Decimal to Fraction Converter
Convert any decimal number to a simplified fraction. Handles terminating and repeating decimals with GCD reduction for the simplest form.
Fraction Calculator
Perform addition, subtraction, multiplication, and division on fractions. Get simplified results using GCD.
Result (Fraction)⧉
17/12
Decimal⧉
1.416667
Planning notes, formulas, and examples
About the Fraction Calculator
The Fraction Calculator performs all four basic arithmetic operations on fractions: addition, subtraction, multiplication, and division. Enter two fractions, select the operation, and get the result simplified to its lowest terms.
Fraction arithmetic is a foundational math skill, but it is also one of the most error-prone when done by hand. Finding common denominators, cross-multiplying, and simplifying can each introduce mistakes. This calculator handles all the steps and always delivers the fully reduced answer.
Whether you're a student working through homework, a cook scaling recipes, a carpenter measuring lumber, or an engineer working with tolerances, this calculator removes the tedium of manual fraction math. It shows both the simplified fraction and the decimal equivalent for maximum flexibility.
When This Page Helps
Manual fraction arithmetic requires multiple steps prone to error. This calculator handles finding common denominators, performing the operation, and simplifying to lowest terms — all in one step.
How to Use the Inputs
- Enter the numerator and denominator for the first fraction.
- Select the arithmetic operation (+, −, ×, ÷).
- Enter the numerator and denominator for the second fraction.
- View the simplified result as a fraction and decimal.
- Use the result for further calculations as needed.
Formula used
Addition: a/b + c/d = (ad + bc) / bd
Subtraction: a/b − c/d = (ad − bc) / bd
Multiplication: a/b × c/d = ac / bd
Division: a/b ÷ c/d = ad / bc
All results simplified by dividing by GCD(numerator, denominator).Example Calculation
Result: 17/12
3/4 + 2/3 = (3×3 + 4×2) / (4×3) = (9 + 8) / 12 = 17/12. GCD(17,12) = 1, so the fraction is already simplified. As a decimal: 1.4167.
Tips & Best Practices
- For addition and subtraction, the calculator finds the common denominator automatically.
- Multiplication is the simplest operation: just multiply numerators and denominators.
- Division flips the second fraction and multiplies.
- Always check your result by converting to decimal — it's a quick sanity check.
- Negative fractions are handled correctly; the sign is placed on the numerator.
- Enter 0 as the numerator for a fraction equal to zero.
Fraction Arithmetic Basics
Fractions represent parts of a whole. The numerator (top) tells how many parts you have, and the denominator (bottom) tells how many equal parts make the whole. Understanding this makes fraction operations intuitive.
Why Simplification Matters
Unsimplified fractions like 6/8 are mathematically correct but harder to interpret than 3/4. Simplification ensures clarity in communication, especially in recipes, measurements, and engineering specifications.
Real-World Applications
Carpenters add fractions when combining measurements. Cooks scale recipes using fraction multiplication. Engineers calculate tolerances with fraction subtraction. This calculator handles these operations while reducing manual errors in professional contexts.
Sources & Methodology
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Frequently Asked Questions
Find a common denominator (typically the product of both denominators), convert both fractions to have that denominator, add the numerators, and simplify. This calculator does all these steps automatically.
Flip the second fraction (swap its numerator and denominator) and multiply. For example, (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8.
Simplifying (or reducing) a fraction means dividing both numerator and denominator by their greatest common divisor (GCD) until no further reduction is possible. 6/8 simplifies to 3/4.
Yes. Enter a negative number for the numerator. The calculator handles negative values correctly for all four operations.
An improper fraction has a numerator larger than its denominator (like 7/4). It represents a value greater than 1. This calculator works with both proper and improper fractions.
The GCD (Greatest Common Divisor) is found using the Euclidean algorithm: repeatedly divide the larger number by the smaller and take the remainder until the remainder is zero. The last non-zero remainder is the GCD.
More in this topic
Fraction to Decimal Converter
Convert any fraction to its decimal equivalent by dividing the numerator by the denominator. Handles proper, improper, and mixed fractions with high precision.
Fraction to Percentage Converter
Convert any fraction to a percentage. Enter the numerator and denominator to calculate the percentage using (numerator/denominator) × 100.