How to add, subtract, multiply and divide fractions
Every fraction operation reduces to a couple of rules. To add or subtract, you need a common denominator; to multiply, you multiply straight across; to divide, you multiply by the reciprocal (flip the second fraction). After any operation the answer is reduced to lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD).
The fraction formulas
add: a/b + c/d = (a·d + c·b) / (b·d)
subtract: a/b − c/d = (a·d − c·b) / (b·d)
multiply: a/b × c/d = (a·c) / (b·d)
divide: a/b ÷ c/d = (a·d) / (b·c)
Worked example
Add 1/2 + 1/3:
Common denominator: 2 × 3 = 6.
Rewrite: 1/2 = 3/6 and 1/3 = 2/6.
Add numerators: 3/6 + 2/6 = 5/6 (already in lowest terms, ≈ 0.8333).
Reminder: a fraction is in lowest terms when the only number that divides both top and bottom is 1. 4/8 reduces to 1/2 because both share a factor of 4.