Free Fraction Calculator
Add, subtract, multiply, or divide two fractions with simplification.
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Inputs
Result
Result (simplified)
13 / 12
lowest terms
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Short answer
For a/b op c/d: add/subtract by finding common denominator (a·d ± b·c)/(b·d), multiply as (a·c)/(b·d), divide as (a·d)/(b·c). Simplify by dividing both by their GCD.
What is the Fraction Calculator?
A four-operation fraction calculator with automatic simplification and decimal/mixed conversions.
How does the Fraction Calculator work?
Apply the appropriate rule for the operation, then divide numerator and denominator by their GCD.
Formula
Variables
gcdGreatest common divisor — used to simplify
Explanation
The Euclidean algorithm reduces to lowest terms after each operation.
Examples
Example 1: 3/4 + 1/3
9/12 + 4/12 = 13/12 = 1 1/12 ≈ 1.083.
Applications
- Homework
- Recipe scaling
- Woodworking measurements
Advantages
- Shows result, decimal, and mixed forms
Limitations
- Two operands per operation — chain manually for more
Common mistakes
- Adding numerators and denominators independently (that's wrong)
Tips
- To add fractions, always find a common denominator first
Related concepts
The Fraction Calculator sits inside the Math Calculators hub, in the algebra & equations cluster. Solving for unknowns and manipulating expressions. Understanding the terms below makes the output easier to interpret and easier to compare against neighbouring measures.
Practical use cases and industry applications
Understanding Fraction
A four-operation fraction calculator with automatic simplification and decimal/mixed conversions. Within math calculators, fraction belongs to the algebra & equations cluster, where it shares terminology and assumptions with closely related tools.
Learning how fraction is calculated
The Euclidean algorithm reduces to lowest terms after each operation. Working through the variables one at a time — gcd — makes the result reproducible by hand and easier to sanity-check.
Using fraction to make a decision
Homework Recipe scaling Woodworking measurements Because outputs depend on the assumptions you enter, run more than one scenario before committing to a figure.
How fraction compares with related measures
equation, root, exponent, logarithm all describe adjacent aspects of algebra & equations. Comparing this calculator's output against those measures — using the related tools listed on this page — prevents a single metric from being read in isolation.
Frequently asked questions
Why do I need a common denominator to add?
You can only add fractions with the same denominator because they must reference the same 'unit size' — 1/4 + 1/3 requires expressing both in twelfths.
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