Math Tools
Add, subtract, multiply, or divide fractions and view the result in simplified form with mixed number notation.
Fraction A
Operation
Fraction B
Enter numerators and denominators as integers or decimals. Denominators cannot be zero.
Result
5/6
0.833333
A fraction calculator is a tool that performs mathematical operations on fractions (parts of a whole expressed as numerator/denominator) and returns results in simplified form. It automates the process of finding common denominators, reducing to lowest terms, and converting between improper and mixed number formats.
Enter two fractions with numerators and denominators (or select an operation type), and the calculator applies the chosen operation. For addition and subtraction, it finds the least common denominator, combines the numerators, then reduces the result. For multiplication, it multiplies numerators together and denominators together. For division, it inverts the second fraction and multiplies. The tool automatically reduces the final answer by dividing both numerator and denominator by their greatest common divisor (GCD).
Addition: (a/b) + (c/d) = (ad + bc) / bd, then simplify | Subtraction: (a/b) − (c/d) = (ad − bc) / bd, then simplify | Multiplication: (a/b) × (c/d) = (ac) / (bd), then simplify | Division: (a/b) ÷ (c/d) = (a/b) × (d/c) = (ad) / (bc), then simplifyIn these formulas, a and c are numerators (top numbers), b and d are denominators (bottom numbers). The final step always reduces by dividing both numerator and denominator by their greatest common divisor until no larger divisor exists.
| Input | Result | Notes |
|---|---|---|
| 1/4 + 1/6 | 5/12 | LCM of 4 and 6 is 12; convert to 3/12 + 2/12 = 5/12, which cannot be simplified further. |
| 3/4 × 2/5 | 3/10 | Multiply: (3 × 2) / (4 × 5) = 6/20, then reduce by dividing both by GCD of 2 = 3/10. |
| 5/8 ÷ 2/3 | 15/16 | Invert second fraction: 5/8 × 3/2 = 15/16, already in simplest form. |
A proper fraction has a numerator smaller than the denominator (e.g., ¾); an improper fraction has a numerator equal to or larger than the denominator (e.g., 7/4). Both are valid; improper fractions can be written as mixed numbers (7/4 = 1¾).
Simplifying reduces a fraction to its lowest terms—the smallest numerator and denominator with the same value. For example, 6/8 simplifies to ¾ because both can be divided by 2. It's clearer and standard in math.
No. Division by zero is undefined in mathematics. The calculator will flag this as an error—choose a different divisor.
Multiply: ½ × ¾ = 3/8. Use the multiplication operation in the calculator and enter both fractions.
Convert the percentage to a fraction first (e.g., 25% = ¼), then use this calculator. Alternatively, use a percentage calculator for those operations.
For addition, no—¼ + ⅓ = ⅓ + ¼. For subtraction, yes—¾ − ¼ ≠ ¼ − ¾. Always enter the first (larger) fraction first unless you want a negative result.