Mixed → Improper: \(w\ \frac{n}{d} = \frac{w\cdot d + n}{d}\). Carry the sign on the whole or the fraction, not both.
Find LCD: Use the least common multiple of denominators.
Make equivalents: Multiply each fraction by \( \frac{\text{LCD}}{\text{den}} \).
Add: Keep denominator = LCD, add all (signed) numerators.
Simplify: Divide numerator & denominator by their GCD.
Improper → Mixed: Whole = ⌊|n|/d⌋, remainder = |n| mod d, keep sign on whole.
Tip: Integers are just fractions with denominator 1 (e.g., 7 = 7/1).
Edge cases & notes
Zero denominators are invalid.
Signs normalize to the numerator (e.g., \(-3/4\) not \(3/-4\)).
Result is shown as a simplified improper fraction and as a mixed number (if applicable).
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