Fraction Calculator
Perform basic arithmetic with fractions effortlessly. This calculator handles addition, subtraction, multiplication, and division for both proper and improper fractions. The final answer is automatically simplified to its lowest terms.
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How Fraction Calculations Work
Fractions may look simple, but they follow clear mathematical rules. Whether you want to add fractions, subtract fractions, multiply fractions, or divide fractions, the process always involves working with numerators and denominators. To simplify a fraction to its lowest terms, we find the Greatest Common Divisor (GCD) of the numerator and denominator and divide both by this value. This ensures your answer is written in its simplest form, which is important for both math students and everyday practical use.
Here are the standard rules of fraction arithmetic:
- Addition (a/b + c/d): First find a common denominator, then use the formula
(ad + bc) / bd. - Subtraction (a/b - c/d): Just like addition, use the formula
(ad - bc) / bd. - Multiplication (a/b × c/d): Multiply the numerators and denominators directly:
(ac) / (bd). - Division (a/b ÷ c/d): Invert the second fraction and multiply:
(ad) / (bc).
These formulas are the foundation of every fraction calculator. By applying them step by step, you can handle problems involving fractions in algebra, trigonometry, ratios, proportions, and everyday math. Whether you’re a student learning the basics or someone who needs quick calculations, understanding how fractions are calculated makes problem-solving faster and more accurate.