Perform addition, subtraction, multiplication, and division on fractions. Get simplified results using GCD. Free online fraction arithmetic tool.
The Fraction Calculator performs all four basic arithmetic operations on fractions: addition, subtraction, multiplication, and division. Enter two fractions, select the operation, and get the result instantly simplified to its lowest terms.
Fraction arithmetic is a foundational math skill, but it is also one of the most error-prone when done by hand. Finding common denominators, cross-multiplying, and simplifying can each introduce mistakes. This calculator handles all the steps and always delivers the fully reduced answer.
Whether you're a student working through homework, a cook scaling recipes, a carpenter measuring lumber, or an engineer working with tolerances, this tool eliminates the tedium of manual fraction math. It shows both the simplified fraction and the decimal equivalent for maximum flexibility.
Understanding this metric in precise terms allows professionals to set achievable targets, measure progress objectively, and continuously refine their approach to time and task management. Tracking this metric consistently enables professionals to identify patterns in how they allocate time and effort, revealing opportunities to work more effectively and accomplish more each day.
Manual fraction arithmetic requires multiple steps prone to error. This calculator handles finding common denominators, performing the operation, and simplifying to lowest terms — all in one step. Regular monitoring of this value helps individuals and teams detect productivity patterns and adjust workflows before small inefficiencies become entrenched and hard to correct.
Addition: a/b + c/d = (ad + bc) / bd Subtraction: a/b − c/d = (ad − bc) / bd Multiplication: a/b × c/d = ac / bd Division: a/b ÷ c/d = ad / bc All results simplified by dividing by GCD(numerator, denominator).
Result: 17/12
3/4 + 2/3 = (3×3 + 4×2) / (4×3) = (9 + 8) / 12 = 17/12. GCD(17,12) = 1, so the fraction is already simplified. As a decimal: 1.4167.
Fractions represent parts of a whole. The numerator (top) tells how many parts you have, and the denominator (bottom) tells how many equal parts make the whole. Understanding this makes fraction operations intuitive.
Unsimplified fractions like 6/8 are mathematically correct but harder to interpret than 3/4. Simplification ensures clarity in communication, especially in recipes, measurements, and engineering specifications.
Carpenters add fractions when combining measurements. Cooks scale recipes using fraction multiplication. Engineers calculate tolerances with fraction subtraction. This calculator handles all these operations instantly, eliminating manual errors in professional contexts.
Find a common denominator (typically the product of both denominators), convert both fractions to have that denominator, add the numerators, and simplify. This calculator does all these steps automatically.
Flip the second fraction (swap its numerator and denominator) and multiply. For example, (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8.
Simplifying (or reducing) a fraction means dividing both numerator and denominator by their greatest common divisor (GCD) until no further reduction is possible. 6/8 simplifies to 3/4.
Yes. Enter a negative number for the numerator. The calculator handles negative values correctly for all four operations.
An improper fraction has a numerator larger than its denominator (like 7/4). It represents a value greater than 1. This calculator works with both proper and improper fractions.
The GCD (Greatest Common Divisor) is found using the Euclidean algorithm: repeatedly divide the larger number by the smaller and take the remainder until the remainder is zero. The last non-zero remainder is the GCD.