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A "mixed fraction", is a number where there is a whole number part, and a fraction part.
Mixed fractions can also be called mixed numbers.
An example of such a number is _{2}\bf{\frac{1}{4}} ,  this is a mixed fraction.
The whole number part is 2, and the fraction part is \bf{\frac{1}{4}}.
In words, this number is two and one quarter.
An "improper fraction", is a fraction in standard form that has a value greater than 1.
Fractions such as \bf{\frac{5}{4}} and \bf{\frac{9}{2}} are examples of improper
fractions.
A mixed fraction/number, is really another way of writing an improper fraction.
With an improper fraction being a fraction with a total value of 1 or greater.
As such, one can convert between the 2 forms when required.
This mixed fraction can converted to improper fraction form with the approach outlined below.
With a negative mixed fraction, the easiest way is to do the conversion sum as usual, but keep a negative sign to the side until the finish.
Or there is another method which is to alter the conversion sum slightly.
The whole number will again multiply the denominator to make the top line of the new fraction, but
the numerator is subtracted instead.
Going the other way with mixed and improper fractions, an improper fraction can also be written as a
mixed number.
The process is slightly different, but just as effective.
For example, to write the improper fraction \bf{\frac{17}{5}} as a mixed number.
We start by dividing 17 by 5.
The  WHOLE NUMBER part of the new mixed number will be 3.
The  FRACTION part will have the remainder 2 as the top line
numerator,
above the original fraction denominator, 5.
Thus \bf{\frac{17}{5}}  can be written as
the mixed number _{3}\bf{\frac{2}{5}}.
With a negative improper fraction, the first step is just to carry out the division as normal.
The WHOLE NUMBER part of the mixed number will be -4.
The FRACTION part will have the positive remainder as the top line numerator, above the original
fraction denominator.
Thus -\bf{\frac{9}{2}} can
be written as the mixed number -_{4}\bf{\frac{1}{2}}.