What Is a Fraction Calculator?
A fraction expresses a part of a whole or a ratio between quantities. In a/b, a is the numerator and b is the denominator. The denominator cannot equal zero. Fractions can be proper, improper, mixed, positive or negative. An improper fraction has a numerator whose absolute value is at least as large as its denominator.
How to Use This Calculator
- Enter the values shown in the calculator above.
- Select the appropriate operation or measurement convention where applicable.
- Review the highlighted result and the supporting breakdown.
- Change one input at a time to compare realistic scenarios.
- Refer to the examples and limitations below when interpreting the result.
Formula
For addition, a/b + c/d = (ad + bc)/bd. Reduce numerator and denominator using their greatest common divisor.
Step-by-Step Example
1/2 + 1/3 = (3 + 2)/6 = 5/6, or approximately 0.833333.
How to add or subtract fractions
Find a common denominator, usually the least common multiple of the denominators. Rewrite each numerator to match the common denominator, then add or subtract the numerators and keep the denominator. For example, 3/4 − 1/6 = 9/12 − 2/12 = 7/12. The calculator uses cross multiplication and then simplifies.
Multiplying and dividing fractions
To multiply a/b by c/d, multiply numerators and denominators: ac/bd. Example: 2/3 × 9/10 = 18/30 = 3/5. To divide, multiply by the reciprocal: (a/b) ÷ (c/d) = ad/bc. Example: 3/5 ÷ 2/7 = 21/10 = 2 1/10. Division by a zero fraction is undefined.
Simplifying fractions and mixed numbers
A fraction is in lowest terms when the numerator and denominator share no integer factor greater than one. Divide both parts by their greatest common divisor (GCD). For example, 18/24 has GCD 6, so 18/24 = 3/4. An improper result such as 11/4 can be written as 2 3/4. Both represent the same amount.
Fractions and decimals
Divide the numerator by the denominator to obtain a decimal. Some fractions terminate, such as 1/8 = 0.125; others repeat, such as 1/3 = 0.333…. A rounded decimal is an approximation, while a reduced fraction can preserve an exact rational result.
Practical uses and common mistakes
Fractions appear in cooking, construction, school mathematics, music and measurements. When adjusting a recipe from 4 servings to 6, scale each ingredient by 6/4 = 3/2. Avoid adding denominators when adding fractions; 1/2 + 1/3 is not 2/5. Check signs and never enter zero as a denominator.