Calculate fraction operations including addition, subtraction, multiplication, and division with step-by-step solutions. Automatically simplifies results and shows equivalent forms.
Understanding Fractions
A fraction represents a part of a whole, written as numerator/denominator. The numerator (top number) shows how many parts we have, while the denominator (bottom number) shows how many equal parts make up the whole.
Fraction Operations
- Addition/Subtraction: Find common denominator, then add/subtract numerators
- Multiplication: Multiply numerators together and denominators together
- Division: Multiply by the reciprocal (flip the second fraction)
- Simplification: Divide both numerator and denominator by their GCD
Types of Fractions
- Proper Fraction: Numerator < Denominator (e.g., 3/4)
- Improper Fraction: Numerator ≥ Denominator (e.g., 7/4)
- Mixed Number: Whole number + proper fraction (e.g., 1¾)
- Unit Fraction: Numerator = 1 (e.g., 1/5)
Finding Common Denominators
To add or subtract fractions, you need a common denominator:
- Least Common Multiple (LCM): Find the smallest number both denominators divide into
- Cross Multiplication: For quick calculations, multiply denominators together
- Prime Factorization: Break down denominators into prime factors
Equivalent Fractions
Fractions that represent the same value:
- 1/2 = 2/4 = 3/6 = 4/8 = 0.5 = 50%
- 1/4 = 2/8 = 3/12 = 25/100 = 0.25 = 25%
- 3/4 = 6/8 = 9/12 = 75/100 = 0.75 = 75%
Converting Between Forms
- Fraction to Decimal: Divide numerator by denominator
- Decimal to Fraction: Use place value (0.25 = 25/100 = 1/4)
- Fraction to Percentage: Convert to decimal, then multiply by 100
- Mixed to Improper: (Whole × Denominator + Numerator) / Denominator
Real-World Applications
- Cooking: Recipe adjustments and measurements
- Construction: Measurements and material calculations
- Finance: Interest rates and proportions
- Time: Parts of hours, days, or years
- Statistics: Probability and data representation