Number Sets and Mathematical Foundations

This page introduces the fundamental number sets in mathematics, establishing a hierarchical structure from basic to complex numbers. The content presents a visual representation of how different number sets relate to each other.

Definition: Number sets are collections of numbers with specific properties and characteristics.

Vocabulary:

• N (Natural Numbers): Positive whole numbers starting from 1
• Z (Integers): Includes all whole numbers, both positive and negative
• Q (Rational Numbers): Numbers that can be expressed as fractions
• R (Real Numbers): Encompasses all rational and irrational numbers

Example: Natural numbers include 1, 2, 3, 4..., while integers also include negative numbers like -2, -1, 0, 1, 2...

Highlight: The progression from N to R shows how number sets become increasingly comprehensive, with each set containing all previous sets.

Operations with Fractions

This section details the fundamental operations involving fractions, providing clear steps for multiplication, division, addition, and subtraction of fractions.

Definition: A fraction consists of a numerator (top number) and denominator (bottom number), representing parts of a whole.

Example: When multiplying fractions, multiply numerators together and denominators together: (a/b) × (c/d) = (ac)/(bd)

Highlight: For addition and subtraction, fractions must have the same denominator, which may require finding a common denominator first.