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Case Study Questions for Class 7 Maths Chapter 9 Rational Numbers

• Last modified on: 7 months ago
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Here in this article, we are providing case study questions for Class 7 Maths Chapter 9 Rational Numbers.

Maths Class 7 Chapter List

Latest chapter list (2023-24).

There is total 13 chapters.

Chapter 1 Integers Case Study Questions Chapter 2 Fractions and Decimals Case Study Questions Chapter 3 Data Handling Case Study Questions Chapter 4 Simple Equations Case Study Questions Chapter 5 Lines and Angles Case Study Questions Chapter 6 The Triangles and its Properties Case Study Questions Chapter 7 Comparing Quantities Case Study Questions Chapter 8 Rational Numbers Case Study Questions Chapter 9 Perimeter and Area Case Study Questions Chapter 10 Algebraic Expressions Case Study Questions Chapter 11 Exponents and Powers Case Study Questions Chapter 12 Symmetry Case Study Questions Chapter 13 Visualising Solid Shapes Case Study Questions

Old Chapter List

Chapter 1 Integers Chapter 2 Fractions and Decimals Chapter 3 Data Handling Chapter 4 Simple Equations Chapter 5 Lines and Angles Chapter 6 The Triangles and its Properties Chapter 7 Congruence of Triangles Chapter 8 Comparing Quantities Chapter 9 Rational Numbers Chapter 10 Practical Geometry Chapter 11 Perimeter and Area Chapter 12 Algebraic Expressions Chapter 13 Exponents and Powers Chapter 14 Symmetry Chapter 15 Visualising Solid Shapes

Deleted Chapter:

• Chapter 7 Congruence of Triangles
• Chapter 10 Practical Geometry

Tips for Answering Case Study Questions for Class 7 Maths in Exam

1. Comprehensive Reading for Context: Prioritize a thorough understanding of the provided case study. Absorb the contextual details and data meticulously to establish a strong foundation for your solution.

2. Relevance Identification: Pinpoint pertinent mathematical concepts applicable to the case study. By doing so, you can streamline your thinking process and apply appropriate methods with precision.

3. Deconstruction of the Problem: Break down the complex problem into manageable components or steps. This approach enhances clarity and facilitates organized problem-solving.

4. Highlighting Key Data: Emphasize critical information and data supplied within the case study. This practice aids quick referencing during the problem-solving process.

5. Application of Formulas: Leverage pertinent mathematical formulas, theorems, and principles to solve the case study. Accuracy in formula selection and unit usage is paramount.

6. Transparent Workflow Display: Document your solution with transparency, showcasing intermediate calculations and steps taken. This not only helps track progress but also offers insight into your analytical process.

7. Variable Labeling and Definition: For introduced variables or unknowns, offer clear labels and definitions. This eliminates ambiguity and reinforces a structured solution approach.

8. Step Explanation: Accompany each step with an explanatory note. This reinforces your grasp of concepts and demonstrates effective application.

9. Realistic Application: When the case study pertains to real-world scenarios, infuse practical reasoning and logic into your solution. This ensures alignment with real-life implications.

10. Thorough Answer Review: Post-solving, meticulously review your answer for accuracy and coherence. Assess its compatibility with the case study’s context.

11. Solution Recap: Before submission, revisit your solution to guarantee comprehensive coverage of the problem and a well-organized response.

12. Previous Case Study Practice: Boost your confidence by practicing with past case study questions from exams or textbooks. This familiarity enhances your readiness for the question format.

13. Efficient Time Management: Strategically allocate time for each case study question based on its complexity and the overall exam duration.

14. Maintain Composure and Confidence: Approach questions with poise and self-assurance. Your preparation equips you to conquer the challenges presented.

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CBSE Expert

CBSE Class 9 Maths Case Study Questions PDF Download

Download Class 9 Maths Case Study Questions to prepare for the upcoming CBSE Class 9 Exams 2023-24. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 9 so that they can score 100% in Exams.

Case study questions play a pivotal role in enhancing students’ problem-solving skills. By presenting real-life scenarios, these questions encourage students to think beyond textbook formulas and apply mathematical concepts to practical situations. This approach not only strengthens their understanding of mathematical concepts but also develops their analytical thinking abilities.

Table of Contents

CBSE Class 9th MATHS: Chapterwise Case Study Questions

Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked. For Class 9 Maths Case Study Questions, there would be 5 case-based sub-part questions, wherein a student has to attempt 4 sub-part questions.

Chapterwise Case Study Questions of Class 9 Maths

• Case Study Questions for Chapter 1 Number System
• Case Study Questions for Chapter 2 Polynomials
• Case Study Questions for Chapter 3 Coordinate Geometry
• Case Study Questions for Chapter 4 Linear Equations in Two Variables
• Case Study Questions for Chapter 5 Introduction to Euclid’s Geometry
• Case Study Questions for Chapter 6 Lines and Angles
• Case Study Questions for Chapter 7 Triangles
• Case Study Questions for Chapter 8 Quadrilaterals
• Case Study Questions for Chapter 9 Areas of Parallelograms and Triangles
• Case Study Questions for Chapter 10 Circles
• Case Study Questions for Chapter 11 Constructions
• Case Study Questions for Chapter 12 Heron’s Formula
• Case Study Questions for Chapter 13 Surface Area and Volumes
• Case Study Questions for Chapter 14 Statistics
• Case Study Questions for Chapter 15 Probability

Checkout: Class 9 Science Case Study Questions

And for mathematical calculations, tap Math Calculators which are freely proposed to make use of by calculator-online.net

The above  Class 9 Maths Case Study Question s will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 9 Maths Case Study Questions have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.

Class 9 Maths Syllabus 2023-24

UNIT I: NUMBER SYSTEMS

1. REAL NUMBERS (18 Periods)

1. Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.

2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.

3. Definition of nth root of a real number.

4. Rationalization (with precise meaning) of real numbers of the type

(and their combinations) where x and y are natural number and a and b are integers.

5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)

UNIT II: ALGEBRA

1. POLYNOMIALS (26 Periods)

Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification of identities:

RELATED STORIES

and their use in factorization of polynomials.

2. LINEAR EQUATIONS IN TWO VARIABLES (16 Periods)

Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax + by + c=0.Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line.

UNIT III: COORDINATE GEOMETRY COORDINATE GEOMETRY (7 Periods)

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations.

UNIT IV: GEOMETRY

1. INTRODUCTION TO EUCLID’S GEOMETRY (7 Periods)

History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Showing the relationship between axiom and theorem, for example: (Axiom)

1. Given two distinct points, there exists one and only one line through them. (Theorem)

2. (Prove) Two distinct lines cannot have more than one point in common.

2. LINES AND ANGLES (15 Periods)

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O and the converse.

2. (Prove) If two lines intersect, vertically opposite angles are equal.

3. (Motivate) Lines which are parallel to a given line are parallel.

3. TRIANGLES (22 Periods)

1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence).

2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).

3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).

4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence)

5. (Prove) The angles opposite to equal sides of a triangle are equal.

6. (Motivate) The sides opposite to equal angles of a triangle are equal.

4. QUADRILATERALS (13 Periods)

1. (Prove) The diagonal divides a parallelogram into two congruent triangles.

2. (Motivate) In a parallelogram opposite sides are equal, and conversely.

3. (Motivate) In a parallelogram opposite angles are equal, and conversely.

4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.

5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.

6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse.

5. CIRCLES (17 Periods)

1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.

2. (Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.

3. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.

4. (Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

5. (Motivate) Angles in the same segment of a circle are equal.

6. (Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.

7. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

UNIT V: MENSURATION 1.

1. AREAS (5 Periods)

Area of a triangle using Heron’s formula (without proof)

2. SURFACE AREAS AND VOLUMES (17 Periods)

Surface areas and volumes of spheres (including hemispheres) and right circular cones.

UNIT VI: STATISTICS & PROBABILITY

STATISTICS (15 Periods)

 Bar graphs, histograms (with varying base lengths), and frequency polygons.

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Benefits of Practicing CBSE Class 9 Maths Case Study Questions

Regular practice of CBSE Class 9 Maths case study questions offers several benefits to students. Some of the key advantages include:

• Deeper Understanding : Case study questions foster a deeper understanding of mathematical concepts by connecting them to real-world scenarios. This improves retention and comprehension.
• Practical Application : Students learn to apply mathematical concepts to practical situations, preparing them for real-life problem-solving beyond the classroom.
• Critical Thinking : Case study questions require students to think critically, analyze data, and devise appropriate solutions. This nurtures their critical thinking abilities, which are valuable in various academic and professional domains.
• Exam Readiness : By practicing case study questions, students become familiar with the question format and gain confidence in their problem-solving abilities. This enhances their readiness for CBSE Class 9 Maths exams.
• Holistic Development: Solving case study questions cultivates not only mathematical skills but also essential life skills like analytical thinking, decision-making, and effective communication.

Tips to Solve CBSE Class 9 Maths Case Study Questions Effectively

Solving case study questions can be challenging, but with the right approach, you can excel. Here are some tips to enhance your problem-solving skills:

• Read the case study thoroughly and understand the problem statement before attempting to solve it.
• Identify the relevant data and extract the necessary information for your solution.
• Break down complex problems into smaller, manageable parts to simplify the solution process.
• Apply the appropriate mathematical concepts and formulas, ensuring a solid understanding of their principles.
• Clearly communicate your solution approach, including the steps followed, calculations made, and reasoning behind your choices.
• Practice regularly to familiarize yourself with different types of case study questions and enhance your problem-solving speed.Class 9 Maths Case Study Questions

Remember, solving case study questions is not just about finding the correct answer but also about demonstrating a logical and systematic approach. Now, let’s explore some resources that can aid your preparation for CBSE Class 9 Maths case study questions.

Q1. Are case study questions included in the Class 9 Maths Case Study Questions syllabus?

Yes, case study questions are an integral part of the CBSE Class 9 Maths syllabus. They are designed to enhance problem-solving skills and encourage the application of mathematical concepts to real-life scenarios.

Q2. How can solving case study questions benefit students ?

Solving case study questions enhances students’ problem-solving skills, analytical thinking, and decision-making abilities. It also bridges the gap between theoretical knowledge and practical application, making mathematics more relevant and engaging.

Q3. How do case study questions help in exam preparation?

Case study questions help in exam preparation by familiarizing students with the question format, improving analytical thinking skills, and developing a systematic approach to problem-solving. Regular practice of case study questions enhances exam readiness and boosts confidence in solving such questions.

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Case Study Questions for Class 9 Maths

• Post author: studyrate
• Post published:
• Post category: class 9th
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Are you preparing for your Class 9 Maths board exams and looking for an effective study resource? Well, you’re in luck! In this article, we will provide you with a collection of Case Study Questions for Class 9 Maths specifically designed to help you excel in your exams. These questions are carefully curated to cover various mathematical concepts and problem-solving techniques. So, let’s dive in and explore these valuable resources that will enhance your preparation and boost your confidence.

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

CBSE Class 9 Maths Board Exam will have a set of questions based on case studies in the form of MCQs. The CBSE Class 9 Mathematics Question Bank on Case Studies, provided in this article, can be very helpful to understand the new format of questions. Share this link with your friends.

If you want to want to prepare all the tough, tricky & difficult questions for your upcoming exams, this is where you should hang out.  CBSE Case Study Questions for Class 9  will provide you with detailed, latest, comprehensive & confidence-inspiring solutions to the maximum number of Case Study Questions covering all the topics from your  NCERT Text Books !

Table of Contents

CBSE Class 9th – MATHS: Chapterwise Case Study Question & Solution

Case study questions are a form of examination where students are presented with real-life scenarios that require the application of mathematical concepts to arrive at a solution. These questions are designed to assess students’ problem-solving abilities, critical thinking skills, and understanding of mathematical concepts in practical contexts.

Chapterwise Case Study Questions for Class 9 Maths

Case study questions play a crucial role in the field of mathematics education. They provide students with an opportunity to apply theoretical knowledge to real-world situations, thereby enhancing their comprehension of mathematical concepts. By engaging with case study questions, students develop the ability to analyze complex problems, make connections between different mathematical concepts, and formulate effective problem-solving strategies.

• Case Study Questions for Chapter 1 Number System
• Case Study Questions for Chapter 2 Polynomials
• Case Study Questions for Chapter 3 Coordinate Geometry
• Case Study Questions for Chapter 4 Linear Equations in Two Variables
• Case Study Questions for Chapter 5 Introduction to Euclid’s Geometry
• Case Study Questions for Chapter 6 Lines and Angles
• Case Study Questions for Chapter 7 Triangles
• Case Study Questions for Chapter 8 Quadilaterals
• Case Study Questions for Chapter 9 Areas of Parallelograms and Triangles
• Case Study Questions for Chapter 10 Circles
• Case Study Questions for Chapter 11 Constructions
• Case Study Questions for Chapter 12 Heron’s Formula
• Case Study Questions for Chapter 13 Surface Area and Volumes
• Case Study Questions for Chapter 14 Statistics
• Case Study Questions for Chapter 15 Probability

The above  Case studies for Class 9 Mathematics will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 9 Maths Case Studies have been developed by experienced teachers of schools.studyrate.in for benefit of Class 10 students.

• Class 9 Science Case Study Questions
• Class 9 Social Science Case Study Questions

How to Approach Case Study Questions

When tackling case study questions, it is essential to adopt a systematic approach. Here are some steps to help you approach and solve these types of questions effectively:

• Read the case study carefully: Understand the given scenario and identify the key information.
• Identify the mathematical concepts involved: Determine the relevant mathematical concepts and formulas applicable to the problem.
• Formulate a plan: Devise a plan or strategy to solve the problem based on the given information and mathematical concepts.
• Solve the problem step by step: Apply the chosen approach and perform calculations or manipulations to arrive at the solution.
• Verify and interpret the results: Ensure the solution aligns with the initial problem and interpret the findings in the context of the case study.

Tips for Solving Case Study Questions

Here are some valuable tips to help you effectively solve case study questions:

• Read the question thoroughly and underline or highlight important information.
• Break down the problem into smaller, manageable parts.
• Visualize the problem using diagrams or charts if applicable.
• Use appropriate mathematical formulas and concepts to solve the problem.
• Show all the steps of your calculations to ensure clarity.
• Check your final answer and review the solution for accuracy and relevance to the case study.

Benefits of Practicing Case Study Questions

Practicing case study questions offers several benefits that can significantly contribute to your mathematical proficiency:

• Enhances critical thinking skills
• Improves problem-solving abilities
• Deepens understanding of mathematical concepts
• Develops analytical reasoning
• Prepares you for real-life applications of mathematics
• Boosts confidence in approaching complex mathematical problems

Case study questions offer a unique opportunity to apply mathematical knowledge in practical scenarios. By practicing these questions, you can enhance your problem-solving abilities, develop a deeper understanding of mathematical concepts, and boost your confidence for the Class 9 Maths board exams. Remember to approach each question systematically, apply the relevant concepts, and review your solutions for accuracy. Access the PDF resource provided to access a wealth of case study questions and further elevate your preparation.

Q1: Can case study questions help me score better in my Class 9 Maths exams?

Yes, practicing case study questions can significantly improve your problem-solving skills and boost your performance in exams. These questions offer a practical approach to understanding mathematical concepts and their real-life applications.

Q2: Are the case study questions in the PDF resource relevant to the Class 9 Maths syllabus?

Absolutely! The PDF resource contains case study questions that align with the Class 9 Maths syllabus. They cover various topics and concepts included in the curriculum, ensuring comprehensive preparation.

Q3: Are the solutions provided for the case study questions in the PDF resource?

Yes, the PDF resource includes solutions for each case study question. You can refer to these solutions to validate your answers and gain a better understanding of the problem-solving process.

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CBSE Class 9 Mathematics Case Study Questions

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If you’re looking for a comprehensive and reliable study resource and case study questions for class 9 CBSE, myCBSEguide is the perfect door to enter. With over 10,000 study notes, solved sample papers and practice questions, it’s got everything you need to ace your exams. Plus, it’s updated regularly to keep you aligned with the latest CBSE syllabus . So why wait? Start your journey to success with myCBSEguide today!

Significance of Mathematics in Class 9

Mathematics is an important subject for students of all ages. It helps students to develop problem-solving and critical-thinking skills, and to think logically and creatively. In addition, mathematics is essential for understanding and using many other subjects, such as science, engineering, and finance.

CBSE Class 9 is an important year for students, as it is the foundation year for the Class 10 board exams. In Class 9, students learn many important concepts in mathematics that will help them to succeed in their board exams and in their future studies. Therefore, it is essential for students to understand and master the concepts taught in Class 9 Mathematics .

Case studies in Class 9 Mathematics

A case study in mathematics is a detailed analysis of a particular mathematical problem or situation. Case studies are often used to examine the relationship between theory and practice, and to explore the connections between different areas of mathematics. Often, a case study will focus on a single problem or situation and will use a variety of methods to examine it. These methods may include algebraic, geometric, and/or statistical analysis.

Example of Case study questions in Class 9 Mathematics

The Central Board of Secondary Education (CBSE) has included case study questions in the Class 9 Mathematics paper. This means that Class 9 Mathematics students will have to solve questions based on real-life scenarios. This is a departure from the usual theoretical questions that are asked in Class 9 Mathematics exams.

The following are some examples of case study questions from Class 9 Mathematics:

Class 9 Mathematics Case study question 1

There is a square park ABCD in the middle of Saket colony in Delhi. Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak,  Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point O in the direction of   XOY, X’OY, X’OY’ and XOY’ . Their balls stopped as shown in the above image.

Answer the following questions:

Answer Key:

Class 9 Mathematics Case study question 2

• Now he told Raju to draw another line CD as in the figure
• The teacher told Ajay to mark  ∠ AOD  as 2z
• Suraj was told to mark  ∠ AOC as 4y
• Clive Made and angle  ∠ COE = 60°
• Peter marked  ∠ BOE and  ∠ BOD as y and x respectively

Now answer the following questions:

• 2y + z = 90°
• 2y + z = 180°
• 4y + 2z = 120°
• (a) 2y + z = 90°

Class 9 Mathematics Case study question 3

• (a) 31.6 m²
• (c) 513.3 m³
• (b) 422.4 m²

Class 9 Mathematics Case study question 4

How to Answer Class 9 Mathematics Case study questions

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Students need to be careful while solving the Class 9 Mathematics case study questions. They should not make any assumptions and should always check their answers. If they are stuck on a question, they should take a break and come back to it later. With some practice, the Class 9 Mathematics students will be able to crack case study questions with ease.

Class 9 Mathematics Curriculum at Glance

At the secondary level, the curriculum focuses on improving students’ ability to use Mathematics to solve real-world problems and to study the subject as a separate discipline. Students are expected to learn how to solve issues using algebraic approaches and how to apply their understanding of simple trigonometry to height and distance problems. Experimenting with numbers and geometric forms, making hypotheses, and validating them with more observations are all part of Math learning at this level.

The suggested curriculum covers number systems, algebra, geometry, trigonometry, mensuration, statistics, graphing, and coordinate geometry, among other topics. Math should be taught through activities that include the use of concrete materials, models, patterns, charts, photographs, posters, and other visual aids.

CBSE Class 9 Mathematics (Code No. 041)

Class 9 Mathematics question paper design

The CBSE Class 9 mathematics question paper design is intended to measure students’ grasp of the subject’s fundamental ideas. The paper will put their problem-solving and analytical skills to the test. Class 9 mathematics students are advised to go through the question paper pattern thoroughly before they start preparing for their examinations. This will help them understand the paper better and enable them to score maximum marks. Refer to the given Class 9 Mathematics question paper design.

QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)

Mycbseguide: blessing in disguise.

Class 9 is an important milestone in a student’s life. It is the last year of high school and the last chance to score well in the CBSE board exams. myCBSEguide is the perfect platform for students to get started on their preparations for Class 9 Mathematics. myCBSEguide provides comprehensive study material for all subjects, including practice questions, sample papers, case study questions and mock tests. It also offers tips and tricks on how to score well in exams. myCBSEguide is the perfect door to enter for class 9 CBSE preparations.

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14 thoughts on “CBSE Class 9 Mathematics Case Study Questions”

This method is not easy for me

aarti and rashika are two classmates. due to exams approaching in some days both decided to study together. during revision hour both find difficulties and they solved each other’s problems. aarti explains simplification of 2+ ?2 by rationalising the denominator and rashika explains 4+ ?2 simplification of (v10-?5)(v10+ ?5) by using the identity (a – b)(a+b). based on above information, answer the following questions: 1) what is the rationalising factor of the denominator of 2+ ?2 a) 2-?2 b) 2?2 c) 2+ ?2 by rationalising the denominator of aarti got the answer d) a) 4+3?2 b) 3+?2 c) 3-?2 4+ ?2 2+ ?2 d) 2-?3 the identity applied to solve (?10-?5) (v10+ ?5) is a) (a+b)(a – b) = (a – b)² c) (a – b)(a+b) = a² – b² d) (a-b)(a+b)=2(a² + b²) ii) b) (a+b)(a – b) = (a + b

MATHS PAAGAL HAI

All questions was easy but search ? hard questions. These questions was not comparable with cbse. It was totally wastage of time.

Where is search ? bar

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FREE CBSE Online Coaching for Class 9 Maths. No Conditions

Extra questions for class 9 maths chapter 1, number systems | real numbers | rational & irrational numbers.

NCERT Class 9 Math / Number System Extra Questions

C hapter 1 of CBSE NCERT Class 9 Math covers number systems. Concepts covered in chapter 1 include rational numbers, irrational numbers, rationalizing irrational numbers by multiplying with their conjugates, decimal expansion of real numbers, operations on real numbers and laws of exponents or rules of indices. The extra questions given below include questions akin to HOTS (Higher Order Thinking Skills) questions and exemplar questions of NCERT.

Here is a quick recap of the key concepts that are covered in this chapter in the CBSE NCERT Class 9 Math text book.

What are rational numbers?

A number that can be written in the form \\frac{p}{q}\\) where p and q are integers and p ≠ 0 is a rational number.

Possibility 1 : If the decimal expansion of the number is terminating it is a rational number. Note: Integers are terminating decimals and are therefore, rational numbers.

Possibility 2 : If the decimal expansion of the number is non-terminating but is recurring , it is rational. Example \\frac{1}{3}\\) = 0.333.. is a non-terminating recurring decimal and is a rational number.

What are irrational numbers?

A number that CANNOT be written in the form \\frac{p}{q}\\) where p and q are integers and p ≠ 0 is an irrational number.

If the decimal expansion of the number is non-terminating AND non-recurring it is an irrational number. Example: \\sqrt{2}\\), π

How to Rationalize Irrational Numbers?

For an irrational number of the form a + √b, a - √b is its conjugate. And for an irrational number of the from a - √b, a + √b is its conjugate.

Important Laws of Exponents (Rules of Indices)

If a > 0 is a real number and m and n are rational numbers, the following laws of exponents hold good.

• a m × a n = a m + n Example .: 10 3 × 10 2 = 10 3 + 2 = 10 5
• (a m ) n = a mn Example : (10 3 ) 2 = 10 (3 \\times\\) 2) = 10 6
• \\frac{a^m}{a^n}\\) = a (m - n) Example : \\frac{10^3}{10^2}\\) = 10 (3 - 2) = 10
• a m b m = (ab) m Example : 2 2 × 5 2 = (2 × 5) 2 = 10 2

Extra Questions for Class 9 Maths - Number Systems

Prime Factorise & Rationalise Denominator: \\frac{14}{{\sqrt {108}} - {\sqrt {96}} + {\sqrt {192}} - {\sqrt {54}}}\\)

Rational numbers - Fractions: Find 5 rational numbers between \\frac{3}{4}) and \\frac{4}{5}).

Express as Fractions Express 1.363636... in the form \\frac{p}{q}), where p and q are integers and q ≠ 0.

Express in the form \\frac{p}{q}) Express 0.4323232… in the form \\frac{p}{q}), where p and q are integers and q ≠ 0.

Simplify the following (a) \({8 + \sqrt{5})}) \({8 - \sqrt{5})}) (b) \({10 + \sqrt{3})}) \({6 + \sqrt{2})}) (c) \{(\sqrt {3} + \sqrt {11})}^2) + \{(\sqrt {3} - \sqrt {11})}^2)

Rationalize the denominator: (a) \\frac{2}{\sqrt{3} - 1}) (b) \\frac{7}{\sqrt{12} - \sqrt{5}}) (c) \\frac{1}{8 + 3\sqrt{5}}) (d) \\frac{1}{4 + \sqrt{2} + \sqrt{5}})

Simplify and find the value of (a) \{(729)}^{\frac{1}{6}}) (b) \{(64)}^{\frac{2}{3}}) (c) \{(243)}^{\frac{6}{5}}) (d) \{(21)}^{\frac{3}{2}} \times {(21)}^{\frac{5}{2}}) (e) \\frac{{(81)}^{\frac{1}{3}}}{{(81)}^{\frac{1}{12}}})

Operation on real numbers & Algebraic identities If x = \\frac{3 - {\sqrt{13}}}{2}\\), what is the value of \x^2 + \frac{1}{x^2}\\)?

Rationalise & find value of cubic expression If x = \\frac{1}{8-\sqrt{60}}\\), what is the value of (x 3 - 5x 2 + 8x - 4) ?

Question 10

Rationalise the denominator \\frac{1}{9 + {\sqrt{5} + \sqrt{6}}}\\)

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CBSE Class 9th Maths 2023 : 30 Most Important Case Study Questions with Answers; Download PDF

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Unit 2: Real numbers

Introduction.

• Intro to rational & irrational numbers (Opens a modal)
• Classifying numbers (Opens a modal)
• Identifying rational numbers Get 3 of 4 questions to level up!
• Classify numbers Get 5 of 7 questions to level up!
• Identifying decimal expansion of rational and irrational numbers Get 3 of 4 questions to level up!

Properties of addition and multiplication

• Properties of addition (Opens a modal)
• Properties of multiplication (Opens a modal)
• Closure, associative and commutative property of rational numbers (1/2) Get 3 of 4 questions to level up!
• Closure, associative and commutative property of rational numbers (2/2) Get 3 of 4 questions to level up!

Prime and composite numbers

• Recognizing prime and composite numbers (Opens a modal)
• Prime factorization exercise (Opens a modal)
• Identify prime numbers Get 5 of 7 questions to level up!
• Identify composite numbers Get 5 of 7 questions to level up!
• Identify co-prime numbers Get 3 of 4 questions to level up!
• Prime factorization Get 5 of 7 questions to level up!

Rational numbers

• No videos or articles available in this lesson
• Additive and multiplicative inverse of a rational number Get 3 of 4 questions to level up!
• Distributive property of rational numbers Get 3 of 4 questions to level up!
• Rational numbers between two rational numbers Get 3 of 4 questions to level up!

Decimal form of rational numbers

• Converting a fraction to a repeating decimal (Opens a modal)
• Converting repeating decimals to fractions (part 1 of 2) (Opens a modal)
• Converting repeating decimals to fractions (part 2 of 2) (Opens a modal)
• Writing fractions as repeating decimals Get 5 of 7 questions to level up!
• Converting repeating decimals to fractions Get 5 of 7 questions to level up!
• Converting multi-digit repeating decimals to fractions Get 3 of 4 questions to level up!

Irrational numbers

• Proof: √2 is irrational (Opens a modal)
• Classify numbers: rational & irrational Get 5 of 7 questions to level up!

Real numbers

Absolute value.

• Absolute value examples (Opens a modal)
• Finding absolute values Get 5 of 7 questions to level up!
• Intro to rational exponents (Opens a modal)
• Evaluating fractional exponents (Opens a modal)
• Unit-fraction exponents Get 3 of 4 questions to level up!
• Fractional exponents Get 3 of 4 questions to level up!
• Evaluate radical expressions challenge Get 3 of 4 questions to level up!

Rationalizing the denominator

• Intro to rationalizing the denominator (Opens a modal)
• Multiplying and dividing irrational numbers Get 3 of 4 questions to level up!
• Multiplying irrational expressions Get 3 of 4 questions to level up!
• Rationalising the denominator (basic) Get 3 of 4 questions to level up!
• Rationalising the denominator (advanced) Get 3 of 4 questions to level up!

Test: Rational Numbers - Class 9 MCQ

20 questions mcq test - test: rational numbers, if   = 3.162, then the value of .

Which of the following is the product of 7/8 and -4/21?

7/8 x -4/21 = -1/6

Option B is the correct answer.

Rationalise the denominator of  .

 5 / (3 + √8)  x  ( (3 - √8) /  (3 - √8)

=  5 ( 3 - √8)/(3 2 - 8 )

= 5 ( 3 - √8 ) / 9 - 8  = 15 - 5√8 

So option C is correct. 

Expression of 2.2323… in the form of a/ b is ________.

The rational number between 1 and 2 is

Remember the general formula to find rational number between two

given number 1/2(a+b)[where a, b are given numbers]

A rational number between 1 and 2 is 1/2(1+2)=3/2

The sum of the digits of a number is subtracted from the number, the resulting number is always divisible by:

Let the three digit number be 439 The sum of digits =16 Difference =439−16=423 which is divisible by 9.

Which of the following lies between 0 and -1?

Any negative number that is greater than -1 but less than 0 falls within the specified range. So the correct answer is C. 

a terminating decimal.

a non terminating recurring decimal

a non terminating non recurring decimal

p/q is a rational number, so p and q must be

Any two integers

One of them positive and the other negative

Both natural numbers

Both integers but q must be non zero

7 / 8 x -4 / 21 = -1/6

So answer is option A . 

From the choices given below mark the co-prime numbers

All the integers are

whole numbers

rational numbers

irrational numbers

natural numbers

The rational numbers include all the integers, plus all fractions, or terminating decimals and repeating decimals. Every rational number can be written as a fraction  a / b , where  a and  b  are integers. For example, 3 can be written as 3/1, -0.175 can be written as -7/40, and 1 1/6 can be written as 7/6. All natural numbers, whole numbers, and integers are rationals, but not all rational numbers are natural numbers, whole numbers, or integers.

Let x = 0.234234234......... (1) Then , multiply both side with 1000 1000x = 234.234234......(2) Now Eq.(2)-(1) 1000x-x = 234.234234- 0.234234 999x = 234 x = 234/999

Between 3 and 4 there are

10,000 rational numbers

1000 rational numbers

Infinitely many rational numbers

500 rational numbers

There is no single number between 3 and 4, there is an infinite amount of numbers. If you are asking for INTEGERS, there are none. If not, you can have unlimited numbers between 3 and 4. For example, a number could be 3.0000000000000000005 or 3.9999999999999997.

X=0.230769 (1) 1000000=230769.230769 

(2) subtracting 

(1) from (2) 230769 =9999999x then, x =230769/9999999 =3/13

Every rational number is

a whole number

a real number

a natural number

Real numbers are the numbers that can be placed on number line And rational number can be placed on number line so all rational numbers are real number.

The product of two numbers is -20/9. If one of the numbers is 4, find the other. 

–9/11

If  5/13 = 0.384615……, then the value of 10/13 _____

What should be added to -5/4 to get -1?

- 5 / 4 + x = -1

x = -1 + 5 / 4

x = (-4 + 5) / 4

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• Important Questions for CBSE Class 7 Maths Chapter 9 - Rational Numbers

CBSE Class 7 Maths Chapter - 9 Important Questions - Free PDF Download

Here, we are presenting important questions for Class 7 Maths Chapter 9 for the students preparing for Class 7 Maths exams but unable to prioritize questions for Chapter 7 Rational Numbers. Refer to Vedantu’s important questions on Rational Number for Class 7 that are prepared by our subject experience teachers after extensive research of the topic and analysis of the past exam trends.

By practicing the questions on Rational numbers for Class 7, you can build your confidence to attempt the questions as you can evaluate your answers with the solutions given and make necessary corrections wherever required. Students are recommended to practice the important questions for Class 7 Maths Chapter 9 repeatedly to understand how tricky problems are solved and to enhance the speed of solving problems, which in turn help in strengthening the time management skills.

Read the article below to know how important questions for rational numbers are effective for your exam preparation. Register Online for NCERT Solutions Class 7 Science tuition on Vedantu.com to score more marks in the CBSE board examination. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students. Maths Students who are looking for better solutions can download Class 7 Maths NCERT Solutions to help you to revise the complete syllabus and score more marks in your examinations.

Study Important Questions for Class 7 Maths Chapter 9 - Rational Numbers

1 Mark Questions

1. Reduce \[\dfrac{55}{66}\] into the standard form.

Ans: We know that both $55$ and $66$ are divisible by $11$,

$\dfrac{55\div 11} {66\div 11} $

$ =\dfrac{5}{6} $

2. Fill in the blanks.

(a)$\dfrac{5}{6}.....\dfrac{9}{5}$

(b)$\dfrac{3}{4}......\dfrac{1}{2}$

(c)$\dfrac{2}{5}.......\dfrac{3}{4}$

Ans: (a)$\dfrac{5}{6}  < \dfrac{9}{5}$

(b)$\dfrac{3}{4} > \dfrac{1}{2}$

(c)$\dfrac{2}{5} < \dfrac{3}{4}$

3. Find the additive inverse of $-\dfrac{3}{8}$.

Ans: $\dfrac{3}{8}$

4. Reduce the following to the simplest form.

(a)$\dfrac{36}{54}$

(b)\[\dfrac{8}{72}\]

(a) HCF of $36$ and $54$ is $18$.

Dividing both numerator and denominator by $18$,

$\dfrac{36\div 18} {54\div 18} $

$ =\dfrac{2}{3} $

(b) HCF of $8$ and $72$ is $8$.

Dividing both numerator and denominator by $8$,

$\dfrac{8\div 8} {72\div 8} $

$ =\dfrac{1}{9} $ 

5. Write four more numbers in the following pattern $-\dfrac{1}{2}$, $-\dfrac{1}{3}$, $-\dfrac{2}{4}$, $-\dfrac{2}{6}$,….

$ -\dfrac{1}{2}\times \dfrac{3}{3}=-\dfrac{3}{6} $

$ -\dfrac{1}{2}\times \dfrac{4}{4}=-\dfrac{4}{8} $ 

$ -\dfrac{1}{3}\times \dfrac{3}{3}=-\dfrac{3}{9}  $  

$ -\dfrac{1}{3}\times \dfrac{4}{4}=-\dfrac{4}{12}  $  

Therefore, $-\dfrac{1}{2}$, $-\dfrac{1}{3}$, $-\dfrac{2}{4}$, $-\dfrac{2}{6}$, $-\dfrac{3}{6}$, $-\dfrac{4}{8}$, $-\dfrac{3}{9}$, $-\dfrac{4}{12}$

6. Do $-\dfrac{4}{9}$ and $-\dfrac{16}{36}$ represent the same number?

Ans: $-\dfrac{4}{9}$ and $-\dfrac{16}{36}$ 

$-\dfrac{4}{9}=-\dfrac{4\times 4}{9\times 4}=-\dfrac{16}{36}$

Or $-\dfrac{16}{36}=-\dfrac{16\div 4}{36\div 4}=-\dfrac{4}{9}$

Hence, both represent the same number.

7. List five rational numbers between $-4$ and $-3$.

$-4\times \dfrac{6}{6}=\dfrac{-24}{6}$

$-3\times \dfrac{6}{6}=\dfrac{-18}{6}$

The rational numbers are

$-\dfrac{23}{6},-\dfrac{22}{6},-\dfrac{21}{6},-\dfrac{20}{6},-\dfrac{19}{6}$

8. Give four equivalent numbers for \[\dfrac{3}{8}\].

$ \dfrac{3}{8}\times \dfrac{2}{2}=\dfrac{6}{16}  $  

$ \dfrac{3}{8}\times \dfrac{3}{3}=\dfrac{9}{24}  $  

$ \dfrac{3}{8}\times \dfrac{4}{4}=\dfrac{12}{32}  $  

$ \dfrac{3}{8}\times \dfrac{5}{5}=\dfrac{15}{40}  $  

9. Draw the number line and represent $-\dfrac{7}{3}$ on it.

Ans: This fraction represents two full parts and one part out of 3 equal parts. The negative sign indicates that it is on the negative side of the number line.

Therefore, each space between two integers on the number line must be divided into 3 equal parts.

(Image will be uploaded soon)

10. Rewrite the following rational numbers in the simplest form.

(a)$\dfrac{12}{36}$

(b)$\dfrac{39}{104}$

(a) HCF of $12$ and $36$ is $12$.

Dividing both numerator and denominator by $12$,

$\dfrac{12\div 12}{ 36\div 12}  $  

$ =\dfrac{1}{3}  $  

(b) HCF of $39$ and $104$ is $13$.

Dividing both numerator and denominator by $13$,

$\dfrac{39\div 13}{ 104\div 13} $  

$ =\dfrac{3}{8}  $  

11. Find the value of $\dfrac{4}{14}\div \dfrac{28}{80}$.

Ans: $\dfrac{4}{14}\div \dfrac{28}{80}$

$ =\dfrac{4}{14}\times \dfrac{80}{28}  $  

$ =\dfrac{40}{49}  $  

12. Find the product of $\dfrac{15}{22}\times \dfrac{11}{5}$.

Ans: $\dfrac{15}{22}\times \dfrac{11}{5}$

$ =\dfrac{3}{2}  $  

$ =1\dfrac{1}{2}  $  

13. Find the value of $\dfrac{5}{8}+\dfrac{1}{3}$.

Ans: LCM of $8$ and $3$ is $24$

$\dfrac{5}{8}\times \dfrac{3}{3}=\dfrac{15}{24}  $  

$ \dfrac{1}{3}\times \dfrac{8}{8}=\dfrac{8}{24}  $  

$ \dfrac{15}{24}+\dfrac{8}{24}  $  

$ =\dfrac{5+8}{24}  $  

$ =\dfrac{23}{24}  $  

3 Marks Questions

14. Find the value of 

(a)$\dfrac{3}{4}+\dfrac{1}{2}$

(b)$\dfrac{5}{8}+\dfrac{3}{4}$

Ans: (a) LCM of $4$ and $2$ is $4$

$ \dfrac{3}{4}\times \dfrac{1}{1}=\dfrac{3}{4}  $  

$ \dfrac{1}{2}\times \dfrac{2}{2}=\dfrac{2}{4}  $  

$ \dfrac{3}{4}+\dfrac{2}{4}  $  

$ =\dfrac{3+2}{4}  $  

$ =\dfrac{5}{4}  $  

(b) LCM of $4$ and $8$ is $8$

$ \dfrac{5}{8}\times \dfrac{1}{1}=\dfrac{5}{8}  $  

$ \dfrac{3}{4}\times \dfrac{2}{2}=\dfrac{6}{8}  $  

$ \dfrac{5}{8}+\dfrac{6}{8}  $  

$ =\dfrac{5+6}{8}  $  

$ =\dfrac{11}{8}  $  

$ =1\dfrac{3}{8}  $  

15. Simplify

(a)$\dfrac{2}{5}-\dfrac{1}{2}$

(b)$\dfrac{1}{5}-\dfrac{3}{4}$

(a) LCM of $5$ and $2$ is $10$

$ \dfrac{2}{5}\times \dfrac{2}{2}=\dfrac{4}{10}  $  

$ \dfrac{1}{2}\times \dfrac{5}{5}=\dfrac{5}{10}  $  

$ \dfrac{4}{10}-\dfrac{5}{10}  $  

$ =\dfrac{4-5}{10}  $  

$ =-\dfrac{1}{10}  $  

(b) LCM of $5$ and $4$ is $20$

$ \dfrac{1}{5}\times \dfrac{4}{4}=\dfrac{4}{20}  $  

$ \dfrac{3}{4}\times \dfrac{5}{5}=\dfrac{15}{20}  $  

$ \dfrac{4}{15}-\dfrac{15}{20}  $  

$ =\dfrac{4-15}{20}  $  

$ =-\dfrac{11}{20}  $  

16. Find the product of 

(a) $\dfrac{14}{3}\times \dfrac{21}{63}$

(b) $\dfrac{2}{5}\times \dfrac{8}{9}$

$ =\dfrac{2\times 7}{1\times 9}  $  

$ =\dfrac{14}{9}  $  

$ =1\dfrac{5}{9}  $  

$ =\dfrac{2\times 8}{5\times 9}  $  

$ =\dfrac{16}{45}  $  

17. Find the value of 

(a) $-\dfrac{2}{3}\div \dfrac{3}{4}$

(b) $\dfrac{1}{4}\div \dfrac{5}{8}$

$ =-\dfrac{2}{3}\times \dfrac{3}{4}  $  

$ =-\dfrac{8}{9}  $  

$ =\dfrac{1}{4}\times \dfrac{8}{5}  $  

$ =\dfrac{2}{5}  $  

18. Insert six rational numbers between  $\dfrac{3}{8}$ and $\dfrac{3}{5}$.

Ans: Convert both the denominators into the same denominator.

$\dfrac{3}{8}\times \dfrac{5}{5}=\dfrac{15}{40}$

$\dfrac{3}{5}\times \dfrac{8}{8}=\dfrac{24}{40}$

Therefore, 

$\dfrac{16}{24}$ $\dfrac{17}{24}$ $\dfrac{18}{24}$ $\dfrac{19}{24}$ $\dfrac{20}{24}$ $\dfrac{21}{24}$ 

Download Important Questions of Rational Numbers Class 7 With Solutions - Free PDF

The collection of important questions of Rational numbers Class 7 with solutions are prepared by the subject experts after carrying a thorough analysis of the past year exam trends and latest syllabus.  All questions on Rational Numbers for Class 7 with accurate solutions will come in handy to revise important topics of the chapter. Moreover, the solutions given here will help students to understand the method to frame the stepwise solutions in Class 7 Maths Exam 2021.

The set of important questions of rational number Class 7 provided here is perfect study material for the quick and effective revision of the chapter before the exam as questions of different formats like short answers, long answers are prepared and provided separately by the subject experts.

If you find any doubt concerning any topic of the chapter, you can clear it by practicing these important questions on Rational Numbers. Hence, students are suggested to download important questions of Rational Number Class 7 free pdf through the link provided here.

A Quick Overview of Class 7 Maths Chapter 9 Rational Numbers

Rational numbers are numbers that can be represented in the form of a fraction. It is a part of the real number system. A number is said to be in rational form if it has both numerator and denominator. More specifically, the definition of rational number states that any number can be represented in the ratio of p and q, where p and q are integers and the value of q is not equals to zero.

As per the Ancient Greek Mathematician, rational numbers are used to measure almost everything. Here are some real-life examples of rational numbers.

Taxes are represented in the form of rational numbers.

Divide pizza or anything among your friends.

Interest rate on saving accounts, loan, and mortgage are expressed in rational form.

When you complete half of the portion of your work, you say 50% of ½  of the work is completed.

Let us now understand some of the important terms of Class 7 Maths Chapter 9 Rational Numbers.

What Are Rational Numbers?

A rational number is defined as a number that can be written in the form of p/q, where p and q are integers, and q does not equal to 0. For example, 3/5 is a rational number because p = 3, and q = 5 are integers.

What are Positive and Negative Rational Numbers

Positive rational numbers are numbers whose both and numerators and denominators are positive integers. For example, 3/5 is a positive rational number because both the numerator and denominator of this number are positive.

Negative rational numbers are numbers whose either numerator or denominator are negative integers. For example, -3/5 is a negative rational number as the numerator of this number is negative.

How rational numbers can be expressed in standard form.

A Rational p/q is said to be in standard form if its denominator that is q is positive and both numerator and denominator i.e. p and q have no other common divisor other than 1.

How to Obtain Rational Numbers Between Two Rational Numbers

We can obtain a rational number between two rational numbers p and q simply by dividing it by 2.

For Example,

The rational number between 3/1 and 4/1 is 7/2 as 3/1 + 4/1 = 7/2.

For a negative and positive rational number like -3/20 and 3/20 is -2/20,-1/20, 0/20, 1/20, etc.

For determining a rational number between two rational numbers with different denominators, we first determine the equivalent fraction with the same denominator then find the rational number between them. For example, we can determine a rational number between -1/3 and 5/20 by converting -1/3 to (-1/3) x (3/3) = -39. Accordingly, we have -2/9,-1/9, 0/9, 1/9, 2/9, 3/9, 4/9.

How to Add Two Rational Numbers?

Two rational numbers with similar denominators can be added simply by adding the numerators while keeping the denominators the same whereas two rational numbers with different denominators can be added taking the LCM of the two denominators. Then, we find the equivalent rational numbers of the given rational number with this LCM as their denominators. Then, we add two rational numbers.

Example: Let us add (-7/5) + (-2/3)

Step 1: LCM of 5 and 3 is 15.

Step 2: (-7/5) +  -2/3 = [-7(3) + (-2)(5)]/15

Step 3: (-7/5) + (-2/3) = [-21 + (-10)]/15 = [-21 -10]/15 = -31/15

How to Subtract Two Rational Numbers?

Two rational numbers with similar denominators can be added simply by subtracting the numerators while keeping the denominators the same whereas two rational numbers with different denominators can be subtracted by making the values of two denominators the same by finding LCM of denominator values.

Example: Let us add (-7/5) - (-2/3)

Step 1: LCM of 5 and 3 is 15

Step 2: (-7/5) - (-2/3) = [-7(3) - (-2)(5)]/15

Step 3: (-7/5) - (-2/3)  = [-21 - (-10)]/15 = [-21 + 10]/15= -11/15

How to Multiply Two Rational Numbers?

The formula two find multiplication of two rational numbers is given by”

Product of Rational Numbers Formula  = ({Product of numerators}/{Product of denominators})

Find the product of 6/5 × 4/3

The product of 6/5 × 4/3 = 24/15

The multiplication of a rational number with its reciprocal is always equal to 1.

How to Divide Two Rational Numbers?

The division of two rational numbers is similar to the division of fractions, Here are the steps to find the division of two rational numbers.

Step 1: Find the reciprocal of the divisor value.

Step 2: Find the product of numerator and denominator to obtain the result.

Find the Value of 6/5 ÷ 9/7

Step 1: The reciprocal of 97is 79

Step 2:  Division of two rational number is

6/5 × 7/9 = 42/45

List of the Topics and Subtopics Covered in Class 7 Maths Chapter 9

9.1: Introduction To Rational Numbers

9.2: Need for Rational numbers

9.3: What are Rational Numbers?

9.4: Positive and Negative Rational Numbers

9.5: Rational Number on Number Line

9.6: Rational Number In Standard Form

9.7: Comparison of Rational Numbers

9.8: Rational Numbers Between Two Rational Number

9.9: Operation on Rational Numbers

9.9.1: Addition

9.9.2: Subtraction

9.9.3: Multiplication

9.9.4: Division

To practice the important question on all the topics discussed below, download Important Questions of Rational Numbers Class 7 free pdf now.

How Solving Questions on Rational Number For Class 7 will be Beneficial for Students?

Here are some of the benefits of solving questions on Rational numbers for Class 7.

Students will be familiarized with the different types of questions, complexity level of questions, and important topics of the chapter to focus on.

Students will be able to develop time management skills and problem-solving skills.

Students can analyse the level of their preparation based on the marks obtained. They can also analyse their strength and weakness and accordingly improve them.

Solving these questions repeatedly will help students to revise the complete chapter thoroughly.

Solving the questions will also help students to attempt the questions asked in the exam more confidently as they will be habitual to solve different types of questions.

Candidates are suggested to solve the questions and then cross their answers from the solutions provided. The attempt helps them to gain real-time exam experience.

Practicing the questions enable students to assess their preparedness and understand the techniques to decode problems asked in the exam.

To explore all the benefits mentioned above, it is recommended to download Questions on Rational for Class 7 free pdf now.

When studying CBSE Class 7 Maths Chapter 9 on Rational Numbers, it's crucial to grasp key concepts. Understanding how to represent fractions, compare them, and perform operations like addition, subtraction, multiplication, and division with rational numbers is fundamental. Additionally, learning to convert fractions into decimals and vice versa is essential. Practice solving word problems and equations involving rational numbers to strengthen your problem-solving skills. Remember to simplify fractions and find the lowest common multiple when needed. By mastering these concepts, you'll be well-prepared to handle rational numbers and their applications in various mathematical problems. Consistent practice and a solid understanding will help you excel in this chapter.

FAQs on Important Questions for CBSE Class 7 Maths Chapter 9 - Rational Numbers

Q1. How can I access NCERT Solutions for Chapter 9 Rational Numbers of Class 7 Maths?

Ans: Using Vedantu’s NCERT Solutions for Chapter 9 Rational Numbers of Class 7 Maths, students will be able to easily prioritise questions for the chapter Rational Numbers. The PDF has questions that are prepared by experienced subject teachers after continuous research of the topic and can be easily downloaded by visiting Vedantu’s official website (vedantu.com) free of cost. The questions are also based on past exam trends. By continuous practice and hard work, the student can gain confidence in tackling problems on rational numbers and solve them. This will also help the student to understand how tricky questions are solved.

Q2. What are rational numbers according to Chapter 9 Rational Numbers of Class 7 Maths?

Ans: Rational numbers can be expressed as numbers that are in the ratio of x and y. Here x (numerator) and y (denominator) are positive integers and y is not equal to 0. X and y should not have any common divisors other than 1. There are positive and negative rational numbers. Positive rational numbers are those whose numerator as well as denominator are positive integers, whereas negative rational numbers have either the numerator or denominator number as negative.

Q3. How can we obtain rational numbers between two rational numbers according to Chapter 9 Rational Numbers of Class 7 Maths?

Ans: Rational numbers refer to numbers that don’t have 0 as the denominator, and where both the denominator and the numerator are integers. To obtain rational numbers between two rational numbers we can simplify it by dividing it by 2. For example; the rational number between 3/2 and 4/2 is 7/4 as 3/2+4/2=7/2.

We can perform all the operations such as add, subtract, multiple and divide with rational numbers. Rational numbers can perform operations only with other rational numbers and will not be able to with irrational numbers.

Q4. What are the Important Topics Covered in NCERT Solutions of Chapter 9 Rational Numbers of Class 7 Maths?

Ans: NCERT Solutions for Class 7 Maths Chapter 9 is one of the most important chapters in Mathematics. There are many important concepts and topics that are covered in this chapter from the examination point of view. The important topics covered are Introduction to rational numbers, need for rational numbers, what are rational numbers, positive and negative rational numbers, rational numbers on the number line,  In the standard form of rational numbers, operations on rational numbers (addition, subtraction, multiplication and division) and obtaining rational numbers between two rational numbers. 

Q5. How do you represent rational numbers in their standard form as explained in Chapter 9 Rational Numbers of Class 7 Maths?

Ans: Rational numbers are a part of the real number system. Rational numbers are represented in terms of a fraction in their standard form. Rational numbers are represented in the ratio of x and y. Here x (numerator) and y (denominator)  are positive integers and y is not equal to 0. Rational numbers are used to represent almost everything. For example; taxes are done in decimals, division of pizza or anything. These numbers are fractions and hence rational numbers. 

Chapterwise Important Questions for CBSE Class 7 Maths

Cbse study materials.

Rational Number Questions

Rational number questions with solutions are provided here for students to practice and prepare for their upcoming examinations. These questions are based on the Class 8 syllabus. They are prepared as per the NCERT (CBSE) guidelines. Solving these questions will help students understand the concept well, and improve their skills.

Also, check:

• Important 2 Marks Questions for Class 8 Maths
• Important 3 Marks Questions for Class 8 Maths
• Important 4 Marks Questions for Class 8 Maths

Rational numbers are the numbers which are represented in the form of p/q, where

(i) p and q are integers

(iii) p and q are co-prime numbers, that is, HCF(p, q) = 1.

Learn more about Rational Numbers .

Rational Number Class 8 Questions with Solution

Let us practice some important rational numbers questions for class 8 to prepare for examinations.

Question 1: Find the additive inverse of the following:

(i) 22/4 (ii) ⅜ (iii) – 24/–5 (iv) 17/(– 6)

The additive inverse of 22/4 is – 22/4 or – 11/2.

The additive inverse of ⅜ is – ⅜.

(iii) – 24/–5

The additive inverse of –24/–5 or 24/5 is – 24/5.

(iv) 17/(– 6)

The additive inverse of 17/(–6) or – 17/6 is 17/6.

Question 2: Find the multiplicative inverse of the following:

(i) 18/7 (ii) 34/6 (iii) 29/3 (iv) –6/7

The multiplicative inverse of 18/7 is 7/18.

The multiplicative inverse of 34/6 is 6/34 or 3/17.

The multiplicative inverse of 29/3 is 3/29.

The multiplicative inverse of –6/7 is –7/6.

Question 3: Evaluate:

\(\begin{array}{l}(i)\: \frac{2}{15}-\frac{17}{9}+\frac{3}{5}-\frac{20}{3}\end{array} \)

\(\begin{array}{l}(ii)\: \frac{254}{105}\times\frac{15}{127}-\frac{150}{169}\times \frac{13}{15}\end{array} \)

\(\begin{array}{l}= \left ( \frac{2}{15}+\frac{3}{5} \right )+\left ( -\frac{17}{9}-\frac{20}{3} \right )\end{array} \)

\(\begin{array}{l}= \left ( \frac{2+9}{15} \right )+\left ( \frac{-17-60}{9} \right )\end{array} \)

\(\begin{array}{l}= \frac{11}{15} – \frac{77}{9} = \frac{33-385}{45}\end{array} \)

\(\begin{array}{l}= -\frac{352}{45} \end{array} \)

\(\begin{array}{l}=\left ( \frac{254}{105}\times\frac{15}{127} \right )-\left ( \frac{150}{169}\times \frac{13}{15} \right )= \frac{2}{7}-\frac{10}{13}\end{array} \)

\(\begin{array}{l}=\frac{26-70}{91}=-\frac{44}{91}\end{array} \)

Question 4: State true or false for the following:

(i) Rational numbers are closed with respect to division.

(ii) Every whole number is a rational number.

(iii) Every integer is a rational number.

(iv) There are infinitely many rational numbers between any two rational numbers.

(v) 1 and –1 are the only rational numbers which are equal to their reciprocal.

(i) Rational numbers are closed with respect to division. (False)

(ii) Every whole number is a rational number. (True)

(iii) Every integer is a rational number. (False)

(iv) There are infinitely many rational numbers between any two rational numbers. (True)

(v) 1 and –1 are the only rational numbers which are equal to their reciprocal. (True)

Question 5: Find five rational numbers between ⅔ and ⅘ .

We have the equivalent fractions,

⅔ = (2 × 5)/(3 × 5) = 10/15 and ⅘ = (4 × 3)/(5 × 3) = 12/15

To find five rational numbers lets multiply both numerator and denominator of the equivalent fractions by 5, we get

(10 × 5)/(15 × 5) = 50/75 and (12 × 5)/(15 × 5) = 60/75

Therefore, five rational numbers between ⅔ = 50/75 and ⅘ = 60/75 are

51/75, 52/75, 53/75, 54/75, 55/75.

• Exponents and Powers
• Algebraic expressions
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• Ratio and Proportion

Question 6: State which property is in the following:

(i) ⅖ + ( –⅚ + ½) = {⅖ + ( –⅚)} + ½

(ii) 3 – 45/7 + 3/2 = (3 + 3/2) – 45/7

(iii) 300 × 45 = (300 × 40) + (300 × 5)

(iv) 2/19 × 19/2 = 1

(v) 3/7 + (–3/7) = 0

Question 7: Find ten rational numbers between 2 and 3.

Multiply and divide both the numbers by 11, we get

(2 × 11)/11 = 22/11 and (3 × 11)/11 = 33/11

Rational numbers between 2 = 22/11 and 3 = 33/11 are:

23/11, 24/11, 25/11, 26/11, 27/11, 28/11, 29/11, 30/11, 31/11, 32/11.

Question 8: From a 50 m cloth, 7/3 m cloth cut out to make a shirt and 14/5 is cut out to make a curtain. Find the remaining length of the cloth?

Total length of the cloth = 50 m

Cloth used for making shirt = 7/3 m

Cloth used for making curtain = 14/5 m

Remaining cloth = 50 – 7/3 – 14/5 = 50 – {7/3 + 14/5}

= 50 – {77/15} = (750 – 77)/15 = 673/15 m

Question 9: A train covers 256 km in an hour. How much distance it would cover in 35/8 hours?

Distance covered by the train in one hour = 256 km

Distance covered in 35/8 hours = 256 × 35/8 = 1120 km

Question 10: The monthly salary of a man is ₹ 65000, one-fifth of his salary is spend paying the rent, 5/26th of his remaining salary is spent in buying groceries, and half of the rest salary is spent miscellaneous expenses. How much his monthly saving?

Total salary = ₹ 65000

Amount spend in paying the rent = ⅕ × 65000 = ₹ 13000

Remaining amount = 65000 – 13000 = ₹ 52000

Amount spend in groceries = 5/26 × 52000 = ₹ 10000

Remaining amount = 52000 – 10000 ₹ 42000

Miscellaneous expenses = ½ × 42000 = ₹ 21000

∴ his monthly savings = ₹ 21000.

Video Lesson on Rational Numbers Class 8

Practice Questions on Rational Numbers Class 8

1. State true or false for the following:

(i) All integers are rational number.

(ii) Multiplicative inverse does not exist for rational numbers.

(iii) 1 is the additive identity for rational numbers.

(iv) ⅔ lies in between the rational numbers ⅛ and 7/9.

2. Find rational numbers between ⅖ and 9/5.

3. Represent the following rational numbers on the number line

(i) ⅔ (ii) ⅗ (iii) –9/4

4. A rational number x is equal to ⅖ times the sum of 34/7 and 1/14. Find the rational number.

5. Reena could run 21/5 m in an hour. How much she can run in 34/7 hours?

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