Add, subtract, multiply, and divide fractions with step-by-step solutions. Simplify fractions, convert between decimals and fractions, and master fraction operations with detailed explanations.
Addition/Subtraction: Find common denominator first
Multiplication: Multiply numerators and denominators
Division: Multiply by reciprocal of second fraction
Simplification: Divide by greatest common divisor (GCD)
Fractions represent parts of a whole. The numerator (top number) shows how many parts we have, while the denominator (bottom number) shows how many equal parts the whole is divided into.
To add or subtract fractions, they must have the same denominator. Find the least common multiple (LCM) of the denominators, convert both fractions, then add or subtract the numerators.
Multiply numerators together and denominators together. Simplify the result by dividing both numerator and denominator by their greatest common divisor (GCD).
To divide fractions, multiply the first fraction by the reciprocal of the second fraction (flip the numerator and denominator of the second fraction).
Fraction calculations are used in cooking measurements, construction planning, financial calculations, scientific research, and everyday problem-solving requiring precise proportional relationships.
This calculator provides mathematical fraction calculations for educational and reference purposes. Results are based on exact fraction arithmetic and maintain perfect accuracy. For critical applications in engineering, science, or financial calculations, always verify results with professional tools and consider context-specific requirements.
This advanced fraction calculator implements comprehensive fraction operations using exact mathematical algorithms. Each calculation follows precise fraction arithmetic principles that form the foundation of proportional mathematics and rational number operations.
Principles: Common denominators, equivalent fractions
Fraction operations maintain exact values without rounding errors, making them essential for precise mathematical calculations and proportional reasoning.
Method: Greatest common divisor (GCD)
Fractions are simplified by dividing both numerator and denominator by their GCD, ensuring results are in simplest form for clarity and accuracy.
Accuracy: Exact or precise approximations
Conversion between fractions and decimals maintains mathematical precision using continued fraction algorithms for optimal accuracy.
Format: Whole numbers with proper fractions
Automatic conversion between improper fractions and mixed numbers provides flexibility in result presentation based on user preference.
To add fractions with different denominators, first find the least common multiple (LCM) of the denominators. Convert both fractions to equivalent fractions with the common denominator by multiplying numerator and denominator by the same factor. Then add the numerators while keeping the denominator the same. Finally, simplify the result if possible. For example, to add 1/2 and 1/3: LCM of 2 and 3 is 6, so 1/2 becomes 3/6 and 1/3 becomes 2/6, resulting in 5/6.
The easiest way to simplify fractions is to divide both numerator and denominator by their greatest common divisor (GCD). The GCD is the largest number that divides both numerator and denominator evenly. For example, to simplify 8/12, the GCD of 8 and 12 is 4, so dividing both by 4 gives 2/3. Our calculator automatically finds the GCD and shows the simplification process step-by-step, making it easy to understand and verify the result.
To convert decimals to fractions, write the decimal as a fraction with denominator power of 10 based on the number of decimal places, then simplify. For terminating decimals like 0.75, write as 75/100 and simplify to 3/4. For repeating decimals, use algebraic methods. Our calculator uses advanced continued fraction algorithms for precise conversions of both terminating and repeating decimals, providing exact fraction equivalents whenever possible.
Mixed numbers combine whole numbers with proper fractions (e.g., 2 1/2), while improper fractions have numerators larger than or equal to denominators (e.g., 5/2). Mixed numbers are often easier to understand intuitively, while improper fractions are more convenient for calculations. Our calculator converts between both formats automatically, allowing you to work with whichever representation you prefer and showing results in both forms for clarity.
Our calculator uses precise mathematical algorithms with exact fraction arithmetic. Results maintain perfect accuracy without rounding errors that can occur with decimal calculations. Fraction operations are performed using integer arithmetic, ensuring exact results for addition, subtraction, multiplication, and division. This makes our calculator ideal for educational purposes where exact values are important, as well as for professional applications requiring precise proportional relationships.
Fraction calculations have countless practical applications including cooking measurements for recipe adjustments, construction planning for material quantities, financial calculations for interest rates and proportions, scientific research for data analysis, engineering for design specifications, and everyday problem-solving requiring precise proportional relationships. These applications demonstrate the essential role of fraction understanding across professional, educational, and personal domains.