve every question and understand the concepts and formulas behind it to score better marks with the help of NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5. An introduction to the number system and the many types of numbers in it can be found in the NCERT answers for Class 9 Mathematics Chapter 1 on number systems. Different categories of numbers, including Natural Numbers, Whole Numbers, Integers, and Rational and Irrational Numbers, have been established for the number system. The NCERT Solutions for Class 9 Mathematics include all the fundamentals of the number system, which is important for laying the groundwork for mathematics. The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5 will help students understand the chapter better.

Benefits Of Class 9 Maths Chapter 1 Exercise 1.5

Rational numbers abide by the Commutative, Associative, and Distributive Rules for Addition And Multiplication. Additionally, students will still obtain a Rational Number if they add, subtract, multiply, or divide two Rational Numbers. The same is explained for Irrational Numbers, as well as how they also obey all of the aforementioned principles, in these solutions. The single exception is that an Irrational Number need not always be produced by addition, subtraction, multiplication, etc. Students can understand better with the help of  NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5. They should use the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5 to know the tricks of solving mathematical problems faster.

NCERT Solutions For Class 9 Maths

Students need to be aware that Extramarks is a platform where they receive support and encouragement from qualified instructors in particular academic fields. To effortlessly review the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5, students must have access to Extramarks’ website. Students can simply access and rely on Extramarks for answers to their questions and concerns. Students should adhere to the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5 as they were created with the assistance of skilled Mathematics professionals from Extramarks and can be easily solved. this will help students decide what career path to choose after Class 10. When students who have taken the science stream are unsure of what to do next, it might be overwhelming for them. The science stream can be challenging at times; students should become familiar with Class 9 early on. Students are recommended to consistently study and maintain the focus on the areas of weakness.

NCERT Solution Class 9 Maths Of Chapter 1 All Exercises

Students can easily access the solutions to every exercise in the NCERT Mathematics book. Students can get access to the other exercises as well as the NCERT Solutions For Class 9 Maths Chapter 1 Exercises. They can also download the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5.  As ‘Number System’ is one of the most important chapters of Class 9. Students must solve every exercise of the given chapter, as Extramarks has provided every solution to each question of Chapter : Number System.

The first exercise, 1.1, consists of four questions with short answers. The second exercise, 1.2, has a total of 4 questions, and every question is of the short answer type. Further, the third exercise 1.3 has a total number of 9 questions of which 8 of them are short answer types and one is a long answer. The fourth 1.4 exercise has a total of 2 questions, and both of the questions are long answer types. The solutions to all of these exercise questions can be accessed via the Extramarks’ website

The fifth exercise 1.5 has a total number of 5 questions of which 4 questions are short answers and 1 question is a long answer. This can be accessible from the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5, and lastly, the sixth exercise has a total number of 3 questions. Exercise 1.5 Class 9 Maths is an easy exercise so students must not forget to solve it again and again. Class 9 Maths Chapter 1 Exercise 1.5 is the key material for students who are facing issues while solving questions.

NCERT Solutions For Class 9

NCERT Solutions for Class 9 offers a variety of study materials that students may access. The website and mobile application of Extramarks have all the course materials. Students are thus recommended to browse the Extramarks website and locate any information that might be beneficial to them. The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5, are also available to students. They can locate notes, significant issues, and model responses for the Class 9 Number System. The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5, may be used by students to access questions from past years and aid them with their solutions.

Chapter 1 Number System

Chapter 2 Polynomials

Chapter 3 Coordinate Geometry

Chapter 4 Linear Equations in Two Variables

Chapter 5 Introduction to Euclids Geometry

Chapter 6 Lines and Angles

Chapter 7 Triangles

Chapter 8 Quadrilaterals

Chapter 9 Areas of Parallelograms and Triangles

Chapter 10 Circles

Chapter 11 Constructions

Chapter 12 Heron’s Formula

Chapter 13 Surface Areas and Volumes

Chapter 14 Statistics

Chapter 15 Probability

CBSE Study Materials For Class 9

Class 9 Maths Chapter 1 Exercise 1.5 Solutions are designed by experts in Mathematics with accuracy and precision so that students would not run into any problems when solving any challenging questions. Students can obtain the study materials for Class 9 from the Extramarks’ website, as they are designed by professionals in a particular subject. Students will be able to quickly and easily get answers to any questions by using the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5, whenever they need them. The Extramarks website provides students with access to Class 9 Mathematics, Science, English, Hindi, and other academic courses.

CBSE Study Materials

The nation’s top management and research organisation is NCERT. The NCERT framework has been followed by Extramarks. An exercise that has to be completed follows each chapter. Students should be aware that NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5, are accessible from Extramarks, where they can obtain CBSE study resources. With the use of the solutions to any question in Class 9 Maths Chapter 1 Exercise 1.5, students can have a clear understanding of all the formulas and methods implemented to solve the questions.

Q.1

Classify the following numbers as rational or irrational:i 2−5  ii 3+23−23  iii 2777iv 12 v 2π

Ans

(i) 2−5=Irrational​ number because 5 is irrational number.(ii)(3+23)−23=3, which is a rational number.(iii) 2777=27, which is in the form of pq form and it is a rational number.(iv) 12=12×22     =22, which is an irrational number becuase 2 is irrational number.(v) 2π=2(3.1415…)   =6.2830…, which is non-terminating and non-repeating. So it is irrational number.

Q.2

Simplify each of the following expressions:(i)(3+3)(2+2) (ii) (3+3)(3−3)(iii) (5+2)2(iv) (5−2)(5+2)

Ans

(i)  (3+3)(2+2)=6+32+23+6(ii)  (3+3)(3−3)=(3)2−(3)2 =9−3=6(iii)  (5+2)2=5+252+2                     =7+210(iv) (5−2)(5+2)=(5)2−(2)2                                  =5−2                                  =3

Q.3

Recall, π is defined as the ratio of the circumference (say c)of a circle to its diameter say d.That is, π=cd.This seemsto contradict the fact that π is irrational.How will youresolve this contradiction?

Ans There is no contradiction. Remember that when you measure a length with a scale or any other device, you only get an approximate rational value. So, you may not realise that either c or d is irrational.

Q.4

Represent 9.3 on the number line.

Ans

Mark a line segment AB = 9.3 on number line. Further, take BC of 1 unit. Draw a semi-circle on AC as diameter. Draw a perpendicular to line AC passing through point B. Let it intersect the semi circle at D. Taking B as centre and BD as radius, draw an arc intersecting number line at E. BE =

9.3 . MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYBg9LrFfeu0dXdh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaaiaacaqabeaadaabauaaaOqaamaakaaabaaceaGaa8xoaiaa=5cacaWFZaaaleqaaOGaaiOlaaaa@3B35@

Q.5

Rationalise the denominators of the following:(i)17(ii)17−6(iii)15+2(iv)17−2

Ans

(i)  17=17×77         =77(ii) 17−6=17−6×7+67+6

[∵(a−b)(a+b)=a2−b2]                =7+67−6                =7+6(iii)  15+2=15+2×5−25−2          =5−25−2                    [∵(a−b)(a+b)=a2−b2]                 =5−23(iv)  17−2=17−2×7+27+2                =7+27−4        [∵(a−b)(a+b)=a2−b2]                =7+23

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FAQs (Frequently Asked Questions)

1. Are the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5 solved topic-wise according to the NCERT book of Maths?

Yes, NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5 have been solved topic-by-topic following the NCERT Mathematics book. The experts always ensure that NCERT books remain at the centre of their study material so that students can easily find the questions in the book after reading from the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5.

2. How can students access NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5?

Students can get NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5 from the Extramarks’ website and mobile application, and download the PDF format from there. These solutions are simple to understand and beneficial to students preparing for board examinations and other entrance examinations.

3. Are the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5 of the updated syllabus of Mathematics Class 9?

Extramarks keeps track of all syllabus updates and new topics. They leave no stone unturned to ensure that students face no difficulties. As a result, the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.5 are from the most recent syllabus, as experts always make changes when something new arises.