Understanding Fractions

A fraction represents a part of a whole, consisting of a numerator (top number) and denominator (bottom number). Fractions are essential in mathematics, cooking, construction, and many other real-world applications.

Basic Fraction Operations

Addition and Subtraction

To add or subtract fractions, you need a common denominator. Multiply each fraction by the appropriate factor to get matching denominators, then combine the numerators.

Multiplication

Multiply the numerators together and denominators together. Simplify the result if possible.

Division

To divide fractions, multiply by the reciprocal (flip the second fraction upside down). Then multiply as normal.

Simplifying Fractions

• Find the greatest common divisor (GCD)
• Divide both numerator and denominator by the GCD
• Result is the simplified fraction
• Example: 8/12 simplifies to 2/3

Common Fraction Types

• Proper Fractions: Numerator less than denominator (1/2)
• Improper Fractions: Numerator greater than denominator (5/3)
• Mixed Numbers: Whole number with proper fraction (1 1/2)
• Equivalent Fractions: Different fractions, same value (1/2 = 2/4)

Real-World Applications

• Cooking measurements
• Construction and carpentry
• Financial calculations
• Time management
• Scientific measurements