How Fraction Arithmetic Works
This calculator performs the operation, then reduces the result to lowest terms using the greatest common divisor (GCD), and also shows it as a mixed number and decimal.
| Operation | Rule | Example |
|---|---|---|
| Addition | a/b + c/d = (ad + cb) / bd | 1/2 + 1/3 = 5/6 |
| Subtraction | a/b − c/d = (ad − cb) / bd | 3/4 − 1/6 = 7/12 |
| Multiplication | a/b × c/d = ac / bd | 2/3 × 3/4 = 1/2 |
| Division | a/b ÷ c/d = ad / bc | 1/2 ÷ 1/4 = 2 |
Simplifying: The GCD Step
6/8 and 3/4 are the same number; dividing numerator and denominator by their GCD (here 2) puts the fraction in lowest terms. The calculator does this automatically — enter 2/4 + 2/4 and you get 1, not 8/8.
Dividing = Multiplying by the Reciprocal
"Keep, change, flip": keep the first fraction, change ÷ to ×, flip the second. 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 2 — there are two quarters in one half, which makes intuitive sense.