Enter each fraction as a numerator and a denominator. A negative sign belongs on the numerator if you type it that way; a negative denominator is folded into the sign before the arithmetic starts.
How to use
- Enter the first numerator and denominator.
- Choose add, subtract, multiply or divide, then enter the second fraction.
- Press Calculate. A zero denominator, or dividing by a zero numerator, stops with an error.
Formula / how it works
Addition and a common denominator. To add 1/2 and 1/3 the denominators 2 and 3 must match. The calculator uses their product, 6, which is a common multiple: 1/2 = 3/6 and 1/3 = 2/6, so the sum is 5/6. It then divides the numerator and the denominator by their greatest common divisor, which for 5 and 6 is 1, so 5/6 is already in lowest terms. Subtraction is the same path with a minus between the adjusted numerators. The sign of the result follows the arithmetic. A negative denominator on the way in is flipped by negating the numerator, so 1/−2 is stored as −1/2 before any operation.
Multiplication. Numerators multiply and denominators multiply, then the fraction is reduced. There is no need for a common denominator. 1/2 × 2/3 becomes 2/6 and reduces to 1/3. Cancellation is the reduction step at the end, not a separate “cross-cancel” display, so the printed problem shows the reduced inputs and the reduced result rather than every intermediate.
Division by the reciprocal. Dividing by a fraction is multiplying by its reciprocal. 3/4 ÷ 1/2 becomes 3/4 × 2/1 = 6/4, which reduces to 3/2. The mixed form of 3/2 is 1 1/2, and the decimal is 1.5. Division by zero is refused both when the second denominator is zero and when the second numerator is zero, because a zero fraction has no reciprocal.
How the three writings relate. The improper fraction keeps a single numerator that may be larger than the denominator. The mixed number pulls out the whole part: the integer is the quotient, and the leftover is the remainder over the denominator. If the remainder is zero, only the integer is shown. The decimal is the numerator divided by the denominator, rounded to six places and trimmed. Repeating decimals such as 5/6 are therefore 0.833333, not a bar over the 3. Use the fraction when you need an exact value and the decimal when you are comparing with a measurement.
Integers and signs. A whole number is a fraction with denominator 1. You can type 4 and 1 to mean 4. The result of an integer stays an integer in the improper line. Opposite signs produce a negative result, printed with a minus. The ratio calculator is the better page when the problem says “3 for every 2” and you are not adding parts of a whole. The percentage calculator is the better page when the question is already “what percent”.
Limits. Numerators and denominators must be whole numbers up to one billion in absolute value. The product of two denominators is still well inside the range JavaScript handles as an exact integer for inputs of that size only up to a point: two denominators near a billion can make a product past the safe integer range. If you are working with enormous textbook numbers, reduce each fraction yourself first. Everyday school and kitchen fractions are far below that line.
What the problem line shows. Inputs are reduced before they are printed, so 2/4 is shown as 1/2 in the problem statement. The operation name is repeated on the last line so a copied result still says whether it was an add or a divide.
Worked examples
Adding halves and thirds
Inputs: First numerator: 1 | First denominator: 2 | Operation: add | Second numerator: 1 | Second denominator: 3
Enter numerator 1 and denominator 2, choose add, then numerator 1 and denominator 3. The common denominator is 6.
Result: Problem: 1/2 + 1/3
Result: 5/6 (mixed 5/6, decimal 0.833333)
Operation: add
3/6 + 2/6 = 5/6, and the decimal is 0.833333.
Dividing by a half
Inputs: First numerator: 3 | First denominator: 4 | Operation: divide | Second numerator: 1 | Second denominator: 2
Enter numerator 3 and denominator 4, choose divide, then numerator 1 and denominator 2. Division multiplies by the reciprocal 2/1.
Result: Problem: 3/4 ÷ 1/2
Result: 3/2 (mixed 1 1/2, decimal 1.5)
Operation: divide
The mixed form is 1 1/2.
Use cases
- School arithmetic that must stay in fractions until the last step.
- Rescaling a recipe written as halves and thirds.
- Checking a mixed number against the improper form before you copy it.
- Seeing the decimal of a fraction without a separate division.
Tips & limitations
- Read the mixed form when the improper numerator is larger than the denominator.
- A repeating decimal is rounded to six places. Trust the fraction for the exact value.
- Put the negative sign on the numerator if you have a choice. A negative denominator is normalised anyway.
- Switch to the ratio page for “for every” problems that are not sums.
FAQ
Why is 1/2 + 1/3 not 2/5?
You cannot add the tops and the bottoms. The denominators have to be the same first. 1/2 is 3/6 and 1/3 is 2/6, so the sum is 5/6.
What is a mixed number here?
The whole part plus the leftover fraction. 3/2 is 1 1/2. If nothing is left over, only the whole number is shown.
How does division work?
The second fraction is flipped and the fractions are multiplied. Dividing by 1/2 doubles the first fraction.
Can a denominator be zero?
No. The page stops, because a fraction with a zero denominator is undefined, and a zero fraction cannot be a divisor.
Are the inputs reduced before the sum?
They are reduced for display and stored in lowest terms. The arithmetic is the same either way.
Do the fractions leave the browser?
No. The reduction and the four operations run locally.
Results are calculated from the values you enter. Double-check measurements and allow a margin before buying materials or making decisions.