Fraction Calculator
Result
Master Fraction Calculations
A fraction calculator performs mathematical operations on fractions including addition, subtraction, multiplication, and division with automatic simplification. Understanding fractions is essential for mathematics, cooking, construction, and everyday problem-solving. This calculator handles all fraction operations, simplifies results to lowest terms, and converts between improper fractions and mixed numbers instantly.
Adding and Subtracting Fractions
To add or subtract fractions, find a common denominator. For 1/2 + 1/4: the common denominator is 4, so convert 1/2 to 2/4, then add: 2/4 + 1/4 = 3/4. For different denominators like 1/3 + 1/4, find the least common multiple (12): 4/12 + 3/12 = 7/12. Subtraction works the same way: 3/4 - 1/2 = 3/4 - 2/4 = 1/4.
Multiplying and Dividing Fractions
Multiplication is straightforward: multiply numerators together and denominators together. For 2/3 × 3/4 = 6/12 = 1/2 (simplified). Division requires multiplying by the reciprocal: 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9. Always simplify final answers by dividing numerator and denominator by their greatest common divisor.
Simplifying Fractions
Simplification reduces fractions to lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD). For 12/18: GCD is 6, so 12÷6 / 18÷6 = 2/3. Always simplify final answers for clarity. The calculator automatically simplifies all results.
Mixed Numbers and Improper Fractions
Mixed numbers combine whole numbers and fractions (2 1/2). Improper fractions have numerators larger than denominators (5/2). To convert mixed to improper: multiply whole number by denominator, add numerator (2 1/2 = 5/2). To convert improper to mixed: divide numerator by denominator (5/2 = 2 remainder 1 = 2 1/2).
Finding Common Denominators
The least common denominator (LCD) is the smallest number divisible by both denominators. For 1/6 and 1/8: multiples of 6 are 6,12,18,24... and multiples of 8 are 8,16,24... so LCD is 24. Convert: 1/6 = 4/24 and 1/8 = 3/24. Now you can add or subtract easily.
Practical Applications of Fractions
Fractions appear everywhere: cooking recipes (1/2 cup flour), measurements (3/4 inch), time (1/4 hour = 15 minutes), money (1/4 dollar = 25 cents), and construction (2 1/4 inches). Understanding fraction operations helps you adjust recipes, calculate materials, split bills, and solve real-world problems efficiently.