The Fraction Compendium
A fraction represents a part of a whole or, more generally, any number of equal parts. It consists of a numerator (the top number) and a denominator (the bottom number), separated by a fractional bar.
Proper vs. Improper
A proper fraction has a numerator smaller than its denominator (e.g., 3/4). An improper fraction has a numerator equal to or larger than its denominator (e.g., 7/4), which can also be expressed as a mixed number (1 3/4).
Lowest Terms
A fraction is in its lowest terms (or simplest form) when the numerator and denominator share no common factors other than 1. Simplification makes fractions easier to understand and compare.
Arithmetic Operations
To add or subtract fractions, they must have a Common Denominator.
Step 2: Adjust both fractions to have this common denominator.
Step 3: Add or subtract the numerators only.
Multiplying fractions is straightforward: simply multiply across.
Example: (2/3) × (4/5) = 8/15
To divide by a fraction, multiply by its reciprocal (flip it).
Example: (1/2) ÷ (1/4) = (1/2) × (4/1) = 2
Divide both the numerator and denominator by their Greatest Common Divisor.
GCD of 12 and 16 is 4.
(12 ÷ 4) / (16 ÷ 4) = 3/4
Practical Usage
Halving or doubling a recipe requires multiplying fractions of cups and spoons.
Measuring in inches often involves halves, quarters, and eighths for perfect fitting.
Stock price changes and interest rates are essentially fractional parts of a whole.