Add, subtract, multiply, and divide fractions with automatic simplification
Quick Answer:To add fractions, find a common denominator, add the numerators, then simplify. For example, 1/3 + 1/4 = 4/12 + 3/12 = 7/12. This calculator handles all four operations and simplifies results using the GCD.
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When working with fractions, always simplify your result using the Greatest Common Divisor (GCD). The Euclidean algorithm is the fastest method: repeatedly divide the larger number by the smaller and take the remainder until you reach zero. The last non-zero remainder is the GCD. This calculator applies it automatically to every result.
To add fractions with different denominators, find a common denominator by multiplying the two denominators together (or finding the LCD). Then convert each fraction: multiply each numerator by the other fraction's denominator. Add the new numerators and place the sum over the common denominator. Finally, simplify by dividing numerator and denominator by their GCD. For example, 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
To simplify a fraction, find the Greatest Common Divisor (GCD) of the numerator and denominator using the Euclidean algorithm. Divide both the numerator and denominator by the GCD. For example, 12/18: GCD(12,18) = 6, so 12/18 simplifies to 2/3. A fraction is fully simplified when the numerator and denominator share no common factors other than 1.
To divide fractions, multiply the first fraction by the reciprocal (flipped version) of the second fraction. For example, (3/4) / (2/5) = (3/4) x (5/2) = 15/8, which as a mixed number is 1 7/8. This method is often remembered as "keep, change, flip." Our calculator performs this operation automatically and simplifies the result.