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Rational numbers are a fundamental concept in mathematics, and understanding them is crucial for success in higher-level math classes. In this worksheet, we will explore the basics of rational numbers, including their definition, properties, and operations.
Infinity Learn offers a treasure trove of free Class 8 Maths worksheets Rational Numbers, meticulously crafted by experienced teachers to support students in mastering mathematical concepts effectively. These worksheets are designed to align seamlessly with the CBSE Syllabus curriculum, ensuring relevance and accuracy in content.
What are Rational Numbers?
A rational number is a number that can be expressed as the ratio of two integers, i.e., p/q, where p and q are integers and q is non-zero. For example, 3/4, 22/7, and -1/2 are all rational numbers.
Properties of Rational Numbers:
- Closure Property: The sum, difference, product, and quotient of two rational numbers is always a rational number.
- Commutative Property: The order of the numbers does not change the result when adding or multiplying rational numbers.
- Associative Property: The order in which we add or multiply rational numbers does not change the result.
- Distributive Property: Rational numbers follow the distributive property of multiplication over addition.
Operations on Rational Numbers:
Addition and Subtraction of Rational Numbers
To add or subtract rational numbers, we need to follow these steps:
- Find the least common multiple (LCM) of the denominators.
- Convert both numbers to have the LCM as the denominator.
- Add or subtract the numerators.
- Simplify the result, if possible.
Example 1: Add 2/3 and 3/4.
Solution: LCM of 3 and 4 is 12. Convert both numbers to have 12 as the denominator: 2/3 = 8/12 and 3/4 = 9/12. Add the numerators: 8 + 9 = 17. So, 2/3 + 3/4 = 17/12.
Multiplication of Rational Numbers
To multiply rational numbers, we multiply the numerators and denominators separately.
Example 2: Multiply 2/3 and 3/4.
Solution: Multiply the numerators: 2 × 3 = 6. Multiply the denominators: 3 × 4 = 12. So, 2/3 × 3/4 = 6/12 = 1/2.
Division of Rational Numbers
To divide rational numbers, we invert the second number (i.e., flip the numerator and denominator) and then multiply.
Example 3: Divide 2/3 by 3/4.
Solution: Invert the second number: 3/4 = 4/3. Multiply: 2/3 × 4/3 = 8/9. So, 2/3 ÷ 3/4 = 8/9.
Exercises:
- Add 1/2 and 2/3.
- Subtract 3/4 from 5/6.
- Multiply 2/5 by 3/7.
- Divide 3/8 by 2/5.
- Simplify the rational number 12/16.
Answers:
- 1/2 + 2/3 = 7/6
- 5/6 – 3/4 = 1/12
- 2/5 × 3/7 = 6/35
- 3/8 ÷ 2/5 = 15/16
- 12/16 = 3/4
Conclusion
Rational numbers are an essential part of mathematics, and understanding their properties and operations is crucial for success in higher-level math classes. Practice the exercises provided to reinforce your understanding of rational numbers.
Class 8 Maths Rational Numbers FAQs
What are rational numbers, and why are they important in mathematics?
Rational numbers are numbers that can be expressed as a fraction of two integers. They are crucial in mathematics as they help us represent quantities that are not whole numbers, such as fractions and decimals. Understanding rational numbers is essential for various mathematical operations and real-world applications.
How can I add and subtract rational numbers effectively?
To add or subtract rational numbers, ensure the denominators are the same by finding a common denominator. Add or subtract the numerators while keeping the denominator constant. Simplify the result if possible. Practice with different examples to improve your skills in adding and subtracting rational numbers.
What are the properties of rational numbers?
Rational numbers exhibit properties such as closure under addition, subtraction, multiplication, and division. They follow the commutative, associative, and distributive properties. Rational numbers also have an additive identity (0) and a multiplicative identity (1). Understanding these properties helps in manipulating rational numbers effectively.
How can I multiply and divide rational numbers accurately?
To multiply rational numbers, multiply the numerators and denominators separately. For division, invert the second number (reciprocal) and then multiply. Simplify the result if needed. Pay attention to signs and ensure proper handling of negative numbers. Practice various multiplication and division exercises to enhance your skills.
How can I practice and improve my understanding of rational numbers through worksheets?
To enhance your understanding of rational numbers, regularly practice worksheets that include a variety of problems on addition, subtraction, multiplication, and division of rational numbers. Challenge yourself with word problems and real-life scenarios involving rational numbers. Seek feedback on your solutions and review any mistakes to learn from them.
