How to Use the Fraction Calculator
Enter the first fraction by typing the numerator (top number) and denominator (bottom number) in the respective fields. For mixed numbers — like 2 and 3/4 — enter the whole number, then the fractional part. Select your operation: addition (+), subtraction (−), multiplication (×), or division (÷). Then enter the second fraction the same way.
The result appears instantly, showing the answer as both an improper fraction and a simplified mixed number where applicable. The step-by-step solution panel below the result walks through the exact working: finding the LCD for addition/subtraction, the GCD for simplification, or the reciprocal for division. This is designed to help students follow and learn the process, not just get an answer.
Use the history panel to review recent calculations and compare results. All calculations run entirely in your browser — no data is sent anywhere. The tool handles edge cases including negative fractions, division by zero detection, and improper fractions with denominators up to several thousand digits.
Why Use a Fraction Calculator?
- Step-by-step solutions — shows the full working including LCD, GCD, and conversion steps for learning
- All four operations — add, subtract, multiply, and divide fractions and mixed numbers in one tool
- Mixed number support — enter and receive results as mixed numbers without manual conversion
- Automatic simplification — results are always reduced to lowest terms using GCD
- Calculation history — review recent problems for comparison or re-use
- Real-world uses — cooking recipe scaling, construction measurements, finance ratios, and student homework
Frequently Asked Questions
How do you add fractions with different denominators?
Find the Least Common Denominator (LCD) — the smallest number that both denominators divide into evenly. Convert each fraction so its denominator equals the LCD by multiplying numerator and denominator by the same factor. Then add the numerators and keep the LCD as the denominator. Example: 1/3 + 1/4. LCD of 3 and 4 = 12. Convert: 1/3 = 4/12 (multiply by 4/4); 1/4 = 3/12 (multiply by 3/3). Add numerators: 4/12 + 3/12 = 7/12. Since 7 and 12 share no common factors, 7/12 is already in simplest form.
How do you multiply fractions?
Multiply numerator by numerator and denominator by denominator, then simplify. Example: 3/4 × 2/5 = (3×2)/(4×5) = 6/20. Simplify using GCD: GCD(6,20) = 2, so 6/20 = 3/10. Tip: cross-cancel before multiplying to keep numbers smaller. For 4/9 × 3/8: note 4 and 8 share factor 4 (reduce to 1/2); 3 and 9 share factor 3 (reduce to 1/3). Result: (1×1)/(3×2) = 1/6 — much simpler than multiplying 12/72 and then simplifying.
How do you divide fractions?
Use the 'keep, change, flip' method: keep the first fraction unchanged, change the division sign to multiplication, flip (take the reciprocal of) the second fraction. Then multiply normally. Example: 2/3 ÷ 4/5 → keep 2/3, change to ×, flip 4/5 to 5/4 → 2/3 × 5/4 = 10/12 = 5/6. The mathematical reason: dividing by a fraction is the same as multiplying by its reciprocal, because the reciprocal of (a/b) is (b/a), and multiplying by (b/a) reverses the division.
How do you simplify a fraction?
Find the Greatest Common Divisor (GCD) of the numerator and denominator — the largest number that divides both evenly. Divide both by the GCD. Example: simplify 18/24. Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. GCD = 6. Divide both: 18÷6 = 3; 24÷6 = 4. Simplified: 3/4. You can also use the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing the larger by the smaller until the remainder is 0 — the last non-zero remainder is the GCD.
What is a mixed number?
A mixed number combines a whole number and a proper fraction — for example, 2 3/4 (two and three-quarters). It is equivalent to an improper fraction where the numerator is larger than the denominator: 2 3/4 = 11/4 (because 2×4 + 3 = 11). To convert mixed to improper: multiply whole number by denominator, add numerator, keep denominator. To convert improper to mixed: divide numerator by denominator; the quotient is the whole number, the remainder is the new numerator, and the denominator stays the same.
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