311302 Basic Mathematics Books/Notes MSBTE Diploma 'K' Scheme

311302 Basic Mathematics

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Basic Mathematics: Foundations and Fundamental Concepts

Introduction

 

1. Numbers:

• Natural Numbers: These are counting numbers starting from 1 (e.g., 1, 2, 3, ...).
• Whole Numbers: Natural numbers including 0 (e.g., 0, 1, 2, ...).
• Integers: Whole numbers and their negatives (e.g., -3, -2, -1, 0, 1, 2, ...).
• Rational Numbers: Numbers that can be expressed as a fraction where the numerator and denominator are integers, and the denominator is not zero.
• Irrational Numbers: Numbers that cannot be expressed as a simple fraction (e.g., the square root of 2, π).

 

2. Basic Operations:

• Addition (+): Combining numbers.
• Subtraction (-): Taking one number away from another.
• Multiplication (x): Finding the total of adding a number, a certain number of times.
• Division (÷): Splitting into equal parts or groups.

 

3. Arithmetic Properties:

• Commutative Property: The order of numbers does not affect the result in addition or multiplication (e.g., 3 + 4 = 4 + 3).
• Associative Property: The way numbers are grouped does not affect the sum or product (e.g., (3 + 4) + 5 = 3 + (4 + 5)).
• Distributive Property: Multiplying a number by a group of numbers added together is the same as doing each multiplication separately (e.g., 5 x (2 + 3) = 5x2 + 5x3).

 

4. Fractions:

• Numerator: The top number, representing parts taken from the whole.
• Denominator: The bottom number, indicating the total number of equal parts.
• Equivalent Fractions: Different fractions that represent the same value (e.g., 1/2 and 2/4).

 

5. Decimals and Percentages:

• Decimal: Represents a number using the base-10 system, with a decimal point to indicate values less than one.
• Percentage: A way to express numbers as a fraction of 100. For instance, 25% is equivalent to 25/100 or 0.25.

 

6. Geometry Basics:

• Points: Exact locations in space.
• Lines: Straight paths that extend in two opposite directions without ending.
• Planes: Flat surfaces that extend indefinitely in all directions.
• Shapes: Two-dimensional (circle, square) or three-dimensional (sphere, cube) figures.

 

7. Measurements:

• Length: Meters, centimeters, inches.
• Weight: Grams, kilograms, pounds.
• Volume: Liters, milliliters, gallons.

 

Conclusion: