Multiple fraction calculator
Add, subtract, multiply or divide 3 to 12 fractions, mixed numbers, integers or terminating decimals. Every intermediate result is reduced exactly.
Calculation steps
How this multiple fraction calculator differs
The general Fraction Calculator solves one operation between two values. This tool is designed for a chain of 3 to 12 values. It preserves exact integer numerators and denominators, reduces after every step and shows the complete running calculation.
How the operations work
Addition and multiplication combine every value. Subtraction and division follow the entered order from top to bottom. For example, subtraction calculates the first value minus the second, then subtracts the third from that result. Division calculates the first value divided by the second, then divides that result by the third.
- Addition: a/b + c/d = (ad + cb)/bd
- Subtraction: a/b − c/d = (ad − cb)/bd
- Multiplication: a/b × c/d = ac/bd
- Division: a/b ÷ c/d = ad/bc, where c is not zero
After each operation, the numerator and denominator are divided by their greatest common divisor. The exact fraction therefore remains reliable even when the displayed decimal repeats.
Checked examples
| Values | Operation | Exact result |
|---|---|---|
| 1/2, 1/3, 1/6 | Add | 1 |
| 2, 1/2, 1/4 | Subtract in order | 5/4 |
| 2/3, 9/10, 5/6 | Multiply | 1/2 |
| 3/4, 1/2, 3/5 | Divide in order | 5/2 |
Limits
- Enter at least 3 and no more than 12 values.
- Each value may contain at most 30 digits and 80 characters.
- Denominators cannot be zero. In division mode, no value after the first may equal zero.
- Decimals must use a point and must terminate. Enter repeating values as exact fractions such as 1/3.
- Mixed-number fractional parts must be proper, such as 2 1/3 rather than 1 4/3.
Related calculators
Use the Fraction Calculator for two values, the Decimal to Fraction Calculator for repeating decimals and scientific notation, or the Solve for X Fraction Calculator for proportions and rational equations.