Numbers and Algebra Basics

Numbers

• Natural Numbers: 1, 2, 3, ... (positive integers)
• Whole Numbers: 0, 1, 2, 3, ... (non-negative integers)
• Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... (positive and negative whole numbers)
• Rational Numbers: fractions (e.g., 3/4, 22/7)
• Irrational Numbers: non-repeating, non-terminating decimals (e.g., π, e)
• Real Numbers: includes all rational and irrational numbers
• Complex Numbers: numbers with real and imaginary parts (e.g., 3 + 4i)

Algebra

• Variables: symbols representing unknown values (e.g., x, y)
• Constants: numbers (e.g., 2, 5)
• Expressions: combinations of variables and constants (e.g., 2x + 5)
• Equations: statements with equal values (e.g., 2x + 5 = 11)
• Inequalities: statements with unequal values (e.g., 2x + 5 > 11)

Geometry

• Points: locations in space (e.g., A, B, C)
• Lines: sets of points extending infinitely in two directions (e.g., AB)
• Rays: portions of lines extending from a point (e.g., →AB)
• Angles: formed by two rays sharing a common endpoint (e.g., ∠AOB)
• Triangles: polygons with three sides (e.g., ΔABC)

Measurement

• Units: standard quantities for measurement (e.g., meters, grams, seconds)
• Conversion: changing units (e.g., inches to feet)
• Ratios: comparisons of quantities (e.g., 3:4, 2:5)

Data Analysis

• Data: collections of information (e.g., numbers, categories)
• Graphs: visual representations of data (e.g., bar charts, histograms)
• Statistics: numerical summaries of data (e.g., mean, median, mode)

Mathematical Operations

• Addition: combining numbers (e.g., 2 + 3 = 5)
• Subtraction: finding the difference (e.g., 5 - 2 = 3)
• Multiplication: repeated addition (e.g., 2 × 3 = 6)
• Division: sharing or grouping (e.g., 6 ÷ 2 = 3)
• Exponents: shorthand for repeated multiplication (e.g., 2³ = 2 × 2 × 2)

Numbers

• Natural numbers are positive integers, starting from 1.
• Whole numbers include 0 and positive integers.
• Integers include positive and negative whole numbers, as well as 0.
• Rational numbers are fractions, such as 3/4 or 22/7.
• Irrational numbers are non-repeating, non-terminating decimals, like π or e.
• Real numbers include all rational and irrational numbers.
• Complex numbers have real and imaginary parts, like 3 + 4i.

Algebra

• Variables represent unknown values, like x or y.
• Constants are numbers, such as 2 or 5.
• Expressions combine variables and constants, like 2x + 5.
• Equations are statements with equal values, like 2x + 5 = 11.
• Inequalities are statements with unequal values, like 2x + 5 > 11.

Geometry

• Points are locations in space, like A, B, or C.
• Lines are sets of points extending infinitely in two directions, like AB.
• Rays are parts of lines extending from a point, like →AB.
• Angles are formed by two rays sharing a common endpoint, like ∠AOB.
• Triangles are polygons with three sides, like ΔABC.

Measurement

• Units are standard quantities for measurement, such as meters, grams, or seconds.
• Conversion involves changing units, like inches to feet.
• Ratios compare quantities, like 3:4 or 2:5.

Data Analysis

• Data is a collection of information, like numbers or categories.
• Graphs are visual representations of data, such as bar charts or histograms.
• Statistics are numerical summaries of data, including mean, median, and mode.

Mathematical Operations

• Addition combines numbers, like 2 + 3 = 5.
• Subtraction finds the difference, like 5 - 2 = 3.
• Multiplication is repeated addition, like 2 × 3 = 6.
• Division involves sharing or grouping, like 6 ÷ 2 = 3.
• Exponents are shorthand for repeated multiplication, like 2³ = 2 × 2 × 2.

Understanding the different types of numbers, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers.