Mixed Number to Improper Fraction Calculator
Convert a mixed number to an improper fraction, decimal and simplest form.
Results update as you type.
About this calculator
A mixed number combines a whole number with a fraction, like 2 3/4. This calculator converts it to an improper fraction (a single numerator over a denominator), a decimal, and its simplest form, showing each step of the conversion.
The rule is: multiply the whole number by the denominator, add the numerator, and keep the same denominator. For 2 3/4 that is (2 × 4 + 3)/4 = 11/4. Dividing gives the decimal, 11 ÷ 4 = 2.75, and dividing top and bottom by their greatest common divisor gives the simplest form (11/4 is already in lowest terms). A negative whole number carries its sign into the result, so −2 3/4 = −11/4.
Improper fractions are the form you need for multiplying, dividing or comparing mixed numbers, and they are how most fraction arithmetic is carried out before converting the answer back. Denominators built only from 2s and 5s (like 4, 8 or 10) give terminating decimals; others (like 3 or 7) repeat and are shown rounded.
Frequently asked questions
How do you turn a mixed number into an improper fraction?
Multiply the whole number by the denominator, add the numerator, and place the total over the original denominator. 2 3/4 = (2×4 + 3)/4 = 11/4.
How do you convert it back to a decimal?
Divide the improper numerator by the denominator. 11/4 = 11 ÷ 4 = 2.75.
What is a mixed number?
It is a whole number written next to a proper fraction, such as 2 3/4, meaning two wholes plus three quarters.
What does the "simplest form" result show?
The improper fraction reduced by its greatest common divisor. For example 2 2/4 becomes 10/4, which simplifies to 5/2.
Can I enter a negative mixed number?
Yes. Enter a negative whole number and the sign applies to the whole value: −2 3/4 converts to −11/4.
When is the decimal exact instead of rounded?
Denominators made only of 2s and 5s (4, 8, 10, 20…) give terminating decimals. Others such as 3 or 7 repeat forever and are shown rounded.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/mixed-number/curl
curl "https://calculator.free/api/v1/mixed-number/?whole=2&num=3&den=4"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/mixed-number/?" + new URLSearchParams({
"whole": "2",
"num": "3",
"den": "4"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.