A worked example: 2 1/4 + 1 1/2
Before adding, each mixed number becomes an improper fraction: 2 1/4 is (2 × 4 + 1)/4 = 9/4, and 1 1/2 is (1 × 2 + 1)/2 = 3/2. Cross-multiplying denominators gives (9 × 2 + 3 × 4)/(4 × 2) = 30/8, which simplifies to 15/4. Converting 15/4 back to a mixed number — dividing 15 by 4 for a whole-number part of 3 with a remainder of 3 — lands on 3 3/4, matching the calculator's decimal output of 3.75.
The formula: improper fraction, arithmetic, then convert back
Every operation follows the same three stages: convert whole1 numerator1/denominator1 and whole2 numerator2/denominator2 into improper fractions (whole × denominator + numerator over the original denominator), run the chosen operation on those two improper fractions exactly as the fraction calculator would, and then split the simplified result back into a whole number and a remainder fraction.
A subtraction and a multiplication: 3 1/3 − 1 2/3 and 1 1/2 × 2 1/3
Subtracting 3 1/3 − 1 2/3 starts from the improper fractions 10/3 and 5/3, giving (10 × 3 − 5 × 3)/(3 × 3) = 15/9, which simplifies to 5/3 — or 1 2/3 as a mixed number, matching the calculator's decimal of 1.66666667. Multiplying 1 1/2 × 2 1/3 instead uses 3/2 and 7/3, giving (3 × 7)/(2 × 3) = 21/6, which simplifies to 7/2, or 3 1/2 as a mixed number — a decimal of 3.5.
Why the negative-result flag exists
Because whole numbers and numerators are entered as non-negative values, a subtraction whose true result is negative can't show that sign on the whole-number part alone — a negative sign belongs to the whole mixed number, not just one piece of it. That's why the calculator reports a separate "Result is negative?" flag alongside a whole number and numerator that represent the magnitude of the answer, rather than trying to attach a minus sign to just the whole-number field.