What the fraction calculator does
Enter two fractions, choose add, subtract, multiply or divide, and the calculator returns the exact result as a fraction in lowest terms, plus its decimal value. It handles improper fractions and reduces automatically, so 3/4 + 5/6 comes back as 19/12 (1.5833), not as an unreduced 38/24. Useful for recipes, woodworking and fabric measurements, homework checking, and anywhere a decimal would hide the exact value.
The four operations
Add: a/b + c/d = (ad + cb) / bd → 3/4 + 5/6 = (18 + 20)/24 = 38/24 = 19/12
Subtract: a/b − c/d = (ad − cb) / bd → 3/4 − 5/6 = (18 − 20)/24 = −2/24 = −1/12
Multiply: a/b × c/d = ac / bd → 3/4 × 5/6 = 15/24 = 5/8
Divide: a/b ÷ c/d = a/b × d/c = ad / bc → 3/4 ÷ 5/6 = 18/20 = 9/10Adding and subtracting need a common denominator; multiplying and dividing do not. Dividing by a fraction is multiplying by its reciprocal (flip it), which is the step most people half-remember.
Reducing to lowest terms
A fraction is reduced by dividing numerator and denominator by their greatest common divisor (GCD). The calculator finds the GCD with Euclid's algorithm — repeatedly replace the larger number with the remainder of dividing it by the smaller until the remainder is zero.
GCD(38, 24): 38 = 1×24 + 14 → 24 = 1×14 + 10 → 14 = 1×10 + 4 → 10 = 2×4 + 2 → 4 = 2×2 + 0
GCD = 2 → 38/24 = 19/12Using the smallest common denominator instead of simply multiplying the denominators keeps intermediate numbers small: 3/4 + 5/6 can be done over 12 rather than 24. The result is the same after reduction.
Mixed numbers, improper fractions and decimals
| Form | Example | When it is used |
|---|---|---|
| Proper fraction | 3/4 | Part of a whole |
| Improper fraction | 19/12 | Calculation results; easiest form for arithmetic |
| Mixed number | 1 7/12 | Measurements and recipes (1 7/12 cups) |
| Decimal | 1.5833… | Money, calculators, spreadsheets |
| Percentage | 158.33% | Rates and comparisons |
To convert a mixed number for entry, multiply the whole part by the denominator and add the numerator: 2 3/8 = (2×8 + 3)/8 = 19/8. To convert back, divide: 19 ÷ 8 = 2 remainder 3, so 2 3/8.
Fractions you meet in real life
- Cooking: scaling a recipe by 1½ turns ⅔ cup into ⅔ × 3/2 = 1 cup; halving ¾ teaspoon gives ⅜, which is why measuring spoons come in odd sizes.
- Imperial measurements: a board measuring 5⅜ in cut from 12 in leaves 12 − 43/8 = 53/8 = 6⅝ in. Tape measures are marked in 16ths; the calculator keeps the exact answer.
- Music: note lengths are fractions of a bar; a dotted quarter is ¼ + ⅛ = ⅜.
- Probability: the chance of two independent events is the product — ⅙ × ⅙ = 1/36 for double sixes.
- Shares and ratios: splitting costs ⅖ and ⅗, or mixing fuel at 1/50.
Why not just use decimals?
Some fractions have no exact decimal: ⅓ is 0.333… forever, and rounding it introduces error that compounds over several steps. Fractions stay exact. Three thirds add to exactly one; three lots of 0.33 add to 0.99. For money and engineering, decimals are the convention; for anything with thirds, sixths or sevenths, fractions are safer until the final answer.