Fraction Calculator

Fractions appear in cooking recipes, construction measurements, probability, and algebra. This calculator handles all four arithmetic operations on fractions and always gives results in simplified form, showing the decimal equivalent too.

• Cooking and baking: Scale recipes up or down by multiplying or dividing fractional measurements.
• Algebra homework: Check fraction arithmetic in equations and verify simplification.
• Woodworking: Add fractional measurements in inches like 3/8 + 5/16.
• Probability: Combine fractional probabilities through multiplication and addition.

1. 1Enter the numerator and denominator for each fraction.
2. 2Select the operation from the dropdown: Add, Subtract, Multiply, or Divide.
3. 3For addition and subtraction, the calculator finds a common denominator (cross-multiplication method).
4. 4For multiplication, it multiplies numerators together and denominators together.
5. 5For division, it multiplies the first fraction by the reciprocal of the second.
6. 6The result is simplified by dividing by the Greatest Common Divisor (GCD).

• Adding fractions by adding numerators and denominators separately: 1/2 + 1/3 is not 2/5. You must find a common denominator first: 3/6 + 2/6 = 5/6. The calculator handles this automatically, but knowing why prevents mental errors.
• Forgetting to simplify the result manually: The calculator simplifies automatically using the GCD. If you are doing it by hand and forget to simplify, the answer is technically correct but not in standard form and may confuse a teacher or colleague.
• Entering mixed numbers incorrectly: If the input expects a mixed number in the format "2 3/4", entering "2.75" or "11/4" may not work as expected. Check the input format instructions before entering a mixed number.
• Dividing fractions without flipping the second one: Dividing by a fraction means multiplying by its reciprocal. 1/2 ÷ 1/4 = 1/2 × 4/1 = 2. The calculator handles this, but it is the step most often done wrong by hand.

• Use the GCD calculator for manual simplification: If you want to simplify a fraction by hand, find the GCD of numerator and denominator using the GCD calculator, then divide both by that number.
• Verify with the decimal equivalent: The calculator shows the decimal alongside the fraction. If 3/4 does not equal 0.75 in the result, something went wrong in the input.
• Use fractions for exact arithmetic in code: Floating-point arithmetic in programming introduces rounding errors. For financial or scientific calculations requiring exactness, fractions avoid the 0.1 + 0.2 ≠ 0.3 problem.
• Convert percentages to fractions for easier mental math: 25% = 1/4, 33% ≈ 1/3, 75% = 3/4. These fractions are often easier to work with mentally than decimal equivalents when estimating.