Fraction Calculator
Add, subtract, multiply, or divide two fractions and get a simplified result.
How this calculator works
Fractions are combined using standard rules, then automatically simplified using the greatest common divisor so the result is always in lowest terms.
Multiplication and division follow the standard cross-multiplication rules.
Working with mixed numbers and negative fractions
For negative fractions, enter the negative sign on either the numerator or denominator (not both) — the calculator will handle the sign correctly in the simplified result. For mixed numbers (like 2½), convert to an improper fraction first by multiplying the whole number by the denominator and adding the numerator.
The simplified result is always reduced to lowest terms automatically, which is useful for checking your own manual fraction work or verifying a homework answer.
A worked example
Adding 3/4 and 5/6: common denominator is 24, giving 18/24 plus 20/24, or 38/24, which simplifies to 19/12, about 1.583 as a decimal.
Multiplying the same two fractions instead: 3/4 times 5/6 equals 15/24, which simplifies to 5/8, or 0.625 — illustrating how multiplication doesn't require a common denominator, unlike addition or subtraction.
Working with fractions by hand
To add or subtract fractions manually, first find a common denominator by multiplying the two denominators (or finding their least common multiple for smaller numbers), then adjust each numerator accordingly before combining. Multiplication is simpler — multiply numerators together and denominators together directly.
Division of fractions uses the 'flip and multiply' rule: dividing by a fraction is the same as multiplying by its reciprocal (flipping the numerator and denominator), which is why the calculator's divide operation cross-multiplies internally.
Frequently asked questions
Is the result automatically simplified?
Yes — the result is always reduced to its simplest form using the greatest common divisor.
Can I use negative numbers?
Yes, enter a negative sign in either the numerator or denominator field.
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and keep the same denominator — for example, 2½ becomes (2×2+1)/2 = 5/2.
Why is my answer shown as a negative fraction differently than I expected?
By convention, the negative sign is typically shown on the numerator in a simplified fraction — mathematically equivalent regardless of which term carries the sign.
Why do I need a common denominator to add fractions?
Fractions represent parts of a whole, and you can only directly add or subtract parts if they're measured in the same-sized pieces — a common denominator ensures that.