Math
Fraction Calculator
Add, subtract, multiply, and divide fractions. Gets the simplified result and decimal equivalent.
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Fraction Operations Reference
Fractions represent parts of a whole. Operations on fractions follow specific rules that differ from whole number arithmetic — essential for cooking, construction, and math courses.
Fraction Operation Rules
- Addition/Subtraction: find common denominator first, then add/subtract numerators. Example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12
- Multiplication: multiply numerators × numerators, denominators × denominators. 2/3 × 3/4 = 6/12 = 1/2
- Division: multiply by the reciprocal (flip the second fraction). 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
- Simplification: divide numerator and denominator by their GCD
Converting Mixed Numbers
- Mixed to improper: multiply whole by denominator, add numerator (2⅓ = 7/3)
- For arithmetic operations, convert mixed numbers to improper fractions first
What is the LCM and why is it needed for fraction addition?
LCM (Least Common Multiple) is the smallest number divisible by both denominators. When adding fractions, you need a common denominator — the LCM gives the smallest one, keeping numbers manageable. For 1/4 + 1/6: LCM(4,6) = 12, so 3/12 + 2/12 = 5/12.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. 3/4 = 0.75. Some fractions produce repeating decimals: 1/3 = 0.333... Common conversions: 1/2 = 0.5, 1/4 = 0.25, 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875.