Free fraction calculator. Add, subtract, multiply and divide fractions, simplify to lowest terms, and convert decimals to fractions and mixed numbers.
A fraction calculator adds, subtracts, multiplies and divides fractions and returns the result simplified to lowest terms, as a mixed number, and as a decimal. To add fractions, convert them to a common denominator first: 1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1 1/4. To divide, multiply by the reciprocal of the second fraction.
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Fraction Calculator
A fraction calculator performs the four basic operations on fractions and always returns the answer in three useful forms: a fraction simplified to lowest terms, a mixed number when the result is improper, and a decimal. A fraction is simply a division written vertically — 3/4 means 3 divided by 4 — with the numerator on top and the denominator on the bottom.
Multiplication is the easiest operation: multiply the numerators together and the denominators together. So 2/3 × 3/5 = 6/15, which simplifies to 2/5. Division works by flipping the second fraction and multiplying: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3. Addition and subtraction need one extra step — a common denominator — which is where most mistakes happen and where the calculator's step-by-step hint is most useful.
Common Denominators
The mistake: adding 1/2 + 3/4 as (1+3)/(2+4) = 4/6. That answer is wrong because halves and quarters are different-sized pieces — you cannot count them together until they are expressed in the same units.
The correct math: rewrite both fractions over a common denominator first. Halves become quarters: 1/2 = 2/4. Now the pieces match, so 2/4 + 3/4 = 5/4, which is the mixed number 1 1/4 or 1.25 as a decimal. The calculator uses the product of the two denominators as the common denominator, then simplifies the result, which always produces the same final answer as using the least common multiple.
Subtraction follows the identical pattern: 5/6 − 1/4 = 10/12 − 3/12 = 7/12. Because the common denominator can make intermediate numbers large, always simplify at the end rather than trying to guess the reduced form mid-calculation.
Lowest Terms
A fraction is fully simplified when the numerator and denominator share no common factor greater than 1. The reliable way to get there is to divide both by their greatest common divisor (GCD). For 8/12, the GCD of 8 and 12 is 4, so 8/12 = 2/3. For 45/60 the GCD is 15, giving 3/4.
Simplifying never changes the value of a fraction — 8/12, 4/6 and 2/3 are all exactly the same number — it only changes how the number is written. Lowest terms is the conventional final form because it makes fractions easy to compare: seeing at a glance that 2/3 is bigger than 3/5 is far easier than comparing 40/60 with 36/60. Negative signs are conventionally written on the numerator, so 3/−4 becomes −3/4.
A quick way to find the GCD by hand is the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing it by the smaller one until the remainder is zero. For 8 and 12: 12 ÷ 8 leaves 4, then 8 ÷ 4 leaves 0, so the GCD is 4. The calculator applies the same algorithm instantly, no matter how large the numbers are.
Mixed Numbers
When a calculation produces a numerator at least as large as the denominator — an improper fraction like 5/4 or 11/3 — it can be rewritten as a mixed number: a whole part plus a proper fraction. Divide the numerator by the denominator; the quotient is the whole part and the remainder stays over the same denominator. So 5/4 = 1 1/4 and 11/3 = 3 2/3.
Both forms are mathematically correct. Mixed numbers are the natural choice for everyday measurements — a recipe calls for 1 1/2 cups, not 3/2 cups — while improper fractions are far more convenient inside a calculation, because multiplying or dividing mixed numbers directly is error-prone. A good workflow is to convert mixed numbers to improper fractions before calculating and back to mixed form only at the end, which is exactly what this calculator does for you.
Decimals
Any terminating decimal converts to a fraction by writing it over a power of ten and simplifying: 0.75 = 75/100 = 3/4, and 0.125 = 125/1000 = 1/8. Repeating decimals are also exact fractions — 0.333… is exactly 1/3 and 0.1666… is exactly 1/6 — but the power-of-ten trick cannot capture them from a truncated input.
That is why this calculator uses the continued-fraction algorithm instead: it finds the best possible fraction with a denominator up to 10,000, so typing 0.333333 returns 1/3 rather than 333333/1000000, and 0.142857 comes back as the elegant 1/7. The same method gives compact, meaningful approximations for irrational numbers, which have no exact fraction at all. When no fraction with a denominator up to 10,000 matches the decimal exactly, the calculator notes that the result is an approximation.
Practical Use Cases
Cooking and baking
Scaling a recipe up or down — half of 3/4 cup, or 1 1/2 times 2/3 cup — without measuring mistakes.
Woodworking and DIY
Adding imperial measurements like 3/8 in + 5/16 in when cutting materials or spacing fixtures.
Checking homework
Verifying each step of fraction arithmetic, including the common denominator and the simplified final answer.
Converting measurements
Turning a decimal from a digital caliper or calculator back into a usable tape-measure fraction.
Splitting quantities
Dividing portions, materials or time into equal fractional shares and expressing the result cleanly.
Convert both fractions to a common denominator, then add or subtract the numerators. For 1/2 + 3/4, the common denominator is 4: 1/2 becomes 2/4, so 2/4 + 3/4 = 5/4, which simplifies to the mixed number 1 1/4. The calculator uses the product of the denominators and then simplifies the result to lowest terms automatically.
Multiply the first fraction by the reciprocal (the flipped version) of the second. For example, 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6, which simplifies to 2/3. Dividing by a fraction that equals zero is undefined, which is why the calculator shows an error when fraction B has a numerator of 0.
A fraction is in lowest terms when its numerator and denominator share no common factor other than 1. To simplify, divide both by their greatest common divisor (GCD). For 8/12, the GCD is 4, so 8/12 = 2/3. Simplified fractions are easier to compare and are the standard form expected in most math classes.
An improper fraction has a numerator larger than (or equal to) its denominator, like 5/4. A mixed number writes the same value as a whole part plus a proper fraction: 5/4 = 1 1/4. Both are correct; mixed numbers are easier to read in everyday contexts, while improper fractions are easier to calculate with.
Write the decimal over a power of ten and simplify: 0.75 = 75/100 = 3/4. This calculator uses the continued-fraction method, which finds the best fraction with a denominator up to 10,000 — so it also handles repeating decimals well, turning 0.333333 into 1/3 rather than an unwieldy 333333/1000000.
Every terminating or repeating decimal is a rational number and has an exact fraction. Irrational numbers like pi or the square root of 2 do not — for those, any fraction is only an approximation. The calculator marks results as approximations when no fraction with a denominator up to 10,000 matches the decimal exactly.