Chapter 1: 9th Class Math Notes are available for students with step-by-step instructions. This chapter is about real numbers.
This chapter requires knowledge of real numbers, including rational numbers, irrational numbers, rationalization methods, and some techniques to solve the variables.
Chapter 1: 9th Class Math Notes
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Class 9 Math Notes – Chapter 1 Summary
This summary covers key concepts and solution methods from Chapter 1 of your 9th class mathematics notes:
Rational Numbers
- Expressing Decimals as Rational Numbers:
- 0.4=4/9, 0.37=37/99, 0.21=21/99.
- Method: Multiply by 10 or 100 to eliminate the decimal, then solve for x.
- Inserting Rational Numbers Between Two Numbers:
- Example: Between 3 and 4, the rational numbers are 7/2 and 15/4.
- Formula: q1=1/2(a+b)), q2=1/2(q1+b).
Properties of Real Numbers
- Key Properties:
- Associative Property: (a+b)+c=a+(b+c).
- Commutative Property: a+b=b+a+b=b+a.
- Additive Identity: a+0=a+0=a.
- Multiplicative Identity: a×1=a×1=a.
- Distributive Property: a(b+c)=ab+ac.
- Trichotomy Property: For any two real numbers aa and bb, exactly one of the following is true: a<b, a=b, or a>b.
Simplification of Expressions
- Rationalizing the Denominator:
- Method: Multiply numerator and denominator by the conjugate of the denominator.
- Simplifying Exponents:
- Example: (8116)3/4=827, (1681)3/4=278.
- Key Rule: (am)n=am×n.
Solving Equations and Word Problems
- Consecutive Integers:
- Example: Three consecutive integers sum to 42. Solution: 13, 14, 15.
- Method: Let the integers be x, x+1, x+2, and solve for x.
- Age Problems:
- Example: Father and son’s ages sum to 72. Six years ago, the father was twice as old as the son. Solution: Son’s age six years ago was 20.
- Method: Set up equations based on given conditions.
- Profit and Loss:
- Example: Selling price for a 15% profit on Rs. 1520 is Rs. 1748.
- Formula: SP=CP+Profit.
Compound Interest and Simple Interest
- Compound Interest:
- Example: Rs. 3,75,000 at 14% for 1 year yields Rs. 52,500.
- Formula: CI=P×(1+R)T−P.
- Simple Interest:
- Example: Rs. 3,50,000 at 7.25% for 2 years yields Rs. 50,750.
- Formula: SI=P×R×T.
Miscellaneous Problems
- Temperature Conversion:
- Example: 48∘C=118.4∘F.
- Formula: °F=95°C+32°F=59°C+32.
- Finding Two Numbers:
- Example: Two numbers sum to 68 and differ by 22. Solution: 45 and 23.
- Method: Solve the system of equations x+y=68 and x−y=22.
Review Exercise
- Multiple Choice Questions:
- Covers topics like rational vs. irrational numbers, properties of real numbers, and simplification of expressions.
- Example: 77 is an irrational number.
- Verification of Properties:
- Example: Verify a(b+c)=ab+ac for a=32, b=53, c=75.