Add, subtract, multiply, and divide fractions with step-by-step solutions. Automatic simplification and mixed number conversion.
To add fractions, find a common denominator, convert both fractions, add the numerators, and simplify. Example: 1/3 + 1/4 → LCD is 12 → 4/12 + 3/12 = 7/12.
If the denominators are the same, simply add the numerators: 2/5 + 1/5 = 3/5. If different, find the Least Common Denominator (LCD), which is the smallest number both denominators divide into evenly. This calculator finds the LCD and shows each step automatically.
To multiply: multiply numerators together and denominators together. To divide: multiply by the reciprocal (flip the second fraction).
Multiplication: 2/3 × 3/4 = 6/12 = 1/2. Division uses "Keep, Change, Flip": 2/3 ÷ 4/5 → keep 2/3, change ÷ to ×, flip 4/5 to 5/4 → 2/3 × 5/4 = 10/12 = 5/6. No common denominator is needed for either operation.
Divide both the numerator and denominator by their Greatest Common Divisor (GCD). Example: 18/24 → GCD is 6 → 18÷6 / 24÷6 = 3/4.
A fraction is in simplest form when the only common factor of the numerator and denominator is 1. To find the GCD, you can list factors or use the Euclidean algorithm (which this calculator uses). If the result is an improper fraction (numerator > denominator), it's also converted to a mixed number.
To add or subtract fractions, they must have the same denominator (bottom number). If they don't, find the Least Common Denominator (LCD), convert both fractions, then add or subtract the numerators.
Multiplication is the easiest fraction operation: multiply straight across (numerator × numerator, denominator × denominator). Division flips the second fraction and multiplies.
Fractions, decimals, and percentages are three ways to express the same value. Converting between them is a fundamental math skill used in cooking, finance, construction, and everyday life.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/8 | 0.125 | 12.5% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333… | 33.3% |
| 1/2 | 0.5 | 50% |
| 2/3 | 0.667… | 66.7% |
| 3/4 | 0.75 | 75% |
| 7/8 | 0.875 | 87.5% |
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Note: This calculator works with integers only. For decimal-to-fraction conversion, multiply both parts by a power of 10 first (e.g., 0.75 = 75/100 = 3/4). Negative fractions are supported — enter a negative numerator.
Fractions represent parts of a whole and are one of the most fundamental concepts in mathematics. Whether you are a student learning arithmetic, a cook adjusting recipes, a carpenter measuring wood, or an engineer calculating tolerances, understanding fraction operations is an essential life skill. This calculator handles all four operations with automatic simplification and step-by-step explanations.
To add fractions, you must first find a common denominator — a number that both denominators divide into evenly. The most efficient approach is to use the Least Common Denominator (LCD). For 1/3 + 1/4: the LCD of 3 and 4 is 12. Convert: 4/12 + 3/12 = 7/12. For subtraction, the process is identical except you subtract the numerators: 3/4 - 1/3 = 9/12 - 4/12 = 5/12.
Multiplication is the simplest fraction operation: multiply numerators together and denominators together. 2/3 × 3/4 = 6/12 = 1/2. No common denominator needed. Division uses the "Keep, Change, Flip" rule: keep the first fraction, change ÷ to ×, flip the second fraction. 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
A fraction is in simplest form when the only common factor of the numerator and denominator is 1. To simplify, divide both by their GCD. This calculator uses the Euclidean Algorithm (the most efficient method, known since 300 BC by the Greek mathematician Euclid) to find the GCD automatically. For 18/24: GCD(18,24) = 6, so 18÷6 / 24÷6 = 3/4. Improper fractions (numerator > denominator) are also converted to mixed numbers: 7/4 = 1 3/4.