A mixed fraction is an improper fraction 
written in the form 
. In common usage such as cooking recipes, 
is often written as 
(e.g., 1 
),
much to the chagrin of mathematicians, to whom 
means 
,
which is quite a different beast from 
.
(The author of this work discovered this fact early in his mathematical career after having points marked off a calculus exam for using the recipe-like notation. Future mathematicians are therefore encouraged to avoid mixed fractions, except perhaps in the kitchen.)
