Fraction & decimal converter
Convert decimal ↔ simplified fraction (GCD) and compute + and ×.
- Instant
- Free
- Private (processed locally)
- No sign-up
Fractions and decimals, both ways
A recipe in 0.75, a calculation in 1/3: switching between them means simplifying. This tool converts decimal ↔ fraction via the GCD and continued fractions, and computes the sum and product of two fractions.
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Enter a number
A decimal (0.75) or a fraction (3/4).
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Read the reduced form
Decimal and irreducible fraction side by side.
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Compute
Enter two fractions for A + B and A × B.
Verified examples
| Input | Result |
|---|---|
| 0.75 | 3/4 |
| 0.333… | 1/3 |
| 1/2 + 1/3 | 5/6 |
| 1/2 × 1/3 | 1/6 |
Simplification relies on the GCD; the decimal is approximated by continued fractions. Everything is computed in your browser.
Frequently asked questions
How does 0.75 become 3/4?
Write 0.75 = 75/100, then divide top and bottom by their greatest common divisor (GCD = 25): 75÷25 = 3 and 100÷25 = 4, giving 3/4. The tool automatically simplifies any fraction by the GCD.
How do you handle 0.333…?
Via continued fractions: instead of a raw division, the algorithm seeks the simplest fraction near the value. It thus recovers 1/3 for 0.3333, 1/7 for 0.142857, etc., far better than a decimal approximation.
How do I add two fractions?
Put them over a common denominator: a/b + c/d = (a·d + c·b) / (b·d), then simplify. For example 1/2 + 1/3 = (3 + 2)/6 = 5/6. Multiplication is simpler: a/b × c/d = (a·c)/(b·d), so 1/2 × 1/3 = 1/6.
What is an irreducible fraction?
A fraction whose numerator and denominator share no common divisor other than 1 (their GCD is 1). 3/4 is irreducible; 6/8 is not, as it simplifies to 3/4. The tool always gives the irreducible form.