For explicitly given integers , , , the mixed fraction is usually written without the plus sign, for example
On the other hand, if one wants to convert e.g. into an improper fraction, one needs first to convert the integer part 8 into fifteenths, obtaining
this fraction is added to the ready fifteenths ; the total amount of fifteenths is ; thus one has
Note. A minus sign in front of a mixed fraction belongs not only for the integer part but also for the fractional part, i.e. for example .
Here the degree of the remainder polynomial is less than the degree of the numerator polynomial , an arithmetic fact that has been well documented for over 4,000 years. Fibonacci in the Liber Abaci used mixed fraction arithmetic in 1202 AD. Archimedes Calculus included mixed fractions to record the area of a parabola. Egyptian scribes in 1650 BCE also used this class of mixed fraction arithmetic. One scribe, Ahmes scaled a volume unit in multiples of 64 so that a quotient recorded 1/64 units and a remainder recorded 1/320 units.
|Date of creation||2013-03-22 19:18:57|
|Last modified on||2013-03-22 19:18:57|
|Last modified by||pahio (2872)|