Fraction Calculator
Add, subtract, multiply, and divide fractions and mixed numbers with step-by-step simplification to simplest terms.
Input Parameters
Live Result
Details
Steps
Find Least Common Denominator: LCD(2, 3) = 6
Convert to equivalent fractions
Add numerators together
Quick Answer & Understanding Your Result
A Fraction Calculator computes rational arithmetic operations (Addition, Subtraction, Multiplication, Division) across proper, improper, and mixed fractions.
Core Fraction Operations
- Addition & Subtraction: Converts unlike fractions to the Least Common Denominator (LCD) before computing numerators (a/b ± c/d = (ad ± bc) / bd).
- Multiplication: Multiplies numerators and denominators directly ((a/b) × (c/d) = (a × c) / (b × d)).
- Division (Reciprocal Law): Inverts the divisor fraction and multiplies ((a/b) ÷ (c/d) = (a × d) / (b × c)).
- Automatic Simplification: Reduces results to simplest terms using Greatest Common Factor (GCF) factorization.
Enter your fraction numerators and denominators above to compute step-by-step results instantly.
Formula & Calculation Logic
Mathematical FormulaFraction rules:
- Numerator (a, c): The top number representing parts taken.
- Denominator (b, d): The bottom number representing total equal divisions (b, d
eq 0).
Step-by-Step Guide
Enter First Fraction (a/b)
Input the numerator and denominator of the first fraction.
Select Arithmetic Operator
Choose Addition (+), Subtraction (-), Multiplication (×), or Division (÷).
Enter Second Fraction (c/d)
Input the second fraction and receive instant simplified output.
Worked Examples Table
| Example | Input Values | Calculated Result | Explanation |
|---|---|---|---|
| Addition: 1/2 + 1/4 | Common denominator is 4: 2/4 + 1/4 = 3/4. | ||
| Multiplication: 2/3 × 3/5 | (2 × 3) / (3 × 5) = 6/15 = 2/5 (simplified by GCF 3). |
Frequently Asked Questions
Evidence-Based Methodology & Authoritative References
NIST Digital Library of Mathematical Functions
Khan Academy - Fractions Operations
Standard: ISO / W3C / IETF Authoritative Domain Standard
Formula: Addition: (a/b) + (c/d) = (ad + bc) / bd
Last Reviewed: August 21, 2026
Primary Source: NIST Digital Library of Mathematical Functions
Reference Document: Khan Academy - Fractions Operations
Computation Privacy: 100% client-side 0ms computation, zero data retention
Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.
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Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.