Mixed Number Calculator
Convert mixed numbers to improper fractions and back, with simplified results and steps.
Written by Golam Rabbani, Founder & Lead Engineer
How to use this mixed number calculator
- Choose a conversion direction using the toggle at the top: "Mixed to Improper" converts a mixed number like 1 2/3 into an improper fraction; "Improper to Mixed" goes the other way.
- For Mixed to Improper mode, enter the whole number part in the left field and the numerator and denominator of the fractional part in the stacked fields on the right.
- For Improper to Mixed mode, enter the numerator in the top field and the denominator in the bottom field of the fraction display.
- Press Convert to see the result, including the converted form, a decimal equivalent, and a step-by-step breakdown of the arithmetic.
- Use Copy Result to copy the answer to your clipboard, or Reset to clear all fields and start a new conversion.
About this mixed number calculator
A mixed number combines a whole number and a proper fraction — for example, 2 3/4 means two wholes plus three-quarters. An improper fraction expresses the same value with a numerator that is greater than or equal to its denominator, such as 11/4.
Converting a mixed number to an improper fraction uses the formula: multiply the whole number by the denominator, add the numerator, then place the result over the original denominator. For 1 2/3 the calculation is (1 x 3 + 2) / 3 = 5/3. The tool shows every step of this arithmetic so you can verify it at a glance.
Going the other direction, an improper fraction converts to a mixed number by dividing: 7 divided by 3 gives a quotient of 2 with remainder 1, producing the mixed number 2 1/3. The tool also simplifies the result to lowest terms using the Euclidean algorithm before displaying it.
Both conversions also display a decimal equivalent so you can quickly sense-check the magnitude of the result. Negative values are fully supported in both directions.
FAQ
- How do you convert a mixed number to an improper fraction?
- Multiply the whole number by the denominator of the fractional part, then add the numerator. Place that total over the original denominator. For example, 2 3/5 becomes (2 x 5 + 3) / 5 = 13/5. The calculator performs this calculation automatically and shows the working.
- How do you turn an improper fraction into a mixed number?
- Divide the numerator by the denominator using integer division. The quotient is the whole number and the remainder becomes the new numerator over the same denominator. For 11/4, dividing gives 2 remainder 3, so the result is 2 3/4.
- What is an improper fraction?
- An improper fraction is a fraction whose numerator is greater than or equal to its denominator, such as 7/3, 5/5, or 9/2. It represents a value of one or more wholes. Every improper fraction with a non-zero denominator can be rewritten as a mixed number or a whole number.
- Does the calculator simplify the result?
- Yes. After converting, the tool reduces the fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor. For example, inputting 4/6 in Improper to Mixed mode will display the simplified form 2/3 alongside the mixed-number result.
- Can it handle negative mixed numbers?
- Yes. Enter a negative whole number (for example, -1 in the whole field with 2/3 in the fraction fields) to represent -1 2/3. The tool propagates the negative sign correctly through both conversion directions and displays the result with the proper sign.
- Is this tool free and private?
- Completely free — no account, no sign-up, no usage limits. All calculations happen locally in your browser; no numbers are sent to any server.