Math Basics: Sets and Fractions

Set Theory

• A set is a collection of unique objects, called elements or members.
• Sets can be represented using roster notation (listing elements inside curly brackets {}) or set-builder notation (describing elements using a rule).
• Union of two sets: all elements from both sets combined (e.g., A ∪ B).
• Intersection of two sets: elements common to both sets (e.g., A ∩ B).
• Complement of a set: all elements not in the set (e.g., A' or U - A).

Comparing Fractions

• A fraction represents a part of a whole, consisting of a numerator (top number) and a denominator (bottom number).
• Equivalent fractions have the same value, but different numerators and denominators (e.g., 1/2 = 2/4).
• To compare fractions, follow these steps:
  1. Convert both fractions to have the same denominator (find the least common multiple, LCM).
  2. Compare the numerators; the fraction with the larger numerator is larger.
• Ordering fractions from least to greatest: arrange fractions in ascending order (e.g., 1/4, 1/2, 3/4).
• Simplifying fractions: divide both numerator and denominator by their greatest common divisor (GCD) to reduce the fraction to its simplest form.