Fraction Calculator

Fraction Calculator

— Simplified Fraction
— Decimal
— Mixed Number

Fraction Calculator – Add, Subtract, Multiply, Divide Fractions

This free online fraction calculator lets you perform all four arithmetic operations on fractions. Simply enter the numerator and denominator for each fraction, choose your operation, and click Calculate. The result is shown as a simplified fraction, a decimal, and a mixed number, along with the step-by-step working so you can understand how the answer was reached.

How Fraction Arithmetic Works

Addition and Subtraction require a common denominator. The calculator cross-multiplies to create the common denominator automatically: a/b + c/d = (a×d + c×b) / (b×d). The result is then simplified using the Greatest Common Divisor (GCD).

Multiplication is straightforward: multiply numerators together and denominators together, then simplify: (a/b) × (c/d) = (a×c) / (b×d).

Division uses the reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d) / (b×c). This is often remembered as "keep, change, flip."

Simplifying Fractions with GCD

After every calculation, the result is automatically reduced to its simplest form. The calculator uses the Euclidean algorithm to find the Greatest Common Divisor (GCD) of the numerator and denominator, then divides both by it. For example, 6/8 simplifies to 3/4 because GCD(6,8) = 2.

Mixed Numbers vs Improper Fractions

An improper fraction has a numerator larger than its denominator (e.g., 7/3). A mixed number expresses the same value with a whole part and a proper fraction (e.g., 2 1/3). Both representations are shown so you can use whichever is appropriate for your context.

Practical Uses of Fraction Calculations

  • Cooking: Scale recipes up or down (e.g., 3/4 cup doubled = 3/2 = 1 1/2 cups).
  • Carpentry: Add measurements in inches expressed as fractions.
  • School math: Check fraction homework and understand the steps.
  • Finance: Work with fractional share quantities or interest rates.

Frequently Asked Questions

Can I enter negative fractions?
Yes. Enter a negative sign in the numerator field. For example, to calculate −1/2 + 1/4, enter −1 as numerator 1 and 2 as denominator 1.
What if my denominator is zero?
A denominator of zero makes a fraction undefined. The calculator will display an error message in that case, as division by zero is not mathematically valid.
How does the calculator simplify fractions?
It uses the Euclidean algorithm to find the Greatest Common Divisor (GCD) of the numerator and denominator, then divides both by that value. This is guaranteed to produce the fully reduced fraction.
Can I use whole numbers (not fractions)?
Yes. To enter a whole number, put that number as the numerator and 1 as the denominator. For example, the whole number 5 is entered as 5/1.
Does it handle improper fractions?
Yes. Enter any numerator larger than the denominator and the calculator will process it correctly, showing the result as both an improper fraction and a mixed number.