Mixed number and fraction calculator

A mixed number such as $2\frac{5}{8}$ is a whole number plus a fraction, for example two whole pizzas and five eighths of a third one. The same amount can be written as a single fraction: two pizzas are sixteen eighths, and with those five it is $\frac{21}{8}$.

Mixed number to fraction

Multiply the whole-number part by the denominator and add the numerator. The denominator stays the same.

Fraction to mixed number

Divide the numerator by the denominator with a remainder. The whole number you get is the whole-number part, and the remainder is the new numerator.

How it works

In general,

$$w\frac{p}{q}=\frac{w\cdot q+p}{q}$$

Here w is the whole-number part, p the numerator and q the denominator of the fraction part.

We convert the mixed number $2\frac{5}{8}$ to a fraction by cutting the two wholes into eighths. That is 2 · 8 = 16 eighths, and we add the five:

$$2\frac{5}{8}=\frac{2\cdot 8+5}{8}=\frac{21}{8}$$

The other way round works by division with remainder. Eight goes into 21 twice, with five left over:

$$21÷8=2,\text{remainder}5\Rightarrow \frac{21}{8}=2\frac{5}{8}$$

For negative numbers the minus sign belongs to the whole mixed number: $-2\frac{5}{8}=-(2+\frac{5}{8})=-\frac{21}{8}$. You can find more about working with fractions in the article on fractions.