Verified Mathematical Model & Formulation
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 Simplification: Divide numerator & denominator by GCD(a, b)
Executes exact rational arithmetic on rational fractions, cross-multiplying to identify the common denominator and reducing the resulting quotient to lowest terms using the Euclidean Greatest Common Divisor (GCD) algorithm.
Configurable Parameters & Standard Units
- Fraction 1 Numerator: (Default: 3 count)
- Fraction 1 Denominator: (Default: 4 count)
- Operation (1=Add +, 2=Subtract -, 3=Multiply ×, 4=Divide ÷): (Default: 1 count)
- Fraction 2 Numerator: (Default: 2 count)
- Fraction 2 Denominator: (Default: 5 count)
Standard Worked Example & Practical Verification
Scenario: Calculating 3/4 + 5/6 step-by-step.
Practical Takeaway: Cross-multiplying and simplifying yields the exact irreducible rational answer.
Frequently Asked Questions
What is an improper fraction vs a mixed number?
An improper fraction has a numerator greater than or equal to its denominator (e.g. 7/4). A mixed number expresses it as an integer plus a proper fraction (e.g. 1 3/4).
How do you divide fractions?
To divide by a fraction, multiply by its reciprocal (invert the second fraction and multiply: a/b ÷ c/d = a/b × d/c).