How the Fractions Calculator Works
This calculator performs the four fundamental operations between fractions -- addition, subtraction, multiplication, and division -- showing intermediate steps and automatically simplifying the result to lowest terms.
Rules for Fraction Operations
Addition and subtraction: when denominators are different, find the common denominator (the product of the denominators). Multiply the numerators by the necessary factors and add (or subtract). The formula is: a/b +/- c/d = (a x d +/- c x b) / (b x d).
Multiplication: multiply the numerators together and the denominators together. The formula is simple: a/b x c/d = (a x c) / (b x d).
Division: multiply the first fraction by the reciprocal of the second. The formula is: a/b / c/d = a/b x d/c = (a x d) / (b x c).
Automatic Simplification
After every operation, the calculator reduces the fraction to lowest terms by dividing the numerator and denominator by their Greatest Common Divisor (GCD), calculated using Euclid's algorithm. For example, the result 6/8 is automatically simplified to 3/4.
Fractions in Mathematics
Fractions are rational numbers -- numbers that can be expressed as a ratio of two integers. Every rational number has infinitely many equivalent fraction representations (1/2 = 2/4 = 3/6 = ...), but only one form reduced to lowest terms.
Fractions are fundamental in algebra, calculus, and everyday life: from cooking recipes (3/4 cup) to interest rates (1/4 = 25%), from probability (1/6 on a die roll) to proportions in geometry.
When to Use the Fractions Calculator
This tool is particularly useful for:
- Students in middle and high school who need to verify their calculations
- Homework verification with detailed steps to understand the process
- Quick calculations with fractions in professional or daily contexts
- Exam preparation in math where simplified results are required