Mixed number calculator

What is a mixed number calculator?

A mixed number calculator turns an improper fraction, where the numerator is larger than the denominator, into a mixed number made up of a whole number and a proper fraction. For example, the improper fraction 7/3 becomes the mixed number 2 1/3. This is the way fractions are most often written in everyday measurements, recipes, and construction, because a mixed number is easier to picture than a top-heavy fraction.

Formula

Given a numerator $n$ and a denominator $d$ (with $d \neq 0$), the whole part and remainder are:

The mixed number is then written as:

How to use

1. Enter the numerator (the top number of the fraction).
2. Enter the denominator (the bottom number; it must not be zero).
3. Read off the whole number and the remainder. Together with the original denominator they form the mixed number whole remainder/denominator.

The results stay blank until both fields are filled in and the denominator is not zero.

Worked example

Convert 7/3 to a mixed number.

• Whole part: $\left\lfloor 7 / 3 \right\rfloor = \lfloor 2.333\ldots \rfloor = 2$
• Remainder: $7 - 2 \cdot 3 = 7 - 6 = 1$

So 7/3 equals the mixed number 2 1/3.

FAQ

What happens if the numerator is smaller than the denominator? The whole part is 0 and the remainder equals the numerator. For instance 2/5 gives a whole part of 0 and a remainder of 2, which is just the proper fraction 2/5 itself.

Why must the denominator not be zero? Division by zero is undefined, so a fraction with a zero denominator has no value. The calculator leaves the results empty whenever the denominator is zero or blank.