Fraction Calculator
Add, subtract, multiply, or divide two fractions. Get the answer in lowest terms, as a decimal, and as a mixed number.
How to use this calculator
Enter the numerator and denominator of each fraction, choose an operation (+ − × ÷), and the calculator shows the simplified result, the decimal equivalent, and the mixed-number form whenever the answer is greater than one. Negative values are supported — just enter a negative numerator.
How fraction arithmetic works
A fraction represents a part of a whole. The number on top is the numerator (how many parts you have) and the number on the bottom is the denominator (how many equal parts the whole is divided into). The four operations each follow a distinct rule.
- Addition and subtraction require a common denominator. You rewrite both fractions so they share the same denominator, then add or subtract only the numerators. The denominator stays the same.
- Multiplication is the most straightforward: multiply the numerators together and the denominators together. No common denominator needed.
- Division is multiplication by the reciprocal. Flip the second fraction (swap numerator and denominator) and then multiply.
After computing, always check whether the result simplifies. Divide the numerator and denominator by their greatest common divisor to get the fraction in lowest terms.
Worked examples
Addition: 1/2 + 1/3
- The least common denominator of 2 and 3 is 6.
- Rewrite: 1/2 = 3/6 and 1/3 = 2/6.
- Add the numerators: 3 + 2 = 5. Result: 5/6 (≈ 0.8333).
- 5 and 6 share no common factor other than 1, so 5/6 is already in lowest terms.
Subtraction: 3/4 − 1/6
- The least common denominator of 4 and 6 is 12.
- Rewrite: 3/4 = 9/12 and 1/6 = 2/12.
- Subtract: 9 − 2 = 7. Result: 7/12 (≈ 0.5833).
Multiplication: 2/3 × 3/5
- Multiply numerators: 2 × 3 = 6.
- Multiply denominators: 3 × 5 = 15.
- Result before simplifying: 6/15. GCD(6, 15) = 3, so 6/15 = 2/5 (= 0.4).
Division: 5/6 ÷ 2/3
- Flip the second fraction: 2/3 becomes 3/2.
- Multiply: 5/6 × 3/2 = 15/12.
- GCD(15, 12) = 3, so 15/12 = 5/4 = 1 1/4 (= 1.25).
Common mistakes to avoid
- Adding denominators directly. A very common error is computing 1/2 + 1/3 = 2/5. This is wrong — denominators never add together. Only numerators add once both fractions share a common denominator.
- Forgetting to simplify. Leaving an answer as 6/8 instead of 3/4 is technically correct but unconventional. Always divide by the GCD for the clearest form.
- Dividing instead of multiplying the reciprocal. When dividing fractions, students sometimes flip the wrong fraction. Remember: keep the first fraction as-is, flip the second, then multiply.
- Mixing up proper and improper fractions. A proper fraction has a numerator smaller than its denominator (like 3/4). An improper fraction has a numerator equal to or greater than its denominator (like 7/4). Both are valid; the mixed-number form (1 3/4) is simply a different way to write an improper fraction.
The formulas
a/b + c/d = (ad + bc) ÷ bd · a/b − c/d = (ad − bc) ÷ bd
a/b × c/d = ac ÷ bd · a/b ÷ c/d = ad ÷ bc
Simplify: divide numerator and denominator by GCD(numerator, denominator)
How we calculate this
Frequently asked questions
How do you add or subtract fractions?
Give both fractions a common denominator, then add or subtract the numerators. For 1/2 + 1/3, use sixths: 3/6 + 2/6 = 5/6. This calculator finds the common denominator and simplifies for you.
How do you multiply and divide fractions?
To multiply, multiply the numerators together and the denominators together: 1/2 × 1/3 = 1/6. To divide, flip the second fraction and multiply: 1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2.
How is the result simplified?
The calculator divides the numerator and denominator by their greatest common divisor (GCD), reducing the fraction to lowest terms — for example 4/8 becomes 1/2 because GCD(4, 8) = 4.
What is a mixed number?
A mixed number combines a whole number and a proper fraction, like 1 1/2 instead of 3/2. The calculator shows the mixed-number form when the result is an improper fraction (numerator greater than denominator).
What is the least common denominator (LCD)?
The LCD is the smallest number that both denominators divide into evenly. For 1/4 and 1/6, the LCD is 12. You can always multiply the two denominators to get a common denominator, though it may not be the least one.
Can I enter negative fractions?
Yes. Enter a negative numerator (for example, −3/4) and the calculator handles the sign correctly through all four operations.
Why does dividing by a fraction make the result larger?
Dividing by a fraction is the same as multiplying by its reciprocal. For example, 4 ÷ 1/2 = 4 × 2 = 8. You are asking how many halves fit in 4, and the answer is 8.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. For 3/4, compute 3 ÷ 4 = 0.75. The calculator shows the decimal equivalent of the result automatically.