Mixed Number to Fraction Calculator — convert to an improper fraction

How it works

A mixed number is a whole number written next to a proper fraction, like 2 1/2, meaning "2 plus 1/2". An improper fraction writes the same value as a single fraction whose numerator is at least as large as its denominator, like 5/2. Converting from mixed to improper takes three steps:

1. Multiply the whole number by the denominator: 2 × 2 = 4.
2. Add the numerator: 4 + 1 = 5. This is the new numerator.
3. Keep the same denominator: 2.

So 2 1/2 = 5/2. Per Wolfram MathWorld, a mixed number w n/d is exactly the improper fraction (w·d + n)/d. The calculator also reduces the result to lowest terms — so 2 2/4 gives 5/2, not 10/4 — and shows the decimal value.

For a negative mixed number, the whole number carries the sign: −2 1/2 means −(2 + 1/2), which is −5/2.

Worked example

Take 2 1/2. Multiply the whole number by the denominator: 2 × 2 = 4. Add the numerator: 4 + 1 = 5. Keep the denominator of 2, giving the improper fraction 5/2, whose decimal value is 2.5.

Frequently asked questions

How do you convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, add the numerator, and keep the same denominator. For 2 1/2, that is (2 × 2 + 1) / 2 = 5/2.

What is 2 1/2 as an improper fraction?

2 1/2 is 5/2. Multiplying the whole number (2) by the denominator (2) gives 4, adding the numerator (1) gives 5, over the denominator 2.

What is the difference between a mixed number and an improper fraction?

They represent the same value. A mixed number (2 1/2) shows a whole part and a fraction separately; an improper fraction (5/2) combines them into a single numerator over denominator.

Does the calculator reduce the result?

Yes. If the improper fraction can be simplified, it is reduced to lowest terms — for example 2 2/4 gives 5/2 rather than 10/4.

How do I convert a negative mixed number?

The whole number carries the sign, so −2 1/2 becomes −5/2. In other words, take the improper fraction of 2 1/2 and apply the negative sign.

How do I go the other way, from improper to mixed?

Divide the numerator by the denominator: the quotient is the whole number and the remainder over the denominator is the fraction. For 5/2, 5 ÷ 2 is 2 remainder 1, giving 2 1/2.