Fraction Calculator
This free fraction calculator adds, subtracts, multiplies, or divides two fractions and simplifies the result to lowest terms automatically. Enter a numerator and denominator for each fraction, pick an operation, and see the answer as a reduced fraction, a mixed number, and a decimal, all updated instantly as you type.
How to Use It
- Enter the numerator and denominator for Fraction A.
- Choose an operation: add, subtract, multiply, or divide.
- Enter the numerator and denominator for Fraction B.
- The simplified result, its mixed number form, and its decimal equivalent appear instantly.
How It Works
Adding or subtracting fractions first requires a common denominator. Rather than finding the least common multiple, this tool cross multiplies: for a/b and c/d, it computes (a×d + c×b) over (b×d) for addition, or (a×d − c×b) over (b×d) for subtraction. This always produces a valid common denominator, even if it isn't the smallest possible one, and the simplification step afterward reduces it to lowest terms regardless.
Formulas
a/b + c/d = (a×d + c×b) ÷ (b×d)
a/b − c/d = (a×d − c×b) ÷ (b×d)
a/b × c/d = (a×c) ÷ (b×d)
a/b ÷ c/d = (a×d) ÷ (b×c)
Multiplying fractions is more direct: multiply the two numerators together and the two denominators together, no common denominator needed. Dividing works the same way after flipping the second fraction (multiplying by its reciprocal), since dividing by a number and multiplying by its reciprocal always give the same answer.
Every result is reduced using the greatest common divisor (GCD) of its numerator and denominator, found with the Euclidean algorithm. A worked example: 1/2 + 1/3 cross multiplies to (1×3 + 1×2) over (2×3), which is 5/6. That's already in lowest terms (its GCD is 1), so 5/6 is both the final fraction and, as a decimal, 0.8333.
When a result is improper (its numerator is larger than its denominator), it's also shown as a mixed number. 7/4, for instance, divides out to 1 remainder 3, so it displays as 1 3/4 alongside the plain fraction and decimal forms.
Frequently Asked Questions
How do you add or subtract fractions with different denominators?
Cross multiply so both fractions share a common denominator, then add or subtract the numerators. For 1/2 + 1/3, that's (1 times 3) plus (1 times 2) over (2 times 3), giving 3/6 + 2/6, which is 5/6. This tool does that cross multiplication for you automatically, whatever denominators you enter.
How does a fraction get simplified to lowest terms?
By dividing both the numerator and denominator by their greatest common divisor (GCD), the largest whole number that divides evenly into both. 4/8's GCD is 4, so dividing both by 4 gives 1/2, the same value in its simplest form. Every result on this page is automatically reduced this way.
What is a mixed number, and how does an improper fraction become one?
A mixed number is a whole number plus a proper fraction, like 1 3/4, instead of an improper fraction like 7/4 where the numerator is larger than the denominator. To convert, divide the numerator by the denominator: the whole number part is how many times the denominator divides in, and the remainder becomes the new numerator over the same denominator. 7 divided by 4 is 1 remainder 3, so 7/4 becomes 1 3/4.
Why does dividing fractions mean multiplying by the reciprocal?
Dividing by a number is the same as multiplying by its reciprocal (flip the numerator and denominator) for any number, fractions included. So 1/2 divided by 1/4 becomes 1/2 times 4/1, which is 4/2, simplified to 2. It works out to the same answer as long division, just easier to compute by hand.
Can I enter negative fractions?
Yes. Put the negative sign on the numerator (for example, -1 for the numerator and 2 for the denominator to represent -1/2). A negative denominator works too and is treated the same as a negative numerator, since -1/2 and 1/-2 are the same value.
What happens if I enter a denominator of 0?
You'll see a clear error instead of an incorrect result. Division by zero is undefined in ordinary arithmetic, so a fraction can never have a denominator of 0. The same error appears if you try to divide by a fraction whose numerator is 0, since that would also require dividing by zero.
How do I read the decimal equivalent?
It is the fraction expressed as a regular decimal number, rounded to 4 decimal places with any trailing zeros trimmed. For example, 5/6 shows as 0.8333, and 1/2 shows as simply 0.5 rather than 0.5000.
Can I enter a mixed number directly?
Not as a separate whole-number field, since a negative mixed number's sign can be ambiguous depending on where it's placed. Instead, convert it to an improper fraction first: multiply the whole number by the denominator and add the numerator. For 1 3/4, that's (1 times 4) plus 3, giving 7/4. The result section then converts any improper result back to a mixed number for you.