What This Fraction Calculator Handles
Enter two fractions — proper (3/4), improper (7/4), mixed (1 3/4), or whole numbers — choose an operation, and get the result simplified to lowest terms with a decimal equivalent.
Quick vocabulary:
- Numerator/denominator — top and bottom numbers
- Proper — top < bottom (3/4); improper — top ≥ bottom (7/4)
- Mixed number — whole + fraction (1 3/4 = 7/4)
- Simplified — numerator and denominator share no common factor (6/8 → 3/4)
The Four Operations, With Rules
Addition & subtraction — need a common denominator
Example: 2/3 + 1/4 = (8 + 3)/12 = 11/12. Using the least common denominator (LCD) keeps numbers small, but any common denominator works — simplification cleans up afterward.
Multiplication — straight across
Example: 2/3 × 3/8 = 6/24 = 1/4. Cross-cancel first (2/3 × 3/8 → 1/1 × 1/4) to keep numbers tiny.
Division — multiply by the reciprocal
Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. "Keep, change, flip."
Mixed Numbers: Convert First
Arithmetic on mixed numbers goes through improper form:
Improper → mixed: divide; quotient is the whole, remainder the numerator 17/6 = 2 5/6
Worked: 2 1/2 × 1 2/3
Convert: 5/2 × 5/3 = 25/6 = 4 1/6. (The tempting wrong path — multiplying wholes and fractions separately — gives 2 2/6 and is off by nearly half.)
Simplifying: GCD in Practice
A result like 84/126 simplifies by the greatest common divisor:
The calculator finds the GCD with the Euclidean algorithm (repeated remainders: 126 mod 84 = 42; 84 mod 42 = 0 → GCD 42) and always reports lowest terms. Handy divisibility checks for manual work: even/even → divide by 2; digit-sums divisible by 3 → divide by 3; both end in 0 or 5 → divide by 5.
Fractions, Decimals, Percents: One Quantity, Three Costumes
| Fraction | Decimal | Percent |
|---|---|---|
| 1/8 | 0.125 | 12.5% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333… | 33.3% |
| 1/2 | 0.5 | 50% |
| 2/3 | 0.667… | 66.7% |
| 3/4 | 0.75 | 75% |
Fractions stay exact where decimals truncate (1/3 ≠ 0.33) — which is why recipes, carpentry, and probability keep them alive. For percent-specific work, the Percentage Calculator; for decimal conversion practice, results here show both forms.
The Bottom Line
Four rules run all of fraction arithmetic: common denominators to add or subtract, straight across to multiply, flip to divide, and simplify by the GCD at the end. The calculator above does the bookkeeping and shows its work — so whether you're checking homework or splitting a recipe by 1 1/2, you get the exact answer and the path to it.