Fraction Calculator
Add, subtract, multiply, divide fractions with simplified result.
A fraction calculator adds, subtracts, multiplies, and divides fractions and mixed numbers, then reduces the answer to lowest terms.
Enter two fractions and choose an operation. The tool returns the exact result as a simplified fraction, and as a mixed number and decimal where helpful.
Fractions follow a few consistent rules; the tricky parts are finding common denominators and remembering to simplify, both of which the calculator handles automatically.
How this calculator works
To add or subtract, the calculator puts both fractions over a common denominator, combines the numerators, and simplifies. To multiply, it multiplies the numerators together and the denominators together. To divide, it multiplies the first fraction by the reciprocal of the second (flip and multiply). Mixed numbers are first converted to improper fractions. The final answer is reduced by dividing the numerator and denominator by their greatest common divisor (GCD), giving the fraction in lowest terms, and converted to a mixed number when the numerator exceeds the denominator.
What affects the number
- Addition and subtraction require a common denominator; multiplication and division do not.
- Dividing by a fraction is the same as multiplying by its reciprocal.
- Mixed numbers must be converted to improper fractions before most operations.
- Simplifying uses the greatest common divisor of the numerator and denominator.
- A negative sign can attach to the numerator or the whole fraction; keep track of it through the steps.
- Improper fractions and mixed numbers represent the same value in different forms.
Frequently asked questions
How do you add fractions with different denominators?
Find a common denominator (the least common multiple works well), rewrite each fraction with it, add the numerators, and simplify. For example, 1/3 + 1/4 becomes 4/12 + 3/12 = 7/12. The calculator does each step automatically.
How do you divide fractions?
Multiply the first fraction by the reciprocal of the second, meaning you flip the second fraction and multiply. So 1/2 divided by 3/4 becomes 1/2 times 4/3, which equals 4/6, simplified to 2/3.
How do you simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. For 8/12, the GCD is 4, so the fraction reduces to 2/3. A fraction is in lowest terms when the numerator and denominator share no common factor other than 1.
What is the difference between an improper fraction and a mixed number?
An improper fraction has a numerator larger than its denominator, like 7/4. A mixed number writes the same value as a whole number plus a proper fraction, like 1 3/4. They are equal; the calculator can show both.
This calculator provides general estimates for educational purposes only and is not financial, medical, legal, or tax advice. Your actual results depend on your specific situation and current rates.