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.

Test your understanding of set theory and fractions, including union, intersection, and complement of sets, as well as comparing and simplifying fractions.