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Fraction Calculator — Add, Subtract, Multiply & Divide Fractions
Free online fraction calculator. Perform addition, subtraction, multiplication, and division with mixed numbers, improper fractions, decimals, and step-by-step reduction derivations.
MMaintained by Mathematics Tools Desk
Published
Fraction Operands
First Fraction
Arithmetic Operation
Second Fraction
Fraction Solution & Derivation
Simplest Form
5/6
Decimal Equivalent
0.833333
83.3333%Step-by-Step Derivation
- 1.Find the Least Common Denominator: LCM(2, 3) = 6.
- 2.Adjust numerators: (1 × 3) / 6 + (1 × 2) / 6 = 3/6 + 2/6.
- 3.Add numerators: 3 + 2 = 5/6.
- 4.Fraction is already in simplest terms: 5/6.
- 5.Decimal equivalent: 0.833333.
MMaintained by Mathematics Tools Desk
Published
Calculation Methodology & Formula
Computes operations by finding the Least Common Multiple (LCM) for denominators or cross-multiplying, then simplifies the quotient using the Greatest Common Divisor (GCD).
\frac{a}{b} \pm \frac{c}{d} = \frac{a \cdot d \pm c \cdot b}{b \cdot d} \quad \Big| \quad \frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b \cdot d} \quad \Big| \quad \frac{a}{b} \div \frac{c}{d} = \frac{a \cdot d}{b \cdot c}Worked Example: Adding Mixed Fractions
Calculate 1 1/2 + 2 1/3.
fraction1:1 1/2 (Improper: 3/2)
fraction2:2 1/3 (Improper: 7/3)
operation:Addition (+)
Expected Output23/6 = 3 5/6 (Decimal: 3.8333)
Common denominator is LCM(2, 3) = 6. (9 + 14) / 6 = 23/6 = 3 5/6.
Technical Constraints & Limitations
- Denominators cannot be zero.
- Inputs are rounded to 32-bit integers to prevent floating-point rounding errors during GCD reduction.
Frequently Asked Questions
What is the difference between a proper, improper, and mixed fraction?
A proper fraction has a numerator smaller than its denominator (e.g., 3/4). An improper fraction has a numerator equal to or greater than its denominator (e.g., 7/4). A mixed number combines a whole number and a proper fraction (e.g., 1 3/4).
How do you divide two fractions?
To divide fractions, multiply the first fraction by the reciprocal (flipped version) of the second fraction: (a/b) ÷ (c/d) = (a/b) × (d/c).
Can this calculator handle negative numbers?
Yes. You can enter negative signs in the whole number, numerator, or denominator. The calculator automatically resolves standard mathematical sign notation.