ncert solutions for class 8 maths chapter 1 provides detailed answers, step-by-step solutions, and key explanations to help students excel in their math exams.
Sample Questions and Answers for Class 8 Maths Chapter 1:
What is the definition of a rational number?
A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero. For example, 1/2, 3/4, and -5/6 are all rational numbers.
How do you convert a decimal to a fraction?
To convert a decimal into a fraction, count the number of decimal places and then write it as a fraction with the denominator being a power of 10. For example, 0.75 becomes 75/100, which simplifies to 3/4.
What is the difference between proper and improper fractions?
A proper fraction is one where the numerator is smaller than the denominator, like 2/3. An improper fraction has a numerator larger than or equal to the denominator, like 5/3.
How can you simplify a fraction?
To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD). For example, 12/16 simplifies to 3/4 by dividing both by 4.
What are like and unlike fractions?
Like fractions have the same denominator, such as 1/4 and 3/4. Unlike fractions have different denominators, like 1/3 and 2/5.
How do you add fractions with the same denominator?
To add fractions with the same denominator, simply add the numerators and keep the denominator the same. For example, 2/5 + 3/5 = 5/5, which simplifies to 1.
How do you subtract fractions with different denominators?
First, find the least common denominator (LCD) of the two fractions. Then, rewrite the fractions with the LCD, and subtract the numerators. Finally, simplify the result if necessary.
What is the process to multiply fractions?
To multiply fractions, multiply the numerators together and the denominators together. For example, 2/3 × 4/5 = 8/15.
How do you divide fractions?
To divide fractions, multiply the first fraction by the reciprocal (flipped version) of the second fraction. For example, 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12, which simplifies to 5/6.
What is the method to convert a fraction to a percentage?
To convert a fraction to a percentage, first divide the numerator by the denominator and then multiply the result by 100. For example, 3/4 becomes 0.75 × 100 = 75%.
How do you calculate the average of a set of numbers?
To calculate the average, add all the numbers together and divide by the total number of values. For example, the average of 4, 5, and 7 is (4 + 5 + 7) / 3 = 5.33.
What is the meaning of a prime number?
A prime number is a number greater than 1 that has no divisors other than 1 and itself. For example, 2, 3, 5, and 7 are prime numbers.
What is a composite number?
A composite number is a positive integer greater than 1 that is not prime, meaning it has divisors other than 1 and itself. For example, 4, 6, and 8 are composite numbers.
How do you find the LCM of two numbers?
To find the least common multiple (LCM) of two numbers, list the multiples of each number and find the smallest multiple that both numbers share. For example, the LCM of 4 and 5 is 20.
How do you find the HCF of two numbers?
To find the highest common factor (HCF) of two numbers, list all the factors of each number and find the greatest factor they have in common. For example, the HCF of 12 and 18 is 6.
What is a decimal fraction?
A decimal fraction is a fraction where the denominator is a power of 10, such as 0.25 (which is 25/100).
How do you add decimals?
To add decimals, line up the decimal points, and then add as you would with whole numbers. If necessary, add zeroes to make the number of decimal places equal in both numbers.
How do you subtract decimals?
To subtract decimals, align the decimal points and subtract as if they were whole numbers. Add zeroes if needed to make the number of decimal places the same.
What are equivalent fractions?
Equivalent fractions are different fractions that represent the same value. For example, 1/2, 2/4, and 4/8 are all equivalent fractions.
How do you round a decimal to the nearest whole number?
To round a decimal to the nearest whole number, look at the digit in the tenths place. If it is 5 or greater, round up. If it is less than 5, round down.
What is the value of pi?
The value of pi (π) is approximately 3.14159. It is the ratio of the circumference of a circle to its diameter.
How do you find the perimeter of a rectangle?
To find the perimeter of a rectangle, add the lengths of all four sides. The formula is P = 2(length + width).
How do you calculate the area of a rectangle?
To calculate the area of a rectangle, multiply the length by the width. The formula is A = length × width.
How do you calculate the area of a square?
The area of a square is calculated by squaring one of its sides. The formula is A = side × side.
How do you find the area of a triangle?
To find the area of a triangle, multiply the base by the height and divide by 2. The formula is A = 1/2 × base × height.
What is the formula for the circumference of a circle?
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle.
How do you find the volume of a cube?
The volume of a cube is calculated by cubing the length of one side. The formula is V = side³.
How do you find the volume of a rectangular prism?
The volume of a rectangular prism is found by multiplying its length, width, and height. The formula is V = length × width × height.
What is the difference between surface area and volume?
Surface area is the total area of the outer surface of a 3D object, while volume is the amount of space inside the object.
How do you calculate the speed of an object?
Speed is calculated by dividing the distance traveled by the time taken. The formula is Speed = Distance / Time.
What is the formula for calculating distance?
The formula for distance is Distance = Speed × Time.
What is the difference between average speed and instantaneous speed?
Average speed is the total distance divided by the total time, while instantaneous speed is the speed of an object at a specific moment in time.
How do you calculate the simple interest?
The formula for simple interest is I = P × R × T, where P is the principal amount, R is the rate of interest, and T is the time period.
What is the formula for calculating compound interest?
The formula for compound interest is A = P(1 + R/n)^(nt), where P is the principal amount, R is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
What is the difference between direct and inverse proportions?
In direct proportion, as one quantity increases, the other also increases. In inverse proportion, as one quantity increases, the other decreases.
How do you calculate the area of a circle?
The area of a circle is calculated by the formula A = πr², where r is the radius.
How do you convert a fraction to a decimal?
To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/4 is equal to 0.75.
What is the relationship between speed, time, and distance?
The relationship is given by the formula Distance = Speed × Time.
What is a parallelogram?
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length.
How do you calculate the area of a parallelogram?
The area of a parallelogram is calculated by multiplying the base by the height. The formula is A = base × height.
What is the perimeter of a triangle?
The perimeter of a triangle is the sum of the lengths of its three sides.
How do you find the mean of a set of numbers?
To find the mean, add all the numbers together and divide by the total number of values.
What is a reflection in geometry?
A reflection is a transformation where each point of a figure is mirrored over a line, creating a mirror image.
What is the difference between a rotation and a translation in geometry?
A rotation turns a figure around a fixed point, while a translation moves a figure from one location to another without rotating or resizing it.
How do you find the area of a trapezium?
The area of a trapezium is calculated by the formula A = 1/2 × (sum of parallel sides) × height.
How do you find the volume of a cone?
The volume of a cone is calculated by the formula V = 1/3 × πr² × h, where r is the radius and h is the height.
What is the relationship between the radius and diameter of a circle?
The diameter of a circle is twice the radius. The formula is d = 2r.
How do you calculate the surface area of a sphere?
The surface area of a sphere is calculated by the formula A = 4πr², where r is the radius.
How do you find the volume of a cylinder?
The volume of a cylinder is calculated by the formula V = πr² × h, where r is the radius and h is the height.
What is a polygon?
A polygon is a closed figure with straight sides. Examples of polygons include triangles, squares, and pentagons.
This covers a range of essential concepts for class 8 maths chapter 1, helping students grasp the basics of fractions, geometry, measurement, and other topics.
Top Indian Books for NCERT Solutions for Class 8 Maths Chapter 1: A Guide for Students
Mathematics for Class 8 by R.D. Sharma, Dhanpat Rai Publications
This book covers detailed solutions for various topics including fractions, rational numbers, and algebra from Chapter 1. It provides a variety of questions ranging from simple exercises to more complex application-based problems to ensure comprehensive understanding.
NCERT Solutions for Class 8 Maths by Arihant Experts, Arihant Publications
This book offers step-by-step solutions to all questions from the NCERT textbook. The content includes both solved and unsolved questions that cater to conceptual understanding and practice. It focuses on easy-to-understand explanations with multiple examples.
Mathematics Class 8 by S. Chand, S. Chand & Co.
S. Chand’s Mathematics for Class 8 includes explanations and exercises based on the NCERT syllabus. Chapter 1 features a range of questions on rational numbers and fractions, helping students grasp the fundamentals and their applications.
Class 8 Mathematics by M.L. Agarwal, Krishna Prakashan Media
This book is designed to help students understand the foundational concepts of Chapter 1 with an emphasis on practice problems. The book presents detailed explanations, tips, and tricks for solving different types of questions.
Guide to Class 8 Maths by R.S. Aggarwal, S. Chand & Co.
R.S. Aggarwal’s book is a comprehensive guide, particularly focused on Chapter 1, which explores rational numbers and fractions. It includes a wide array of practice problems, detailed solutions, and is useful for self-study.
Mathematics for Class 8 by R. S. Verma, M. L. Aggarwal, Bharati Bhawan Publishers
The book includes NCERT-style questions, practice exercises, and solutions to make it easier for students to understand Chapter 1. It’s excellent for in-depth practice and ensuring conceptual clarity.
Practical Mathematics for Class 8 by S.K. Gupta, Laxmi Publications
This book provides detailed explanations, examples, and exercises for the initial chapters, including fractions and rational numbers. It’s perfect for students looking for clear, easily comprehensible content.
Mathematics Class 8 by J.P. Agarwal, Vikas Publishing House
This book not only covers solutions to Chapter 1 but also offers valuable insights into problem-solving techniques. It includes a variety of questions and practical applications of mathematical concepts in everyday life.
Class 8 Mathematics Workbook by Xtreme Maths, Xtreme Publishers
A workbook dedicated to Class 8, this book includes a variety of fun and interactive problems along with solutions that help reinforce the key concepts of Chapter 1. It’s ideal for active problem-solving practice.
Comprehensive Mathematics for Class 8 by R.K. Bansal, Bharti Bhawan Publications
This book covers the NCERT syllabus in detail with focus on the basics of rational numbers. It includes numerous practice problems, examples, and provides step-by-step solutions to each question.
NCERT Math Solutions by D. D. Sharma, Mahavir Publishers
This book provides a clear and easy explanation of Chapter 1 of Class 8 Mathematics, particularly focused on rational numbers and fractions. The practice sets are designed for building strong problem-solving skills.
Mathematics Class 8 by M.S. Malik, Goyal Publishers
The book covers various exercises, worked examples, and practice questions for Chapter 1. It is highly recommended for students who want to practice and consolidate their understanding of rational numbers.
New Mathematics Today for Class 8 by Dr. M. S. Chouhan, Orient Black Swan
This book offers detailed explanations and numerous practice exercises. It focuses on foundational mathematical concepts, such as rational numbers and their properties, with varied types of questions.
Target Class 8 Mathematics by R. Gupta, Bharti Bhawan Publications
This book provides complete solutions and practice questions based on Chapter 1. The content is structured to help students develop skills through challenging exercises while reinforcing the key concepts.
Modern Mathematics for Class 8 by R.N. Gupta, Modern Publishers
Modern Mathematics focuses on helping students understand rational numbers and fractions. It provides simple, clear solutions to the problems in Chapter 1 and includes practical exercises for honing skills.
Mathematics: A Textbook for Class 8 by S. K. Aggarwal, Golden Publishers
This book offers a thorough understanding of the NCERT syllabus with in-depth discussions on fractions and rational numbers. The variety of questions allows students to engage with the topic from multiple angles.
Comprehensive Guide for Class 8 Maths by Cengage Learning, Cengage Publications
This guide offers detailed solutions to Chapter 1 and provides both basic and challenging problems to build a strong mathematical foundation.
Mathematics Practice Book for Class 8 by J.P. Saxena, Vikas Publishing
This book provides a good collection of problems that cover the entire Chapter 1 of Class 8 Maths. Each problem is explained step-by-step to ensure that students grasp the concepts thoroughly.
Simplified Mathematics for Class 8 by D.N. Awasthi, Pearson Publications
This book focuses on making mathematical concepts simple and easy to understand. It provides a variety of exercises and solutions for Chapter 1, including problem-solving strategies and hints.
NCERT Math Solutions: Class 8 by K. V. Singh, Vidya Prakashan
This book contains solutions to all questions from Chapter 1 of the NCERT Class 8 Maths textbook. It provides detailed answers and solutions that help students develop a deep understanding of the material.
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