Mastering Chapter 1: Rational Numbers for Jawahar Navodaya Vidyalaya Class 9 Entrance Exam in English/Hindi
Introduction: Welcome to jnvmaths.com, your ultimate resource for excelling in mathematics and preparing for the Jawahar Navodaya Vidyalaya (JNV) class 9 entrance exam. In this comprehensive blog post, we'll dive into Chapter 1: Rational Numbers, a fundamental topic that forms the basis of many mathematical concepts. We'll guide you through this chapter, offering insights, tips, and strategies to help you conquer it with confidence.
Understanding Rational Numbers: Chapter 1 of your JNV entrance exam syllabus focuses on rational numbers. These numbers can be expressed as a quotient or fraction of two integers, where the denominator is not zero. To master this chapter, it's essential to have a strong grasp of the following key concepts:
1. Understanding Rational Numbers:
Definition and properties of rational numbers.
Converting fractions to decimals and vice versa.
Identifying rational and irrational numbers.
2. Operations with Rational Numbers:
Addition, subtraction, multiplication, and division of rational numbers.
Simplification of rational numbers.
Properties of these operations.
Tips for Effective Preparation:
1. Conceptual Clarity:
Start by understanding the basic definitions and properties of rational numbers. Ensure you can distinguish between rational and irrational numbers.
2. Practice Regularly:
Practice is key to success in mathematics. Solve a variety of problems related to rational numbers to strengthen your skills.
3. Create a Study Plan:
Organize your study sessions with a well-structured plan. Allocate time for learning, practicing, and revising.
4. Use Online Resources:
Explore online tutorials, videos, and interactive exercises to reinforce your understanding.
5. Seek Help When Needed:
Don't hesitate to ask your teachers or peers for assistance if you encounter challenging concepts or problems.
Sample Questions and Exercises:
To help you get started with your rational number preparation, here are some sample questions and exercises:
1. Simplify the following expressions:
12181812
721217
25505025
2. Perform the following operations:
23+4532+54
38−1483−41
56×2565×52
34÷2343÷32
1. An integer can be:
a) Only positive
b) Only negative
c) Both positive and negative
d) None of the above
Answer: (c)
Explanation: An integer can be both positive and negative as well as zero.
2. A rational number can be represented as:
a) p/q
b) pq
c) p+q
d) pq
Answer: (A)
Explanation: A rational number can be represented as p/q where p and q are integers and q is not equal to zero.
3. The value of ½ x ⅗ is equal to:
a) ½
b) 3/10
c)⅗
d)⅖
Answer: (B)
Explanation: ½ x ⅗ = (1×3)/(2×5) = 3/10
4. The value of (½) ÷ (⅗) is equal to:
a) 3/10
b)⅗
c) 6/5
d) ⅚
Answer: (D)
Explanation: (½) ÷ (⅗) = (½) x (5/3) = (1×5)/(2×3) = ⅚
5. The value of ½ + ¼ is equal to:
a) ¾
b) 3/2
c) ⅔
d) 1
Answer: (A)
Explanation: ½ + ¼
Making the denominators equal:
2/4 + ¼ = (2+1)/4 = ¾
6. The value of 5/4 – 8/3 is:
a) 17/12
b) -17/12
c) 12/17
d) -12/17
Answer: (B)
Explanation: 5/4 - 8/3
Making the denominators equal:
[(5/4) x (3/3)] - [(8/3) x (4/4)]
15/12 – 32/12
= (15-32)/12
= -17/12
7. Associative property applies to the following:
a) Addition and subtraction
b) multiplication and division
c) Addition and multiplication
d) subtraction and division
Answer: (c)
Explanation: According to associative property:
A+B = B+A
AB = BA
Where A and B are two integers.
8. The value of (-10/3) x (-15/2) x (17/19) x 0 is:
a) 0
b) 22.66
c) 20
d) 35
Answer: (A)
Explanation: Any number multiplied by zero is equal to zero.
9. The additive identity of rational numbers is:
a) 0
b) 1
c) 2
d) -1
Answer: (A)
Explanation: Any number added to zero equals that number.
Example: 5+0 = 5
10. The multiplicative identity of rational numbers is:
a) 0
b) 1
c) 2
d) -1
Answer: (B)
Explanation: Any number multiplied by 1 is equal to the number
Example: 5 x 1 = 5
1. एक पूर्णांक हो सकता है:
a) केवल धनात्मक
b) केवल ऋणात्मक
c) धनात्मक और ऋणात्मक दोनों
d) उपरोक्त में से कोई नहीं
उत्तर: (c)
स्पष्टीकरण: एक पूर्णांक धनात्मक और ऋणात्मक दोनों के साथ-साथ शून्य भी हो सकता है।
2. एक परिमेय संख्या को इस रूप में दर्शाया जा सकता है:
a) p/q
b) pq
c) p+q
d) pq
उत्तर: (a)
स्पष्टीकरण: एक परिमेय संख्या को पी/क्यू के रूप में दर्शाया जा सकता है जहां पी और क्यू पूर्णांक हैं और क्यू शून्य के बराबर नहीं है।
3. ½ x ⅗ का मान बराबर है:
a) ½
b) 3/10
c) ⅗
d) ⅖
उत्तर: (b)
स्पष्टीकरण: ½ x ⅗ = (1×3)/(2×5) = 3/10
4. (½) ÷ (⅗) का मान बराबर है:
a) 3/10
b) ⅗
c) 6/5
d) ⅚
उत्तर: (d)
स्पष्टीकरण: (½) ÷ (⅗) = (½) x (5/3) = (1×5)/(2×3) = ⅚
5. ½ + ¼ का मान बराबर है:
a) ¾
b) 3/2
c) ⅔
d) 1
उत्तर: (a)
स्पष्टीकरण: ½ + ¼
हर को बराबर बनाना:
2/4 + ¼ = (2+1)/4 = ¾
6. 5/4 – 8/3 का मान है:
a) 17/12
b) -17/12
c) 12/17
d) -12/17
उत्तर: (b)
स्पष्टीकरण: 5/4 - 8/3
हर को बराबर बनाना:
[(5/4) x (3/3)] - [(8/3) x (4/4)]
15/12 – 32/12
= (15-32)/12
= -17/12
7. साहचर्य गुण निम्नलिखित पर लागू होता है:
a) जोड़ और घटाव
b) गुणा और भाग
c) जोड़ और गुणा
d) घटाव और भाग
उत्तर: (c)
स्पष्टीकरण: साहचर्य संपत्ति के अनुसार:
ए+बी = बी+ए
एबी = बीए
जहाँ A और B दो पूर्णांक हैं।
8. (-10/3) x (-15/2) x (17/19) x 0 का मान है:
a) 0
b) 22.66
c) 20
d) 35
उत्तर: (a)
स्पष्टीकरण: किसी भी संख्या को शून्य से गुणा करने पर वह शून्य के बराबर होती है।
9. परिमेय संख्याओं की योगात्मक पहचान है:
a) 0
b) 1
c) 2
d) -1
उत्तर: (a)
स्पष्टीकरण: शून्य में कोई भी संख्या जोड़ने पर वह संख्या के बराबर होती है।
उदाहरण: 5+0 = 5
10. परिमेय संख्याओं की गुणात्मक पहचान है:
a) 0
b) 1
c) 2
d) -1
उत्तर: (b)
स्पष्टीकरण: किसी भी संख्या को 1 से गुणा करने पर वह संख्या के बराबर होती है
उदाहरण: 5 x 1 = 5
हमें उम्मीद
Conclusion:
Chapter 1: Rational Numbers is a crucial building block for your success in the JNV class 9 entrance exam. With dedication, practice, and a clear understanding of the concepts, you can excel in this chapter and lay a strong foundation for your overall mathematics preparation.
Stay tuned to jnvmaths.com for more valuable resources, tips, and guidance to help you ace your entrance exam. Remember, your commitment to learning and preparation will pave the way for your success in the JNV entrance exam and beyond.
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