Quick answerA mixed fraction calculator performs exact addition, subtraction, multiplication, and division with whole numbers, numerators, and denominators. It simplifies the result and can show improper-fraction and decimal forms.
Working with mixed numbers
A mixed number combines a whole number and a proper fraction, such as 2 3/4. Before arithmetic, it is converted to an improper fraction: multiply the whole number by the denominator, add the numerator, and keep the same denominator. For 2 3/4, that gives 11/4.
After the operation, the result is reduced by dividing numerator and denominator by their greatest common divisor. An improper answer can then be converted back to a mixed number by division, with the remainder becoming the new numerator.
Adding, multiplying, and dividing fractions
Addition and subtraction require a common denominator. Multiplication combines numerators and denominators directly, followed by simplification. Division multiplies the first fraction by the reciprocal of the second, provided the second value is not zero.
Keeping the calculation as whole-number ratios avoids the small binary rounding errors that can appear when fractions are converted to decimals too soon. Decimal form is helpful for interpretation, but the simplified fraction remains the exact result.
How to use this mixed fraction calculator
- Enter a whole number, numerator, and nonzero denominator for each value.
- Choose an arithmetic operation.
- The result is reduced exactly using integer arithmetic before a decimal is shown.
Formula and method
Inputs are whole integers. A leading negative whole number makes the fractional part negative as part of the same mixed number.
Mixed fraction example
Add 1 1/2 and 2 2/3. The improper fractions are 3/2 and 8/3. Using a common denominator of 6 gives 9/6 + 16/6 = 25/6.
Dividing 25 by 6 gives 4 with remainder 1, so the simplified mixed-number answer is 4 1/6. Its decimal approximation is 4.1666 repeating.
How to enter a whole number or a negative fraction
For a simple fraction such as 3/4, set the whole-number field to 0, numerator to 3 and denominator to 4. For the whole number 5, enter whole 5, numerator 0 and denominator 1. For −2 1/3, enter whole −2, numerator 1 and denominator 3: the leading minus sign applies to the entire mixed number.
A negative fraction without a whole part, such as −1/2, uses whole 0 and numerator −1. Keep the denominator positive. The exact result comes from integer fraction arithmetic; a repeating decimal is a display approximation.
| Operation | Calculation | Reduced answer |
|---|---|---|
| Add | 1/2 + 3/4 | 5/4 = 1 1/4 |
| Subtract | 2 1/3 − 1 5/6 | 1/2 |
| Multiply | 1 1/2 × 2/3 | 1 |
| Divide | 3/4 ÷ 1/2 | 3/2 = 1 1/2 |
To check subtraction, convert the inputs to 7/3 and 11/6. A common denominator gives 14/6 − 11/6 = 3/6, which reduces to 1/2. Dividing by a zero-valued fraction is undefined even if its denominator is valid.
Use the scientific calculator for decimal expressions with functions, or the average calculator when you need the mean of a number list.
Common mistakes to avoid
- Adding denominators along with numerators.
- Forgetting to convert the whole-number part of a mixed number.
- Dividing fractions without flipping the second fraction.
- Using a zero denominator, which never defines a valid fraction.
Accuracy and practical limits
Fraction operations use integer arithmetic and simplify exact ratios, so repeating decimals do not reduce the accuracy of the fraction answer. Decimal display is rounded, and extremely large inputs may be less practical to read even when the ratio remains exact.
Method basis: Standard mathematical definitions and the assumptions stated above. See our editorial and testing standards.
Frequently asked questions
Can a denominator be zero?
No. Division by zero is undefined and is rejected.
How is the fraction simplified?
The numerator and denominator are divided by their greatest common divisor.
Is the displayed fraction exact?
Yes. Fraction operations use arbitrary-size integers; only the decimal display is approximate.