Fraction Calculator
Fractions Don't Simplify Themselves
Adding two fractions with different denominators, multiplying a pair together, or dividing one by another all require finding a common footing first — and then, just as importantly, reducing the result back down to its simplest terms. Skipping that last step is how "6/8" ends up in a final answer instead of "3/4". This calculator carries out the arithmetic and the simplification in the same step, using the greatest common divisor to guarantee the lowest-terms result.
The Formulas
Subtraction: (a/b) − (c/d) = (a×d − c×b) / (b×d)
Multiplication: (a/b) × (c/d) = (a×c) / (b×d)
Division: (a/b) ÷ (c/d) = (a×d) / (b×c)
After computing the raw numerator and denominator, the result is divided by their greatest common divisor (GCD) to reduce it to lowest terms, and a decimal equivalent is included alongside the simplified fraction.
Where Fraction Arithmetic Is Unavoidable
- Cooking and baking — combining or scaling recipe measurements given in fractional cups or spoons.
- Construction and woodworking — adding measurements given in fractions of an inch.
- Coursework — checking fraction arithmetic in arithmetic and pre-algebra classes.
| Operation | Expression | Simplified | Decimal |
|---|---|---|---|
| Add | 1/4 + 1/6 | 5/12 | 0.416667 |
| Subtract | 3/4 − 1/3 | 5/12 | 0.416667 |
| Multiply | 2/3 × 3/8 | 1/4 | 0.25 |
| Divide | 1/2 ÷ 2/5 | 5/4 | 1.25 |
How to Use This Calculator
- Choose an operation: Add, Subtract, Multiply, or Divide.
- Enter the numerator and denominator of the first fraction (Numerator 1, Denominator 1).
- Enter the numerator and denominator of the second fraction (Numerator 2, Denominator 2).
- Select Calculate to see the simplified fraction and its decimal equivalent.
Related Calculations
Need to convert a single fraction to a decimal, or a decimal back to a fraction? See the Fraction to Decimal Converter and the Decimal to Fraction Converter.