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Class 9 Maths: Real Numbers

Jun 29, 2024

Class 9 Maths: Real Numbers

Introduction to Real Numbers

  • Real numbers: Numbers that are not imaginary.
  • Numbers that exist and can be experienced in day-to-day life.
  • Natural Numbers: Counting numbers like 1, 2, 3, 4, ..., countable and have no limit.
  • Whole Numbers: Natural numbers including zero (0 + natural numbers).
  • Integers: Combination of natural numbers, zero, and negative natural numbers (e.g., -1, -2).
  • Right side of number line for positive integers.
  • Left side of number line for negative integers.

Definitions:

  1. Natural Numbers: 1, 2, 3, 4, ..., countable and encountered in daily life.
  2. Whole Numbers: Natural numbers + 0. (E.g., 0, 1, 2, 3, 4, ...)
  3. Integers: Whole numbers + negative numbers. (E.g., ..., -3, -2, -1, 0, 1, 2, 3, ...)
    • Positive Integers: All integers right of zero (1, 2, 3, ...)
    • Negative Integers: All integers left of zero (-1, -2, -3, ...)

Key Points to Remember

  • 0 is the neutral element in integers (neither positive nor negative).
  • Integers are both positive and negative along with 0.

True/False Statements:

  1. All natural numbers are whole numbers? True
  2. All whole numbers are natural numbers? False (as whole numbers include 0)
  3. All whole numbers are integers? True
  4. All integers are whole numbers? False

Rational Numbers

  • Definition: Any number in P/Q form, such that Q тЙа 0.
  • Rational numbers include all numbers that can be written as a fraction: (E.g., 1/2, -3/4).
  • Rational = practical or existing numbers.

Relationship with Other Numbers

  1. Natural Numbers: All can be written as n/1.
  2. Whole Numbers: Includes 0, which can be written as 0/1.
  3. Integers: Includes positive and negative (e.g., -3 = -3/1).

True/False Practice with Rational Numbers

  1. All natural numbers are rational numbers? True (because they can be expressed as n/1)
  2. All rational numbers are natural numbers? False
  3. All whole numbers are rational numbers? True
  4. All rational numbers are whole numbers? False
  5. All integers are rational numbers? True
  6. All rational numbers are integers? False

Fractions and Rational Numbers

  • Fractions represent parts of a whole (e.g., 1/2 or 0.5 as half).
  • Fractions can always represent parts between integers on the number line.
  • Rational numbers encompass fractions and integers.

Conclusion

  • Rational numbers and their role in expressing parts and wholes.
  • Understanding through practical examples enhances comprehension.
  • Resources available at www.magnetbrains.com for detailed studies across levels and subjects.

Next Steps

Expect more topics to be covered in the next lecture. Utilize the given resources for additional practice and clarity.

Thank you!

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