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ToolBoxGenie

Fraction Calculator

Calculators · Added 15 August 2026

Work with fractions and mixed numbers exactly, not approximately. Every result is reduced to lowest terms and shown as a fraction, a mixed number, a decimal and a percentage — and because the arithmetic uses whole numbers throughout, a third plus a third plus a third is exactly one.

Operation
First fraction

Leave the left box blank for a simple fraction.

Second fraction

Leave the left box blank for a simple fraction.

How to use the fraction calculator

  1. 1Choose the operation: add, subtract, multiply or divide.
  2. 2Enter the first fraction. Leave the left-hand box empty for a simple fraction, or fill it in for a mixed number like 2 ½.
  3. 3Enter the second fraction the same way.
  4. 4Press Calculate.
  5. 5The result appears in lowest terms, with the mixed-number, decimal and percentage forms underneath.

Examples

Adding unlike denominators

Input
1/2 + 1/3
Result
5/6 — or 0.833333 as a decimal

The calculator cross-multiplies to a common denominator of 6, then reduces.

Dividing fractions

Input
1/2 ÷ 1/4
Result
2

Dividing by a quarter is multiplying by four. The answer being larger than either input surprises people, and it is correct.

Mixed numbers

Input
2 1/3 + 1 3/4
Result
49/12, which is 4 1/12

Mixed numbers are converted to improper fractions internally, then converted back for display.

About the fraction calculator

Why denominators have to match for addition

Adding 1/2 and 1/3 by adding the tops and the bottoms gives 2/5, which is wrong — and wrong in an instructive way, since 2/5 is smaller than 1/2 alone. The reason is that a fraction's denominator says what size the pieces are, and you cannot add halves to thirds any more than you can add metres to feet without converting first.

The conversion is to a common denominator: rewrite both fractions with the same denominator, and only then add the numerators. 1/2 becomes 3/6 and 1/3 becomes 2/6, so the sum is 5/6. Any common denominator works; the least common multiple simply keeps the numbers small.

Multiplication needs none of this, which is why it feels easier and is genuinely simpler: multiplying straight across is correct. Two thirds of three quarters is six twelfths, and the reduction to one half happens afterwards. The asymmetry between addition and multiplication here is the single thing most worth internalising about fraction arithmetic.

Where exactness earns its keep

In everyday arithmetic the difference between 1/3 and 0.333 is negligible. In three places it is not, and all three are common.

The first is repeated operations. Rounding error accumulates, and a chain of additions on rounded decimals drifts measurably. Recipes scaled repeatedly, measurements summed across a plan, or fractions added across many terms all suffer from this in a way exact arithmetic does not.

The second is comparison. Is 7/16 larger or smaller than 3/7? As decimals they are 0.4375 and 0.428571…, which requires enough digits to separate them. As fractions the comparison is a single cross-multiplication with no rounding at all. The third is presentation: trades, recipes and music all conventionally use fractions, and converting to decimals and back for the sake of a calculator introduces error and loses the form the reader expects. Working in fractions throughout avoids the round trip entirely.

Frequently asked questions

Why use fractions instead of decimals?
Because many fractions have no exact decimal form. One third is 0.333… forever, so any decimal you use is an approximation and the errors accumulate. This calculator keeps everything as whole-number numerators and denominators, which means 1/3 + 1/3 + 1/3 comes out as exactly 1 — something that fails if you add 0.3333 three times.
How do I enter a mixed number?
Put the whole part in the left-hand box and the fractional part in the two boxes to its right. For 2 ½, enter 2, then 1 over 2. Leave the left box empty for an ordinary fraction. Negative mixed numbers take the minus sign on the whole part.
How does dividing fractions work?
You multiply by the reciprocal — flip the second fraction and multiply. Dividing by 1/4 is the same as multiplying by 4, which is why dividing by a fraction smaller than one makes the answer bigger. The rule is not arbitrary: division is defined as multiplication by the multiplicative inverse, and flipping a fraction is exactly how you find that inverse.
What does simplifying actually do?
It divides the numerator and denominator by their greatest common divisor, giving the same value written with the smallest possible whole numbers. 6/8 and 3/4 are the same quantity; 3/4 is the reduced form. The sign is also normalised onto the numerator, so you see −3/4 rather than 3/−4.

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