1. Assignment #4 Brandon Hagrave
Performing Division Mentally Via My Algorithm
Preface
This algorithm was created with the intention of allowing one to perform division of complex
numbers without the use of a calculator, or pen and paper. The procedure itself is derived from the long
division process taught in public schools. Though it may be relatively simple in theory, in practice a
considerable amount of concentration is required to follow this procedure. The Algorithm reiterates
after each digit calculated, and with each new iteration one must mentally perform two separate
mathematical operations; a multiplication and subtraction. From these operations, two new numbers are
computed which need to be temporarily memorized, in order to find the next digit and perform each
consecutive operation. Furthermore, each set of numbers calculated can and often will vary greatly in
complexity, thus the time it takes for each new digit to be found varies greatly.
Procedure Description
Before reading ahead, a certain level of mathematical vocabulary must be established, as this is
crucial to understanding the following steps. The two most important terms are the numerator and the
denominator. These are the two numbers that comprise a division operation, thus each division is
represented as the numerator divided by denominator. Moreover, the product, difference and quotient
refer to the outcome of multiplication, subtraction and division operations respectively.
It is first determined if the denominator fits into the numerator. If it doesn't, the quotient
(outcome) will equal less than one. The numerator is multiplied by 10, and any number calculated is
now written after the decimal. If the opposite is true of the first question, one will proceed as normal.
March 1st
2012

2. Assignment #4 Brandon Hagrave
The number of times that the denominator can fit into the numerator is calculated mentally. This
number is simply recorded in the digit, of the quotient, currently being computed. No fiddling with
decimal places is necessary and the number is simply written down as is.
This number is now multiplied by the denominator to produce a product of equal or less value
than the numerator. This product is then subtracted from the numerator to produce a new number.
A mental comparison is performed to see if the denominator is greater than this number. If this
is the case, the number is multiplied by 10. If the denominator is still greater than this number, it is
further multiplied by 10 once again, and a zero is recorded while one moves on to the next digit of the
quotient. Regardless, if either of the aforementioned conditions are true, or the denominator is less than
the given number, this number becomes the new denominator.
A decimal point is written in if at has not been already, as at-least everything before the decimal
point of the quotient has now been computed. The algorithm now reiterates and the new denominator is
used in the initial comparison with the existing value of denominator.
Each new iteration contributes to a running total of the digits, after the decimal place, of the
quotient. This process can be continued indefinitely, though often times it will stop after only a few
digits; an indication that the number has been fully computed. When this happens, the numerator equals
out to zero, rendering any further calculations impossible.
March 1st
2012

3. Assignment #4 Brandon Hagrave
By using this method, with minimal practice I was able to calculate a new digit every 45
seconds on average. With constant practice, mental discipline, and a more refined process, the speed
and efficiency of this method could be both easily and drastically improved . I believe this could open
up an entire new realm of capabilities that were once alien to the human mind. Similar methods to this
could even one day serve to render the modern calculator obsolete.
March 1st
2012