Enter two fractions and pick an operation. The calculator returns the result reduced to lowest terms, as a mixed number when it's improper, and as a decimal.
How the fraction calculator works
Every fraction operation comes down to getting the numerators and denominators to cooperate. Addition and subtraction need a common denominator; multiplication just multiplies straight across; division flips the second fraction and multiplies. The calculator does the operation, then reduces the answer by the greatest common divisor so you always see it in lowest terms — plus the mixed-number form when the result is improper, and the decimal equivalent.
The formulas
a/b + c/d = (a·d + c·b) ÷ (b·d)
a/b × c/d = (a·c) ÷ (b·d)
a/b ÷ c/d = (a·d) ÷ (b·c)
a and c are the numerators, b and d the denominators. Subtraction is addition with the second numerator negated. After the operation, both parts are divided by their GCD to simplify.
Worked example
2/3 + 3/4: the common denominator is 3 × 4 = 12, so rewrite as 8/12 + 9/12 = 17/12.
17 and 12 share no common factor, so 17/12 is already in lowest terms. As a mixed number it's 1 5/12, and as a decimal ≈ 1.4167.
Why "flip and multiply" actually works
Division asks "how many times does the divisor fit?" — and multiplying by the reciprocal answers exactly that question. Dividing by 1/2 doubles a number because halves fit into anything twice as many times as wholes do. This is also why dividing by a fraction smaller than 1 makes the answer bigger, which trips people up constantly: (2/3) ÷ (3/4) = 8/9, which is larger than 2/3. If your division answer grew and you expected it to shrink, you probably didn't make an error — you divided by something less than one.
Frequently asked questions
How do I add fractions with different denominators?
Rewrite both fractions over a common denominator, then add the numerators. The quick method: multiply each numerator by the other fraction's denominator, add those products, and put the sum over the product of the denominators. Then simplify: 2/3 + 3/4 = (2×4 + 3×3)/(3×4) = 17/12.
How do I simplify a fraction to lowest terms?
Divide the numerator and denominator by their greatest common divisor (GCD). For 8/12 the GCD is 4, so 8/12 = 2/3. A fraction is fully simplified when the GCD of its numerator and denominator is 1.
How do I divide one fraction by another?
Flip the second fraction and multiply — dividing by 3/4 is the same as multiplying by 4/3. So (2/3) ÷ (3/4) = (2/3) × (4/3) = 8/9. You can't divide by a fraction equal to zero, just as you can't divide by zero itself.
What is a mixed number and when should I use one?
A mixed number combines a whole number and a proper fraction, like 1 5/12 instead of 17/12. Both mean the same thing. Mixed numbers are easier to read in everyday contexts (recipes, measurements), while improper fractions are easier to calculate with.
Why does my calculator show a different decimal than the fraction?
Many fractions produce repeating decimals — 1/3 is 0.3333... forever. Any displayed decimal is rounded, so the fraction form is the exact answer. That's why this calculator always shows the simplified fraction first and treats the decimal as a convenience.