Fraction Calculator
Add, subtract, multiply, and divide fractions. Simplifies results using GCD and shows mixed number form.
Fraction Calculator
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The fraction calculator performs addition, subtraction, multiplication, and division with fractions. Enter two fractions — or whole numbers (denominator 1) — select the operation, and get an instant result in three forms: simplified fraction, decimal, and mixed number (if the result is an improper fraction). Fractions appear everywhere in everyday maths: cooking recipes (½ cup + ¾ cup), carpentry measurements (3/8 inch + 5/16 inch), time calculations (¼ hour + 1/3 hour), and school maths problems. This calculator handles all of those cases correctly, simplifying the result automatically using the greatest common divisor (GCD) algorithm so you never need to reduce fractions manually. The simplify button lets you reduce a single fraction to its lowest terms without performing an operation — useful when you have a fraction like 12/18 and want to see it as 2/3.
How to Use the Fraction Calculator
The Fraction Calculator is designed to give you an accurate answer in seconds. Follow these steps:
- 1Enter the numerator and denominator for the first fraction
- 2Select the operation: + (add), − (subtract), × (multiply), or ÷ (divide)
- 3Enter the numerator and denominator for the second fraction
- 4Click Calculate to get the result in simplified form
- 5See the mixed number form and decimal equivalent, plus the step-by-step working
No account or sign-up required. All calculations run locally in your browser — nothing is stored or transmitted to any server.
How It Works
a/b + c/d = (ad + bc) / bd, then simplify by GCD
The four fraction operations use standard arithmetic rules: Addition and Subtraction: a/b ± c/d = (ad ± bc) / bd, then simplify by GCD. Multiplication: a/b × c/d = (a×c) / (b×d), then simplify. Division: a/b ÷ c/d = a/b × d/c = (a×d) / (b×c), then simplify. Simplification uses the Euclidean algorithm to find the greatest common divisor (GCD) of numerator and denominator, then divides both by it. For example, 12/18 → GCD(12,18) = 6 → 12÷6 / 18÷6 = 2/3. Mixed number conversion: if the result is an improper fraction (numerator > denominator), it displays as a whole number plus a proper fraction. 7/4 = 1 and 3/4 (one and three-quarters).
Frequently Asked Questions
How do I add fractions with different denominators?
To add fractions with different denominators, find a common denominator (the LCM of both denominators), convert both fractions, then add the numerators. Example: 1/4 + 1/3. Common denominator = 12. 1/4 = 3/12, 1/3 = 4/12. Sum = 7/12. This calculator handles all denominator conversions automatically — just enter the fractions and click Calculate.
How do I simplify a fraction?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For 18/24: GCD(18,24) = 6. 18÷6 = 3, 24÷6 = 4. Simplified fraction = 3/4. Use the Simplify button in this calculator to reduce any single fraction automatically. The result is always shown in lowest terms.
What is a mixed number?
A mixed number combines a whole number and a proper fraction. 7/4 (seven-quarters) as a mixed number is 1¾ — one whole plus three-quarters. To convert an improper fraction to a mixed number: divide numerator by denominator, the quotient is the whole part, the remainder over the original denominator is the fractional part. 11/4 → 11÷4 = 2 remainder 3 → 2¾.
How do I divide fractions?
To divide fractions, multiply the first fraction by the reciprocal of the second. "Keep, change, flip": keep the first fraction, change division to multiplication, flip the second fraction. Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. This is why dividing by a fraction makes the result larger — you are effectively multiplying by its reciprocal.
Is the fraction calculator free?
Yes — completely free with no sign-up needed. Enter any two fractions, select your operation, and get a simplified result with decimal and mixed number equivalents. All calculations run in your browser.