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Case Study Questions for Class 7 Maths Chapter 9 Rational Numbers

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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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Chapter 8 Class 7 Rational Numbers

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Get solutions of all NCERT Questions, and also understand the concepts of Chapter 8 Class 7 Rational Numbers free at teachoo. All NCERT exercise questions and examples are solved. 

In concept wise, we have first divided the chapter into concepts. When you click on a concept, first the concept is explained, and then its related questions are solved from easy to difficult.

In this chapter, we will study

• What are rational numbers
• All natural numbers, whole numbers and integers are rational numbers
• Finding equivalent rational numbers
• Writing rational numbers in Standard Form
• Drawing rational numbers on the number line
• Comparing rational numbers (with same, as well as different denominators)
• Finding rational numbers between two rational numbers
• And then we will study how to add and subtract rational numbers (with same, as well as different denominators)
• As well as how to multiply
• and divide rational numbers

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NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers

Ncert solutions for class 7 maths chapter 9 rational numbers ex 9.1.

• Class 7 Maths Rational Numbers Exercise 9.1 
• Class 7 Maths Rational Numbers Exercise 9.2

Ex 9.1 Class 7 Maths Question 9.

Class 7 Maths Chapter 9 Exercise 9.2

NCERT Solutions Maths Science Social English Sanskrit Hindi RD Sharma

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NCERT Solutions

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NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers are provided below. Our solutions covered each questions of the chapter and explains every concept with a clarified explanation. It helps the students to understand slowly and to get practice well to become perfect and again a good score in their examination. Below we have listed NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Exercise 9.1 and Ex 9.2.

These materials are prepared based on Class 7 NCERT syllabus, taking the types of questions asked in the NCERT textbook into consideration. Further, all the CBSE Class 7 Solutions Maths Chapter 9 Rational Numbers are in accordance with the latest CBSE guidelines and marking schemes

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.2

Class 7 Maths Chapter 9 Rational Numbers Textbook Solutions

Given below are some of the concepts present in this chapter.

• Need For Rational Numbers
• What Are Rational Numbers
• Positive And Negative Rational Numbers
• Rational Numbers On a Number Line
• Rational Numbers in Standard Form
• Comparison of Rational Numbers
• Rational Numbers Between Two Rational Numbers
• Addition of Rational Numbers
• Subtraction of Rational Numbers
• Multiplication of Rational Numbers
• Division of Rational Numbers

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• NCERT Exemplar
• NCERT Exemplar Class 7
• Class 7 Maths
• Class 7 Maths Chapter 8

NCERT Exemplar Solutions for Class 7 Maths Chapter 8 Rational Numbers

The NCERT Exemplar Solutions for Class 7 Maths Chapter 8 Rational Numbers PDF is useful for students to understand the question pattern and types of problems. It is essential to learn about different problems and figure out the best solutions to them. Students can find NCERT Exemplar Solutions for Class 7 Chapter 8 and understand how to solve problems.

In Chapter 8 – Rational Numbers, we can see that a rational number is expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number. Some of the important topics covered in this chapter are

• Positive and Negative Rational Numbers
• Rational Numbers on a Number Line
• Rational Numbers in Standard Form
• Comparison of Rational Numbers
• Operations on Rational Numbers

Download the PDF of NCERT Exemplar Solutions for Class 7 Maths Chapter 8 Rational Numbers

Access Answers to Maths NCERT Exemplar Solutions for Class 7 Chapter 8 Rational Numbers

Exercise Page: 242

In each of the following questions 1 to 12, there are four options, out of which, only one is correct. Write the correct one.

1. A rational number is defined as a number that can be expressed in the form p/q, where p and q are integers and

(a) q = 0 (b) q = 1 (c) q ≠ 1 (d) q ≠ 0

A number that can be expressed in the form p/q , where p and q are integers and q ≠ 0, is called a rational number.

2. Which of the following rational numbers is positive?

(a) (-8/7) (b) (19/-13) (c) (-3/-4) (d) (-21/13)

(c) (-3/-4)

When the numerator and denominator both are positive integers or both are negative integers, it is a positive rational number.

3. Which of the following rational numbers is negative?

(a) – (-3/7) (b) (-5/-8) (c) 9/8 (d) (3/-7)

When either the numerator or the denominator is a negative integer, it is a negative rational number.

4. In the standard form of a rational number, the common factor of numerator and denominator is always:

(a) 0 (b) 1 (c) – 2 (d) 2

A rational number is said to be in the standard form, if its denominator is a positive integer and the numerator and denominator have no common factor other than 1.

5. Which of the following rational numbers is equal to its reciprocal?

(a) 1 (b) 2 (c) ½ (d) 0

We know that, the numerator and denominator have no common factor other than 1.

Reciprocal of 1/1 = 1

6. The reciprocal of ½ is

(a) 3 (b) 2 (c) – 1 (d) 0

The reciprocal of ½ = 2/1

7. The standard form of -48/60 is

(a) 48/60 (b) -60/48 (c) -4/5 (d) -4/-5

The standard form of -48/60 is = (-4/5)

Divide both numerator and denominator by 12

8. Which of the following is equivalent to 4/5 ?

(a) 5/4 (b) 16/25 (c) 16/20 (d) 15/25

Solution: –

4/5 is equivalent = (4 × 4)/(5 × 4)

9. How many rational numbers are there between two rational numbers?

(a) 1 (b) 0 (c) unlimited (d) 100

(c) unlimited

10. In the standard form of a rational number, the denominator is always a

(a) 0 (b) negative integer (c) positive integer (d) 1

(c) positive integer

A rational number is said to be in the standard form, if its denominator is a positive integer.

11. To reduce a rational number to its standard form, we divide its numerator and denominator by their

(a) LCM (b) HCF (c) product (d) multiple

12. Which is greater number in the following:

(a) -½ (b) 0 (c) ½ (d) -2

In Questions 13 to 46, fill in the blanks to make the statements true.

13. –(3/8) is a rational number.

–(3/8) is a negative rational number.

14. 1 is a rational number.

1 is a positive rational number

15. The standard form of (-8/-36) is .

The standard form of (-8/-36) is 2/9.

-8/-36 = 8/36

So, HCF of 8 and 36 is 4

Then, divide both numerator and denominator by 4.

16. The standard form of 18/-24 is

The standard form of 18/-24 is -3/4.

So, HCF of 18 and -24 is 6

Then, divide both numerator and denominator by 6.

Now, multiplying -1 to both numerator and denominator.

= (3 × -1)/(-4 × -1)

17. On a number line, -½ is to the ______ of zero (0).

On a number line, -½ is to the left of zero (0).

On a number line, rational number present to the left of the zero (0) are negative rational numbers and rational numbers present to the right of the zero (0) are positive rational numbers.

18. On a number line, 4/3 is to the of zero (0).

On a number line, 4/3 is to the right of zero (0).

19. -½ is than 1/5.

-½ is smaller than 1/5.

20. -3/5 is than 0.

-3/5 is smaller than 0.

21. -16/24 and 20/-16 represent rational numbers.

-16/24 and 20/-16 represent different rational numbers.

So, HCF of -16/24 is 4

Then divide both numerator and denominator by 4.

HCF of 20/-16 is 1

Therefore, -16/24 and 20/-16 represent different rational numbers.

22. -27/45 and -3/5 represent rational numbers.

-27/45 and -3/5 represent same rational numbers.

So, HCF of -27/45 is 9

Divide both numerator and denominator by 9.

Then, HCF of -3/5 is 1

Therefore, -27/45 and -3/5 represent same rational numbers.

23. Additive inverse of 2/3 is ______.

Additive inverse of 2/3 is -2/3.

24. (-3/5) + (2/5) = .

(-3/5) + (2/5) = -1/5.

= (-3/5) + (2/5)

= (-3 + 2)/5

25. (-5/6) + (-1/6) = .

(-5/6) + (-1/6) = -1.

= (-5/6) – (1/6)

= (-5 – 1)/6

26. (3/4) × (-2/3) = .

(3/4) × (-2/3) = -1/2.

= (3 × -2)/ (4 × 3)

= (1 × -1)/ (2 × 1)

27. (-5/3) × (-3/5) = .

(-5/3) × (-3/5) = 1.

= (-5 × -3)/ (3 × 5)

= (-1 × -1)/ (1 × 1)

28. (-6/7) = ( /42)

(-6/7) = (-36/42)

Let us assume the missing letter be x.

(-6/7) = (x/42)

(-6/7) × 42 = x

(-6 × 6) = x

x = – 36

29. (1/2) = (6/ )

(1/2) = (6/12)

(1/2) = (6/x)

(2/1) × 6 = x

30. (-2/9) – (7/9) =

(-2/9) – (7/9) = -1

= (-2 – 7)/9

In questions 31 to 35, fill in the boxes with the correct symbol >, < or =.

31. (7/-8) [ ] (8/9)

(7/-8) [<] (8/9)

Negative rational number is less than positive rational number.

32. (3/7) [ ] (-5/6)

(3/7) [>] (-5/6)

33. (5/6) [ ] (8/4)

(5/6) [<] (8/4)

The LCM of 6 and 4 is 12

∴ (5/6) = [(5 × 2)/ (6 × 2)] = (10/12)

and (8/4) = [(8 × 3)/(4 × 3)] = (24/12)

Now, 10 < 24

⇒ (10/12) < (24/12)

Hence, (5/6) < (8/4)

34. (-9/7) [ ] (4/-7)

(-9/7) [<] (4/-7)

Let us write (4/-7) with a positive denominator.

So, (-9/7) < (-4/7)

35. (8/8) [ ] (2/2)

(8/8) [=] (2/2)

(8/8) divide both denominator and numerator by 8

Then, 1/1 = 1

(2/2) divide both denominator and numerator by 2

Therefore, 1 = 1

36. The reciprocal of ______ does not exist.

The reciprocal of 0 does not exist.

37. The reciprocal of 1 is ______.

The reciprocal of 1 is 1.

Reciprocal of 1 = (1/1) = 1

38. (-3/7) ÷ (-7/3) = .

(-3/7) ÷ (-7/3) = 9/49.

(-3/7) ÷ (-7/3)

= (-3/7) × (3/-7)

= (-3 × 3)/ (7 × -7)

39. 0 ÷ (-5/6) = .

0 ÷ (-5/6) = 0.

We know that, division of zero by any number is zero.

40. 0 × (-5/6) = .

0 × (-5/6) = 0.

We know that, multiplication of zero by any number is zero.

41. × (-2/5) = 1

(-5/2)× (-2/5) = 1

Let u assume the missing rational number be y.

y × (-2/5) = 1

42. The standard form of rational number –1 is ______.

The standard form of rational number –1 is -1.

43. If m is a common divisor of a and b, then (a/b) = (a ÷ m)/ .

If m is a common divisor of a and b, then (a/b) = (a ÷ m)/(b ÷ m).

44. If p and q are positive integers, then p/q is a ______ rational number and – p/q is a ______ rational number.

If p and q are positive integers, then p/q is a positive rational number and – p/q is a negative rational number.

As we know that, When the numerator and denominator both are positive integers or both are negative integers, it is a positive rational number. When either the numerator or the denominator is a negative integer, it is a negative rational number.

45. Two rational numbers are said to be equivalent or equal, if they have the same ______ form.

Two rational numbers are said to be equivalent or equal, if they have the same simplest form.

If the numerator and denominator of a rational number are multiplied or divided by a non-zero integer, we get a rational number which is said to be equivalent to the given rational number.

46. If p/q is a rational number, then q cannot be ______.

If p/q is a rational number, then q cannot be zero.

State whether the statements given in question 47 to 65 are True or False.

47. Every natural number is a rational number but every rational number need not be a natural number.

48. Zero is a rational number.

Zero can be written as 0 = 0/1

We know that a number of a form p/q where p, q are integers and q is not equal to zero is a rational number.

Hence, zero is a rational number.

49. Every integer is a rational number but every rational number need not be an integer.

6/3 is rational number. Since if we simplify 6/3 to its lowest term we get 2/1 = 2, which is an integer.

Every integer is a rational number but every rational number is not an integer.

50. Every negative integer is not a negative rational number.

51. If p/q is a rational number and m is a non-zero integer, then

(p/q) = (p × m)/(q × m)

A fraction is not changed whether the both numerator and denominator are multiplied by the same number or divided by the same number.

52. If p/q is a rational number and m is a non-zero common divisor of p and q, then

p/q = (p ÷ m)/(q ÷ m)

53. In a rational number, denominator always has to be a non-zero integer.

54. If p/q is a rational number and m is a non-zero integer, then (p/q) = (p × m)/(q × m) is a rational number not equivalent to p/q.

We know that, a fraction is not changed whether the both numerator and denominator are multiplied by the same number or divided by the same number.

55. Sum of two rational numbers is always a rational number.

Let us consider the two rational numbers (1/2) and (3/4)

Then, sum of two rational numbers = (1/2) + (3/4)

LCM of 2 and 4 is 4

= (2/4) + (3/4)

= (2 + 3)/4

= 5/4 is a rational number.

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• NCERT Exemplar for Class 7 Maths Solutions Chapter 8 Rationals Numbers
• Textbook Solutions

Class 7 Maths NCERT Exemplar Solutions Chapter 8 Rationals Numbers

Students can download free PDF NCERT Exemplar for Class 7 Maths Chapter - 8 Rational Numbers solved by expert maths teachers on Vedantu as per NCERT (CBSE) book guidelines. Students of class 7 have to be very attentive while going through chapter 8, Rational Numbers. They will notice that NCERT Exemplar for such a chapter of the subject is fairly easy to understand along with being very helpful. 

Putting in some effort that can help the students to prepare using such study material is one of the main things that the teachers stress the most. The NCERT Exemplar for Rational Numbers contains a good amount of questions, both short and long ones, which can thoroughly guide the student to get ready for their exams and pass with great marks. 

This chapter is very significant in terms of the fact that it builds a foundation for Maths that will be introduced to the students at the time of their higher studies. 

The students of class 7 should get started with their studies and learn in a chapter-wise manner to get a good understanding of their subjects, especially Maths. 

About Rational Numbers

Rational number is a number denoted in the form of a/b, where a and b are integers, and b is not equal to zero. 

The set of rational numbers include all the integers, each of which can be written as a quotient with the integer as the numerator and one as the denominator. 

For more information on rational numbers, download the solutions from Vedantu.

Every NCERT Solution is provided to make the study simple and interesting on Vedantu. Subjects like science, maths, english will become easy to study if you have access to NCERT Solution for Class 7 Science , Maths solutions and solutions of other subjects. You can also download NCERT Solutions for Class 7 Maths to help you to revise the complete syllabus and score more marks in your examinations.

FAQs on NCERT Exemplar for Class 7 Maths Solutions Chapter 8 Rationals Numbers

1. Does the NCERT Exemplar Class 7 Maths Solutions Chapter 8 Rational Numbers provide good preparations for exams?

The NCERT Exemplar for Class 7 Maths Solutions Chapter 8 Rational Numbers is the best bet for the students to get on top of their preparations and get the necessary help with upping their overall scores. The subject is tough, but study material like this can change the way one prepares as it is easy and quick to understand. Good preparations for any of the exams or tests can come hand in hand with good study material, and the NCERT Exemplar for class 7 provides just that.  

2. How can the students of class 7 study for maths in a chapter-wise manner for their exams?

It is of utmost significance for the students of class 7 to get their Maths exam preparations done thoroughly. The NCERT Exemplar for Class 7 Maths comes with several solutions in the same chapter-wise manner that allows the students to learn in the same way as well. The students can take up the NCERT Exemplars of each chapter one by one and thoroughly after their revision. They can then work on the various problem areas that they identify, and ensure that they have full knowledge of the particular chapters. 

3. Why must a student refer to NCERT Exemplar Class 7 Maths Solutions Chapter 8 Rational Numbers?

The best reasons to study for exams from the NCERT Exemplar Class 7 Maths Solutions Chapter 8 Rational Numbers are:

Students can understand the focus points of the various chapters

They can memorize all the details in an effective manner

They can figure out their weak points and work on them more.

They can build a stronger foundation for their higher studies. 

They have the solutions to refer to that can help them at the time of their exams. 

4. Which platform works the best for downloading the NCERT Exemplar Class 7 Maths Solutions Chapter 8 Rational Numbers?

When it comes to downloading any type of study material, like NCERT Exemplar Class 7 Maths Solutions Chapter 8 Rational Numbers, Vedantu is your best bet. The platform is essentially created to provide students with the necessary study materials for any subject, class, and type. The students only have to put in their search query after registering and download the PDF that can be accessed from their computer, laptop, phone, etc. The students of class 7 can simplify their learning with advances like this.

5. How can the NCERT Exemplar Class 7 Maths Solutions Chapter 8 Rational Numbers help the students in preparing for their exams?

The NCERT Exemplar Class 7 Maths Solutions Chapter 8 Rational Numbers comes well equipped with a variety of questions in it, no matter whether they are long answer type questions or short answer type questions, subjective or objective. These ensure that the students only get the kind of study material that can very well help them excel in their studies and make the preparations simple as well as effective. The students can also find the solutions to be easy to understand, grasp the formulas and procedures very quickly. 

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Review articles, unit 1: proportional relationships, unit 2: rates and percentages, unit 3: integers: addition and subtraction, unit 4: rational numbers: addition and subtraction, unit 5: negative numbers: multiplication and division, unit 6: expressions, equations, & inequalities, unit 7: statistics and probability, unit 8: scale copies, unit 9: geometry.