Fraction Operations
This calculator performs all four basic operations on fractions and shows the work step by step.
Adding Fractions
Formula: a/b + c/d = (ad + bc) / bd
Example: 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6
Subtracting Fractions
Formula: a/b - c/d = (ad - bc) / bd
Example: 3/4 - 1/2 = (3×2 - 1×4) / (4×2) = 2/8 = 1/4
Multiplying Fractions
Formula: a/b × c/d = ac / bd
Example: 2/3 × 3/4 = 6/12 = 1/2
Dividing Fractions
Formula: a/b ÷ c/d = a/b × d/c = ad / bc
Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2
Understanding Fractions
Parts of a Fraction
- Numerator: The top number (how many parts you have)
- Denominator: The bottom number (total equal parts)
Types of Fractions
- Proper: Numerator < denominator (e.g., 3/4)
- Improper: Numerator ≥ denominator (e.g., 5/3)
- Mixed: Whole number + fraction (e.g., 1⅔)
Simplifying Fractions
To simplify, find the greatest common divisor (GCD) and divide both parts by it.
Example: 12/18 → GCD is 6 → 12÷6 / 18÷6 = 2/3