Rational Numbers class 8 easy and helpful to understand
- 1. MNR Teacher Education College Kukatpally, Hyderabad BED (2023-2025) SEMESTER 3 Rational Numbers PRESENTED BY Name: RSS.Tarunya Roll No: 248623701046
- 2. Introduction to Rational Numbers ● Rational numbers are a key concept in mathematics! They are numbers that can be expressed as fractions. ● Rational numbers include whole numbers, integers, and decimals. ● They are relevant in everyday life, like measuring ingredients or calculating expenses.
- 3. Understanding Rational Numbers What Are Rational Numbers?: ● A rational number is any number that can be written as a fraction, where: ● The numerator is the top number. ● The denominator is the bottom number (cannot be zero). ● For example, 1/2, -3/4, and 5 are all rational numbers.
- 4. Positive and Negative Fractions Various Rational Numbers include positive fractions like 1/2, 3/4, and 5/1, as well as negative fractions such as -1/3 and -2/5. Examples of Rational Numbers Whole Numbers Rational numbers can also be whole numbers, such as 2, which can be expressed as 2/1. Rational numbers can be positive, negative, or whole!
- 5. Properties of Rational Numbers Key Properties: ● Closure Property: The sum or product of two rational numbers is always a rational number. ● Commutative Property: The order of addition or multiplication does not change the result. ● Associative Property: The grouping of numbers does not affect the sum or product. ● Identity Elements: ● The additive identity is 0 (a + 0 = a). ● The multiplicative identity is 1 (a × 1 = a).
- 6. Methods for Comparison Common Denominator: Convert fractions to have the same denominator before comparing. Number Lines: Visualize rational numbers on a number line to see which is larger or smaller. Comparing Rational Numbers
- 7. Adding Rational Numbers How to Add: ● Find a common denominator. ● Adjust the numerators accordingly. ● Add the numerators and keep the common denominator. ● Example: 1/4 + 1/2 = 1/4 + 2/4 = 3/4
- 8. Subtracting Rational Numbers How to Subtract: ● Find a common denominator. ● Adjust the numerators accordingly. ● Subtract the numerators and keep the common denominator. ● Example: 3/4 - 1/2 = 3/4 - 2/4 = 1/4
- 9. How to Multiply Multiply the numerators together and the denominators together. Simplify the fraction if possible. Example: (2/3) × (3/4) = (2 × 3) / (3 × 4) = 6/12 = 1/2 Multiplying Rational Numbers
- 10. How to Divide To divide by a rational number, multiply by its reciprocal. The reciprocal of a fraction is obtained by flipping the numerator and denominator. Example: (1/2) ÷ (3/4) = (1/2) × (4/3) = 4/6 = 2/3 Dividing Rational Numbers
- 11. Applications of Rational Numbers Real-Life Applications: ● Cooking: Recipes often use fractions for ingredient measurements. ● Measurements: Lengths and weights are often expressed as rational numbers. ● Financial Transactions: Prices and discounts can be represented as fractions.
- 12. Simplification Techniques Divide the numerator and denominator by their greatest common factor (GCF). This makes fractions easier to work with. Example: Simplifying 8/12 by dividing both by 4 gives 2/3. Simplifying Rational Numbers
- 13. Recap: Fundamental Concepts Key Points Summary: ● Rational numbers can be expressed as fractions. ● They have specific properties that govern their operations. ● We can add, subtract, multiply, and divide rational numbers using common techniques.
- 14. Interactive Q&A Session Engage with Students: ● What questions do you have about rational numbers? ● Can anyone give an example of a rational number? ● How do we find a common denominator?
- 15. Homework Assignment Practice Problems: ● Add the following: 1/3 + 1/6 ● Subtract: 5/8 - 1/4 ● Simplify: 15/25 Practice makes perfect!
- 16. Wrap-Up Rational numbers are essential in mathematics and everyday life! They help us measure, compare, and calculate. Understanding rational numbers will empower you in many real- life situations. Keep exploring the world of numbers! Conclusion .
- 17. THANK YOU .