Fraction Calculator
How Does This Calculator Work?
This calculator simplifies fraction arithmetic by following a standard mathematical process:
- Convert to Improper Fractions: Any mixed numbers (like 1 ½) are first converted into improper fractions (like 3/2). This creates a consistent format for all calculations.
- Find a Common Denominator: For addition and subtraction, the calculator finds the least common multiple (LCM) of the denominators to create equivalent fractions that can be easily combined.
- Perform the Operation: The calculator then adds, subtracts, multiplies, or divides the numerators and denominators according to standard fraction rules.
- Simplify the Result: The final result is automatically simplified to its lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD). The answer is then presented as a mixed number and a decimal.
The Surprising History of Fractions
Fractions may seem like a basic school subject, but their history is ancient and complex. The ancient Egyptians, over 4,000 years ago, had a unique and cumbersome system. They primarily worked with unit fractions—fractions with a numerator of 1 (like ½, ⅓, ¼, etc.).
To represent a more complex fraction like ⅗, they would express it as a sum of distinct unit fractions, such as ½ + ⅒. This system, recorded on texts like the Rhind Mathematical Papyrus, made their arithmetic incredibly complicated. The symbols they used for fractions were often based on parts of the "Eye of Horus" mythology. It wasn't until the Babylonians and later the Greeks that more flexible systems for representing and calculating with fractions began to emerge, eventually leading to the numerator/denominator format we use today.
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While you're here, check out some of our other popular math and finance calculators:
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Frequently Asked Questions (FAQ)
How do I enter a whole number?
To enter a whole number like '5', simply type '5' into the first box on the left and leave the smaller numerator and denominator boxes blank for that fraction.
How does the calculator simplify fractions?
After performing a calculation, the calculator finds the Greatest Common Divisor (GCD) of the resulting numerator and denominator. It then divides both numbers by the GCD to reduce the fraction to its simplest form. For example, 12/16 would be simplified to 3/4 because the GCD of 12 and 16 is 4.
What happens if I enter a zero in the denominator?
Division by zero is mathematically undefined. If you enter '0' in a denominator field, the calculator will show an error message, as a valid fraction cannot have a zero in the denominator.