math ToolUpdated 2026-09-19
Fraction Calculator
Simplify fractions and perform arithmetic operations including addition, subtraction, multiplication, and division with common denominator breakdowns.
Formula & Mathematical Methodology
a/b ± c/d = (ad ± bc) / bd
Fractions are adjusted to a common denominator before adding or subtracting, and multiplied across for products.
How to Use This Fraction Calculator
- Enter numerators and denominators for both fractions.
- Select your desired arithmetic operation.
- View the simplified result and decimal equivalent.
Step-by-Step Worked Example
Scenario: 3/4 + 2/5
1. Common denominator: 4 × 5 = 20
2. Convert fractions: (3 × 5)/20 + (2 × 4)/20 = 15/20 + 8/20
3. Sum numerators: 23/20 = 1 3/20
Final Calculated Result: 23/20 (or 1 3/20)
What Does Your Result Mean?
Displays both the irreducible reduced fraction and equivalent mixed number and decimal representation.
Common Practical Applications:
- Baking and culinary scaling
- Carpentry and construction measurements
- Academic mathematics
Important Limitations & Assumptions:
- Denominators cannot equal zero.
Frequently Asked Questions
How do you divide fractions?
Invert the second fraction (take its reciprocal) and multiply the numerators and denominators.
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