Math
Fraction Calculator
Add, subtract, multiply or divide two fractions and get the answer three ways: as a fully simplified fraction, as a mixed number, and as a decimal. Each fraction accepts an optional whole number, so you can work with mixed numbers like 2 1/4 directly — handy for recipes, woodworking measurements, and homework. The calculator finds the common denominator, does the arithmetic in exact whole numbers, then reduces the result using the greatest common divisor, so you never get a rounding error. Best of all, it shows every step, so you can follow the math and learn the method, not just copy the answer. It runs entirely in your browser and guards against dividing by zero.
Enter two fractions
Enter two fractions and an operation
The result is always reduced to lowest terms.
How the fraction calculator works
Every operation works on two fractions written as a numerator over a denominator. A mixed number like 2 1/4 is first converted to an improper fraction (2 × 4 + 1 = 9, so 9/4) before any math happens. The rules are the ones you learned in school:
The four operations
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)For addition and subtraction the calculator puts both fractions over the common denominator b·d, combines the numerators, then reduces. To reduce, it divides the numerator and denominator by their greatest common divisor (GCD), found with the Euclidean algorithm. The same reduced fraction is then expressed as a mixed number and as a decimal.
Notes & assumptions
- A denominator of zero is rejected — division by zero is undefined.
- Dividing by a fraction equal to zero (numerator 0) is also rejected.
- Negative fractions are allowed; put the minus sign on the whole number or the numerator.
- The decimal is rounded for display, but the fraction and mixed number are exact.
Worked example
Take 1/2 + 1/3. The denominators 2 and 3 are different, so the common denominator is 2 × 3 = 6. Rewrite each fraction over 6: 1/2 becomes 3/6 and 1/3 becomes 2/6. Now add the numerators: 3 + 2 = 5, giving 5/6. Since 5 and 6 share no common factor greater than 1, the answer is already in lowest terms: 5/6, which is about 0.833 as a decimal and has no whole-number part. For a multiplication example, 2 1/4 × 1 1/3 first becomes 9/4 × 4/3; multiply straight across to get 36/12, which reduces to 3 — a clean whole number. The step-by-step panel shows each of these stages so you can check your own work or teach the method.
Frequently asked questions
How do I add two fractions with different denominators?
Find a common denominator — multiplying the two denominators together always works — then rewrite each fraction with that denominator, add the numerators, and reduce. For 1/2 + 1/3, the common denominator is 6, the fractions become 3/6 and 2/6, and the sum is 5/6. This calculator does each of those steps for you and shows them, so you can follow along or double-check homework.
How do I divide fractions?
To divide by a fraction, multiply by its reciprocal — flip the second fraction upside down and multiply. So 3/4 ÷ 2/5 becomes 3/4 × 5/2 = 15/8, which is 1 7/8 as a mixed number. The one rule to watch is that you can't divide by zero, so the numerator of the fraction you're dividing by can't be zero. The calculator blocks that case automatically.
How do I turn an improper fraction into a mixed number?
Divide the numerator by the denominator. The whole-number part of that division is the whole number, the remainder becomes the new numerator, and the denominator stays the same. For 9/4, 9 ÷ 4 is 2 with a remainder of 1, so the mixed number is 2 1/4. This tool shows the mixed-number form automatically alongside the simplified fraction.
What does it mean to simplify or reduce a fraction?
Reducing means dividing the numerator and denominator by their greatest common divisor so the fraction is written in the smallest equivalent whole numbers. For example, 6/8 reduces to 3/4 because both share a factor of 2. The value doesn't change — only how it's written. This calculator always returns the fully reduced form so you don't have to simplify by hand.
Can I use mixed numbers and negative fractions?
Yes. Enter the whole-number part in the "Whole" box and the fractional part in the numerator and denominator boxes; 2 1/4 means a whole of 2, numerator 1, denominator 2. For negatives, put the minus sign on the whole number (or the numerator if there's no whole part). The calculator converts everything to a single improper fraction before computing, so signs are handled correctly.
Why can't the denominator be zero?
A fraction means "numerator divided by denominator," and division by zero has no defined value in mathematics — there's no number you could multiply by zero to get a nonzero numerator. So any fraction with a zero denominator is invalid, and dividing by a fraction whose value is zero is likewise undefined. The calculator detects both situations and shows an error instead of a wrong answer.