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To add fractions you need a common denominator. Cross-multiplying gives (a·d + c·b)/(b·d), which is then reduced by dividing both parts by their greatest common divisor.
Adding fractions
a/b + c/d = (ad + cb) / bd, then divide by gcd
(1×6 + 1×3)/18 = 9/18, which reduces to 1/2.
No. Any common denominator works; using the LCD just means less reducing at the end.