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?" 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.