How to Use
Select an operation: Add, Subtract, Multiply, Divide, or Simplify.
Enter the whole part (optional) and the numerator and denominator for the first fraction.
For two fraction operations, enter the second fraction the same way.
Click Calculate to see the result, the full working, and the decimal equivalent.
Click Reset to clear all fields and start over.
How the Fraction Calculator Works
For addition and subtraction the calculator finds the Lowest Common Denominator (LCD), which is the Least Common Multiple of the two denominators, then rewrites each fraction with that LCD before combining the numerators. Multiplication is straightforward: numerator times numerator over denominator times denominator. Division flips the second fraction and multiplies. Every result is then simplified by dividing both parts by their Greatest Common Divisor, found with the Euclidean algorithm. If the simplified result is improper (numerator larger than or equal to the denominator) it is also expressed as a mixed number.
Worked Example: 3/4 + 1/6
- Find LCD of 4 and 6: LCD(4, 6) = 12
- Convert fractions: 3/4 = 9/12, 1/6 = 2/12
- Add numerators: 9 + 2 = 11
- Result: 11/12
- GCD(11, 12) = 1 — already in simplest form
- Decimal equivalent: 11 ÷ 12 ≈ 0.9166666667
When to Use This Calculator
- Checking homework or working through fraction problems one step at a time
- Simplifying a fraction to its lowest terms quickly
- Converting an improper fraction like 7/4 to its mixed number 1 3/4
- Solving recipe or measurement problems that involve fractional quantities
- Adding or subtracting fractions with different denominators
- Understanding how fraction division works by seeing the reciprocal method in action
Important Note
This calculator accepts integers only. Decimal values in the numerator or denominator fields (e.g. 1.5/3) are not supported. Convert them to whole number fractions first. For very large integers, precision may be limited by JavaScript's floating point representation. Results are mathematically exact for typical fraction inputs.
Fractions vs. Decimals: When Each is Clearer
Key Features
Full Working Shown
Every calculation walks through the LCD, equivalent fractions, simplification, and final result so you can follow (or verify) the logic.
Mixed Number Support
Enter mixed numbers like 1 3/4 using the optional Whole Part field alongside the numerator and denominator.
Auto Simplification
Results are reduced to lowest terms automatically using the Euclidean algorithm to find the GCD.
Simplify Mode
Reduce a single fraction, convert it to a mixed number, or get its decimal value without entering a second operand.
Frequently Asked Questions
Can I enter negative fractions?
Place the negative sign on the whole part or the numerator. The calculator handles sign propagation automatically when converting mixed numbers to improper fractions.
What happens with very large numbers?
JavaScript uses 64 bit floating point internally, so intermediate products of very large numerators and denominators (above roughly 2^53) may lose precision. For typical homework and measurement fractions this is never an issue.
Why does simplify mode show a mixed number?
When the numerator is larger than the denominator (an improper fraction), the calculator automatically converts it to a mixed number alongside the simplified improper form and decimal equivalent.