What is a Fraction Calculator?
A fraction calculator performs arithmetic operations on fractions — add, subtract, multiply, and divide — and returns the result in its simplest form. It also accepts mixed numbers (like 2¾) and shows step-by-step working so you can understand the math, not just get the answer. This makes it useful for students learning fraction arithmetic as well as anyone who needs quick, verified results.
How Does the Fraction Calculator Work?
Enter the numerator and denominator for each fraction (and optionally a whole number for mixed fractions). Select your operation. The result shows immediately in two forms: as a fraction in lowest terms and as a decimal. The steps panel explains each stage of the calculation.
Formulas Used
Addition/Subtraction: Find the LCD (LCM of denominators), convert both fractions: a/b + c/d = (a×d + b×c) / (b×d), then simplify by GCD.
Multiplication: (a/b) × (c/d) = (a×c) / (b×d), then simplify by GCD.
Division: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d) / (b×c), then simplify by GCD.
GCD (Euclidean algorithm): GCD(a, b) = GCD(b, a mod b), repeat until remainder = 0.
Mixed to improper: whole × denominator + numerator over denominator.
Benefits of Using a Fraction Calculator
- Instant step-by-step solutions help you learn and verify your work
- Handles mixed numbers automatically — no manual conversion needed
- Always simplifies to lowest terms using GCD
- Shows both fraction and decimal results
- Works offline — no server needed, all calculations run in your browser
Frequently Asked Questions
How do you add fractions with different denominators?
Find the LCD (smallest number both denominators divide into), convert each fraction, then add the numerators. For 1/3 + 1/4: LCD = 12, so 4/12 + 3/12 = 7/12.
How do you multiply fractions?
Multiply numerators together and denominators together, then simplify: 2/3 × 3/4 = 6/12 = 1/2. No common denominator needed for multiplication.
How do you divide fractions?
Keep the first fraction, change ÷ to ×, flip the second fraction (reciprocal): 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
How do you convert a mixed number to an improper fraction?
(Whole × denominator + numerator) / denominator. Example: 2¾ = (2×4 + 3)/4 = 11/4.
What is the GCD and why is it used to simplify fractions?
GCD (Greatest Common Divisor) is the largest number that divides both numerator and denominator evenly. Dividing both by GCD gives the simplest form: 12/18 → GCD=6 → 2/3.
How do you subtract fractions?
Same as addition: find LCD, convert both fractions, then subtract numerators. 3/4 − 1/3: LCD=12, so 9/12 − 4/12 = 5/12.
What is an improper fraction?
A fraction where the numerator ≥ denominator (e.g., 7/4). It represents a value ≥ 1 and equals the mixed number 1¾.
Can this calculator handle negative fractions?
Yes. Enter a negative numerator (e.g., -3) for a negative fraction like −3/4. All operations work correctly with negative values.