Fraction Calculator

Simplify Fraction Arithmetic

Working with fractions can be tricky, but this Fraction Calculator makes it easy. It allows you to add, subtract, multiply, and divide two fractions, providing the result in its simplest, reduced form. It's a great tool for students learning fractions or anyone needing a quick fraction calculation.

The Formulas Explained

Let the two fractions be a/b and c/d.

• Addition: (a*d + c*b) / (b*d)
• Subtraction: (a*d - c*b) / (b*d)
• Multiplication: (a*c) / (b*d)
• Division: (a*d) / (b*c) After the operation, the resulting fraction is simplified by dividing the numerator and denominator by their greatest common divisor.

How to Use the Calculator

1. Enter Fractions: Input the numerator (top number) and denominator (bottom number) for both fractions.
2. Select Operation: Choose the arithmetic operation you want to perform (+, -, ×, ÷).
3. Calculate: The result will be displayed in its simplest form.

Real-World Example

You want to calculate 1/4 + 3/8.

• Fraction 1: Numerator = 1, Denominator = 4
• Fraction 2: Numerator = 3, Denominator = 8
• Operation: +
• Calculation: (1*8 + 3*4) / (4*8) = (8 + 12) / 32 = 20 / 32
• Simplified Result: The greatest common divisor of 20 and 32 is 4. So, 20/4 = 5 and 32/4 = 8. The final result is 5/8.

Frequently Asked Questions (FAQ)

• What is an improper fraction? An improper fraction is one where the numerator is larger than the denominator (e.g., 7/3). This calculator will provide results as either proper or improper fractions, but not mixed numbers (e.g., 2 1/3).
• What happens if I enter a denominator of 0? Division by zero is undefined. The calculator will show an error if you enter 0 as a denominator.
• How does simplification work? The calculator finds the Greatest Common Divisor (GCD) of the numerator and denominator and divides both by it. For example, in 20/32, the GCD is 4, so the simplified fraction is (20/4) / (32/4) = 5/8.