Fraction Calculator
Fraction Calculator — add, subtract, multiply, and divide fractions. See the simplified result, decimal value, and mixed number. Free, no signup.
About Fraction Calculator
The Fraction Calculator handles the four basic operations — addition, subtraction, multiplication, and division — on any two fractions, and gives you the result in three forms at once: the simplified fraction, the decimal value, and the mixed number (when the result is greater than 1). Enter two numerator/denominator pairs, pick an operation, and the answer appears instantly with the original calculation shown alongside it so you can check the work.
Fractions trip up almost everyone at some point, not because the rules are hard but because the bookkeeping is fiddly. You have to find a common denominator for addition and subtraction, multiply across for multiplication, flip and multiply for division — and then simplify the result. Miss a step, and the answer is wrong. The calculator does the bookkeeping for you and shows every step of the result so you can verify each one.
How fraction math works
Addition and subtraction require a common denominator. The general formula is a/b ± c/d = (a·d ± b·c) / (b·d). This always works, though the result may need simplifying. For 1/2 + 1/3: multiply across to get (1·3 + 1·2) / (2·3) = 5/6. Since 5 and 6 share no common factor, the answer is already simplified.
Multiplication is the easy one — just multiply numerators together and denominators together: a/b × c/d = (a·c) / (b·d). No common denominator needed. For 2/3 × 4/5 = 8/15.
Division uses the “keep, change, flip” rule: a/b ÷ c/d = a/b × d/c. You flip the second fraction (reciprocal) and multiply. For 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2.
Simplification is the final step. The calculator uses the Euclidean algorithm to find the greatest common divisor (GCD) of the numerator and denominator, then divides both by it. This turns 6/12 into 1/2, or 20/6 into 10/3. Always simplify — the unsimplified form is technically correct but harder to read.
Where you’ll actually use this
Cooking and recipes. Doubling a recipe with 3/4 cup of flour means 3/4 × 2 = 6/4 = 1 1/2 cups. Halving 2/3 teaspoon of salt gives 1/3 teaspoon. The mixed number form is what you’d actually write in a recipe; the improper fraction form is the easiest to calculate with.
Construction, DIY, and woodworking. Lumber and drill bits are still measured in fractions of an inch in many places. A board that’s 3 1/2 inches wide minus a 5/8 inch cut leaves 2 7/8 inches. Tile and trim work runs on the same kind of arithmetic.
Schoolwork and tutoring. Showing both the simplified result and the original calculation is exactly what teachers want to see — the answer plus the working. The decimal and mixed forms make it easy to spot whether an answer looks reasonable.
Probability and statistics. Combining probabilities almost always involves multiplying or adding fractions — 1/2 × 1/6 for two independent events, or 1/4 + 1/4 + 1/4 for adding compatible outcomes. Keeping the answer as a fraction is often clearer than a decimal.
Free, no signup, works on any device.
Frequently asked questions
To add a/b + c/d, give both fractions a common denominator and add the numerators. The shortcut is (a·d + b·c) / (b·d), then simplify. For 1/2 + 1/3, multiply across: (1·3 + 1·2) / (2·3) = 5/6. The calculator does this automatically and shows the simplified result, the decimal value, and the original expression.
Subtraction works the same way as addition, but you subtract the cross-products: a/b − c/d = (a·d − b·c) / (b·d). For 3/4 − 1/3 = (3·3 − 1·4) / (4·3) = 5/12. If the result is negative, the sign goes on the numerator and the denominator stays positive.
Multiply numerator by numerator and denominator by denominator: a/b × c/d = (a·c) / (b·d). For 2/3 × 4/5 = 8/15. You do not need a common denominator for multiplication. Always simplify at the end — for example, 2/3 × 3/4 = 6/12, which simplifies to 1/2.
Flip the second fraction and multiply ("keep, change, flip"). a/b ÷ c/d = a/b × d/c = (a·d) / (b·c). For 1/2 ÷ 1/4 = (1·4) / (2·1) = 4/2 = 2. Division by zero is undefined, so the second fraction cannot have a numerator of 0.