The Fraction Calculator adds, subtracts, multiplies, and divides two fractions and shows its working: the common denominator chosen, the converted fractions, the operation, and the simplified result, given also as a mixed number when it exceeds one and as a decimal. It is built for homework checking and kitchen-and-workshop arithmetic alike.
How It Works
Addition and subtraction first convert both fractions to a common denominator, the least common multiple of the two denominators, then combine the numerators. Multiplication multiplies straight across, numerator by numerator and denominator by denominator. Division inverts the second fraction and multiplies. Every result is simplified by dividing out the greatest common divisor, and improper fractions are also expressed as mixed numbers. A zero denominator, or dividing by a fraction whose numerator is zero, is rejected with an explanation rather than a silent infinity.
Parameters
| Input | Required | Meaning | |---|---|---| | First numerator and denominator | Yes | The left fraction | | Operator | Yes | Add, subtract, multiply, or divide | | Second numerator and denominator | Yes | The right fraction; denominators cannot be zero |
Worked examples
2/3 + 3/4: the LCM of 3 and 4 is 12, so the fractions convert to 8/12 and 9/12, and the sum is 17/12, which is 1 5/12 or about 1.4167. 5/6 - 1/4: LCM 12 again, giving 10/12 - 3/12 = 7/12. 2/3 x 3/4 = 6/12, simplified to 1/2, the cancellation you can see before multiplying (the 3s cancel) once you know to look. 2/3 divided by 3/4 inverts to 2/3 x 4/3 = 8/9: dividing by a fraction less than one makes the answer larger than the starting fraction, which is correct and the result students most often "fix" into an error.
The steps are the point
Most fraction mistakes are procedural, not conceptual: adding denominators straight across (2/3 + 3/4 is not 5/7), forgetting to scale both numerators when converting, or inverting the first fraction instead of the second in division. Because the calculator prints its steps (the LCD chosen, both conversions, the combination), comparing your working line by line against it locates the exact step where a hand calculation leaves the rails, which is substantially more useful than an answer key. For teaching, cover the result and predict each step before revealing it.
Mixed numbers and decimals
An improper fraction such as 17/12 converts to the mixed number 1 5/12 by dividing: 12 goes into 17 once with 5 left over. The decimal form is a ratio, not an equal citizen: 1/3 is exact, while 0.333 is a rounding, and chaining rounded decimals through several operations accumulates error that fractions never incur. Keep fractions through the working and decimalize only the final answer, the discipline this calculator's dual output encourages. In measurement contexts (recipes, carpentry), the mixed number is usually the most usable of the three forms.
Limitations
Inputs are whole-number numerators and denominators as entered; mixed numbers should be entered as improper fractions (1 1/2 becomes 3/2) and negative values work through the sign of the numerator. Extremely large inputs are bounded by ordinary number precision. The calculator performs the four operations on a pair of fractions; it does not chain expressions or handle algebraic fractions with variables.
Frequently Asked Questions
Why does the calculator use the least common denominator?
Any common denominator works mathematically, but the least one keeps numbers small and often lands already simplified or one step from it. The printed steps show the LCD so your working can follow the same path.
Can I enter a whole number as a fraction?
Yes: write it over 1 (3 becomes 3/1). Whole numbers are fractions whose denominator is one, and all four operations then behave exactly as expected.
What happens if I divide by a fraction with numerator zero?
It is rejected, correctly: a zero numerator makes the second fraction zero, and division by zero is undefined, no matter how it is dressed up.