Fraction Calculator: Add, Subtract, Multiply, or Divide Fractions
Add, subtract, multiply, and divide fractions with step-by-step working
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For exact values, especially repeating decimals, refer to the fraction representation.
Result: 5/6 = 0.833333.
A fraction calculator performs the four arithmetic operations on fractions. Addition and subtraction require a common denominator (multiply each fraction by the other's denominator over itself). Multiplication multiplies numerators and denominators directly. Division multiplies by the reciprocal of the second fraction. Always simplify by dividing numerator and denominator by their greatest common divisor (GCD).
This comprehensive fraction calculator performs all four fundamental arithmetic operations—addition, subtraction, multiplication, and division—on any two fractions. It provides immediate, accurate results in three user-friendly formats: an improper fraction, a precise decimal value (rounded to six places), and a mixed number when the result is greater than one. Beyond just giving answers, the calculator offers clear, step-by-step working for each operation, demonstrating the process of finding common denominators, cross-multiplication, and simplification. It also handles negative numerators and ensures denominators are non-zero, making it an ideal educational tool for students and a reliable utility for anyone needing quick and detailed fraction arithmetic.
What is a fraction?
Use this fraction calculator to perform any of the four fundamental arithmetic operations on fractions — addition, subtraction, multiplication, or division — with clear, step-by-step working. Enter the numerators and denominators for two fractions and select your desired operation. The tool instantly returns the result in three convenient formats: as an improper fraction, a precise decimal value rounded to six places, and a mixed number when the result is greater than one. This calculator is built against standard K-12 and college-algebra fraction-arithmetic conventions, incorporating educational best practices and drawing examples from reputable sources like Khan Academy and Common Core curriculum references. It's an ideal tool for students, educators, or anyone needing quick and accurate fraction calculations, ensuring clarity and understanding of each step involved.
The formula
- a, c — numerators of the two fractions
- b, d — denominators (must be non-zero)
Source: Standard arithmetic of rational numbers.
Worked examples
1Addition with unlike denominators
1/2 + 1/3 = (1×3 + 1×2) / (2×3) = (3 + 2) / 6 = 5/6 ≈ 0.833. Already in lowest terms — gcd(5, 6) = 1.
2Subtraction (negative result possible)
1/4 − 1/2 = (1×2 − 1×4) / (4×2) = (2 − 4) / 8 = −2/8 = −1/4. The negative sign moves to the numerator by convention.
3Multiplication with cross-cancellation
2/3 × 3/4. The 3 in the first denominator cancels with the 3 in the second numerator, giving 2/1 × 1/4 = 2/4 = 1/2. Cross-cancellation keeps numbers small before multiplying.
How to use this calculator
- Numerator 1 — Top number of the first fraction.
- Denominator 1 — Bottom number of the first fraction. Must be non-zero.
- Operation (default: add)
- Numerator 2 (default: 1)
- Denominator 2 (default: 3)
- Read the result. Use the worked examples below to sanity-check against a known scenario.
The four operations side-by-side, with 1/2 and 1/3
| Operation | Setup | Result |
|---|---|---|
| Addition | (1×3 + 1×2) / (2×3) | 5/6 |
| Subtraction | (1×3 − 1×2) / (2×3) | 1/6 |
| Multiplication | (1×1) / (2×3) | 1/6 |
| Division | (1×3) / (2×1) | 3/2 = 1½ |
Notice subtraction and multiplication coincidentally give 1/6 here — they generally don't.
Frequently asked questions
How do you add fractions with different denominators?
How do you multiply fractions?
How do you divide fractions?
What's the difference between an improper fraction and a mixed number?
How do I simplify a fraction?
What's the lowest common denominator?
Can I add fractions to a whole number?
What happens when I divide by zero?
Fraction glossary
How we built this calculator
Methodology
For addition and subtraction, the calculator uses the cross-multiplication shortcut: a/b ± c/d = (ad ± bc)/(bd). This works for any pair of fractions but doesn't always produce the lowest common denominator (LCD). For lowest-common-denominator results, divide both numerator and denominator of the result by their GCD.
This calculator was written by Numora math team and reviewed by Numora statistics review team before publication. Both names link to full bios with verifiable credentials.
Sources & references
Every numeric assumption traces to a primary source.