Math

Fraction Calculator

Add, subtract, multiply and divide fractions with instant simplification.

Fraction Calculator

Numerator 1

Denominator 1

Operation

Numerator 2

Denominator 2

Results

How to Use Fraction Calculator

1 Enter the numerator and denominator for the first fraction
2 Select the operation (Add, Subtract, Multiply, or Divide)
3 Enter the second fraction values
4 Click Calculate to see the result in simplified form and as a decimal

Formula & Methodology

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

Results are automatically simplified using GCD (Greatest Common Divisor).

About Fraction Calculator

Our fraction calculator handles all four arithmetic operations on fractions and automatically simplifies the result. Whether you're a student learning fractions or a professional needing quick calculations, this tool gives you accurate results with the simplified fraction form.

How Fraction Operations Work

When adding or subtracting fractions, you need a common denominator. The easiest method is to multiply the denominators (cross-multiply). For 1/2 + 1/3: convert to 3/6 + 2/6 = 5/6.

For multiplication, simply multiply numerators together and denominators together. For division, multiply by the reciprocal of the second fraction.

Frequently Asked Questions

To add fractions, find a common denominator, convert both fractions, then add the numerators. For example, 1/3 + 1/4 = 4/12 + 3/12 = 7/12. Our calculator handles this automatically.

Multiply the numerators together and the denominators together. For example, (2/3) × (3/4) = (2×3)/(3×4) = 6/12 = 1/2. Always simplify the result.

To divide by a fraction, multiply by its reciprocal. For example, (2/3) ÷ (4/5) = (2/3) × (5/4) = 10/12 = 5/6.

A mixed number combines a whole number and a proper fraction, like 2½. To convert it to an improper fraction: multiply the whole number by the denominator, add the numerator. So 2½ = (2×2+1)/2 = 5/2.

Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. For example, 12/18: GCD is 6, so 12/18 = 2/3.

An improper fraction has a numerator larger than or equal to the denominator, such as 7/4 or 5/5. It represents a value ≥ 1 and can be converted to a mixed number (7/4 = 1¾).

Yes. Treat the negative sign as belonging to the numerator. For example, −3/4 + 1/2 = −3/4 + 2/4 = −1/4. The same rules for addition, subtraction, multiplication, and division apply.

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