How to Calculate Fractions
A fraction represents a part of a whole, expressed as a numerator (top number) divided by a denominator (bottom number). Operations on fractions follow specific rules depending on whether the denominators are the same or different.
Adding and Subtracting Fractions
Same denominator: a/b ± c/b = (a±c)/b
Different denominator: a/b ± c/d = (ad ± bc) / (bd)
Different denominator: a/b ± c/d = (ad ± bc) / (bd)
Always simplify the result by dividing both numerator and denominator by their Greatest Common Divisor (GCD).
Multiplying Fractions
(a/b) × (c/d) = (a×c) / (b×d)
Dividing Fractions
(a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d) / (b×c)
To divide, multiply by the reciprocal of the second fraction.
Simplifying Fractions
A fraction is in its simplest form when the GCD (Greatest Common Divisor) of the numerator and denominator is 1. Example: 6/8 → GCD(6,8)=2 → 3/4.