Fraction Calculator
Do fraction arithmetic the easy way — common denominators and simplification handled for you.
This fraction calculator adds, subtracts, multiplies, and divides fractions, then reduces the answer to lowest terms automatically. Enter two fractions, pick the operation, and you get the exact result — shown both as a simplified fraction and, where it helps, as a mixed number and a decimal.
Fractions are one of the few areas where a normal calculator makes things worse: 1/3 becomes 0.3333…, and the exactness is gone. Working symbolically, this tool keeps 1/3 + 1/6 as exactly 1/2 — no rounding, no recurring decimals. It handles the tedious parts (finding common denominators, reducing by the greatest common divisor) that cause most homework mistakes.
Useful for schoolwork, recipe scaling, and workshop measurements in inches. Free, instant, and entirely in-browser.
How to calculate with fractions
- Enter the numerator and denominator of the first fraction.
- Choose the operation: add, subtract, multiply, or divide.
- Enter the second fraction.
- Read the simplified result — shown as a fraction, a mixed number, and a decimal.
- Change any value to recalculate instantly.
The rules the calculator applies for you
Addition and subtraction need a common denominator: 1/4 + 1/6 becomes 3/12 + 2/12 = 5/12. Multiplication is straight across: 2/3 × 3/5 = 6/15, reduced to 2/5. Division flips the second fraction and multiplies: 1/2 ÷ 3/4 = 1/2 × 4/3 = 2/3. After every operation the result is divided by the greatest common divisor of numerator and denominator, so you always see lowest terms.
Improper results like 7/4 are also shown as the mixed number 1 3/4 — the form most recipes, tape measures, and teachers expect.
A worked example, step by step
Take 2/3 + 3/4. The denominators are 3 and 4, whose least common denominator is 12. Rewrite each fraction over 12: 2/3 becomes 8/12 and 3/4 becomes 9/12. Now the numerators add directly: 8 + 9 = 17, giving 17/12. Because 17 and 12 share no common factor, that fraction is already in lowest terms.
Since 17/12 is improper, it also reads as the mixed number 1 5/12, and as roughly 1.417 in decimal. The fraction calculator runs every one of these steps for you and shows all three forms, but seeing the working once makes it clear why the answer is not the tempting-but-wrong 5/7 you would get by adding tops and bottoms straight across.
Reading the three forms of the answer
Every result appears three ways because different tasks want different forms. The simplified fraction (say 3/8) is the exact, canonical answer a teacher expects. The mixed number (1 1/2 rather than 3/2) is how measurements, recipes, and everyday speech phrase quantities greater than one. The decimal (0.375) is what you need when the next step involves money, a calculator, or a measuring device marked in tenths.
They are the same value wearing different clothes, so pick by context rather than treating one as more correct. When a decimal ends in a string like 0.8333…, that is your cue that the fractional form (5/6 here) is the exact one and the decimal has been rounded for display.
When fractions beat decimals
Fractions keep values exact where decimals cannot. One third is exactly 1/3, but as a decimal it is 0.3333… forever; add three of them as decimals and you may get 0.9999 instead of a clean 1. Any time a quantity divides into thirds, sixths, sevenths, or ninths, the fraction stays precise while the decimal has to be cut off and rounded.
This matters most when results feed further calculations. Doubling a recipe, scaling a cutting list, or chaining several operations compounds rounding error if you switch to decimals early. Working in fractions until the very end — which is what this calculator does internally — keeps the final answer honest, and you can convert to a decimal only when you actually need one.
Where fraction math shows up in real life
Cooking is the everyday case: halving a recipe that calls for 3/4 cup means 3/4 ÷ 2 = 3/8 cup, and scaling three batches of 2/3 cup means 2/3 × 3 = 2 cups. Woodworking and DIY are the other big one, because tape measures in inches are marked in halves, quarters, eighths, and sixteenths — adding 3/8 inch to 5/16 inch (13/16) is a fraction problem whether you like it or not.
Beyond that, fractions appear in dividing time (2/3 of an hour is 40 minutes), splitting costs, reading sheet music, and of course schoolwork, where showing the exact fraction rather than a rounded decimal is usually the point. The same rules cover all of them, which is why one fraction calculator handles the kitchen and the workshop alike.
Common fraction mistakes
The classic error is adding numerators and denominators straight across — writing 1/2 + 1/3 as 2/5. Addition and subtraction always need a common denominator first; only multiplication goes straight across. Another frequent slip is forgetting to flip when dividing: a ÷ b/c means multiply by c/b, not by b/c. And many answers are technically right but left unreduced, like 4/8 instead of 1/2.
Sign handling trips people up too: subtracting a larger fraction from a smaller one gives a negative result, and a minus sign belongs to the whole fraction, not just its top. The calculator applies the common denominator, the flip, the reduction, and the sign rules automatically, so these mistakes disappear — but knowing them helps you sanity-check an answer that looks off.
Related conversions and tools
Fractions sit next to several other everyday calculations. To turn a fraction into a percentage, divide the numerator by the denominator and multiply by 100 — 3/8 is 37.5% — which links directly to a percentage calculator. Going the other way, a repeating decimal like 0.75 is simply 3/4, and a terminating one can always be written over a power of ten and then reduced.
Averaging fractions, scaling ratios, or splitting a quantity are all built on the same arithmetic this tool performs. Once a fraction is expressed as a decimal here, it slots straight into any calculation that expects a plain number, so you can start exact and finish in whatever form the next step needs.
Frequently asked questions
Is the fraction calculator free?
Yes, free with no sign-up and no limits, on any device with a browser.
Does it simplify fractions automatically?
Yes. Every answer is reduced to lowest terms — 6/8 is returned as 3/4 — using the greatest common divisor.
Can I work with mixed numbers like 2 1/2?
Convert to an improper fraction first: 2 1/2 is 5/2 (multiply the whole number by the denominator and add the numerator). The result is shown back as a mixed number where applicable.
Why does dividing by a fraction make the answer bigger?
Dividing by a number less than 1 asks how many small pieces fit into the total. 1/2 ÷ 1/4 = 2 because two quarters fit in a half. The calculator uses the flip-and-multiply rule to get there.
Can it convert fractions to decimals?
Yes — every result includes a decimal equivalent. Note that some fractions (like 1/3) have infinitely repeating decimals, which is exactly why the fractional form is kept exact.
Does it work with negative fractions?
Yes. Enter a minus sign on the numerator and the sign rules are applied correctly through every operation.