Fractions trip up students, home cooks, and professionals alike — especially when denominators differ or results need to be expressed as mixed numbers. This free fraction calculator handles all four operations with full step-by-step solutions, automatic simplification, and mixed number conversion. Enter any two fractions, pick your operation, and get the answer instantly.
How the Fraction Calculator Works
Select the operation (Add, Subtract, Multiply, or Divide) using the tabs above the inputs. Enter the numerator and denominator for each fraction, then click Calculate. The calculator finds the LCD for addition and subtraction, cross-multiplies for division, and reduces the result to simplest form using the Greatest Common Divisor. You also get the decimal equivalent and mixed number form. The step-by-step breakdown shows every intermediate result so you can follow (and learn) the method.
3 Real-World Examples
Recipe calls for ¾ cup flour, you want to make 1.5× the recipe. ¾ × 3/2 = 9/8 = 1⅛ cups. Fractions appear constantly in cooking — memorizing this shortcut saves time.
A board is 7/8 inch thick. You need to cut 3 boards to fit in a 3-inch space. 3 × 7/8 = 21/8 = 2⅝ inches. The gap remaining: 3 − 2⅝ = ⅜ inch. Exact fractions matter in woodworking and construction.
You scored ⅗ on a quiz, ¾ on an assignment, and 7/10 on a test. Average: (⅗ + ¾ + 7/10) ÷ 3. Common denominator 20: (12/20 + 15/20 + 14/20) ÷ 3 = 41/60 ≈ 68.3%.
Tips
- Before multiplying, cross-cancel common factors to keep numbers manageable — it gives the same answer with less arithmetic.
- For division, remember "keep, change, flip": keep the first fraction, change ÷ to ×, flip the second fraction.
- When adding mixed numbers, convert them to improper fractions first, then add and convert back.
- A negative result with a negative denominator is a positive fraction — the calculator normalizes the sign automatically.
Understanding the Greatest Common Divisor (GCD)
The GCD is the largest number that divides both the numerator and denominator without a remainder. It is the key to simplifying fractions. For 36/48: factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 48 include 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The GCD is 12, so 36/48 simplifies to 3/4. This calculator computes the GCD using the efficient Euclidean algorithm and applies it automatically to every result.