The Egyptians used a base ten system but they did not use decimals. They did use fractions, but only unit fractions. This means that translating fractions is not as easy as translating whole numbers. Egyptian fractions are expressed as an Egyptian numeral under an oval. To express nonunit fractions they would add several unit fractions. However certain rules apply to expressing Egyptian fractions. No unit fraction can be used twice to represent a single nonunit fraction, also no representation can go beyond four unit fractions in length. An example of an Egyptian fraction is,

1
- =
3

To translate Hindu Arabic fractions into Egyptian notation, you find the highest unit fraction that can be subtracted from the fraction you have, you subtract this fraction from the original fraction. You then analyze the difference from the last step, if it is a unit fraction that you are done and the fraction you subtracted plus this fraction is your answer. If the result is not a unit fraction than you repeat the proccess by finding and subtracting the highest unit fraction. If you have four unit fractions but haven't fully broken down the Hindu Arabic fraction, you just stop and take those four as your answer. This procedure can be summarized by this list of steps,
1 find the highest unit fraction that can be subtracted from the fraction you have
2 is the fraction a unit fraction? if yes you have the answer, if no than go to step one
3 if you get to four unit fractions stop. Remember the Egyptian attitude of "close enough"
An example of this proccess is converting 9/10 into Egyptian fractions.
1. 9/10-1/2=4/10
2. 4/10-1/3=1/15
3. 1/2+1/3+1/15=9/10
Finally you convert your answer into Egyptian fractions,

The G rule

There is another method which can be effective for breaking up nonunit fractions. The G rule states that "1/2x=1/3x+1/6x" This can be used effectivly with even fractions to help break them up. For example take 2/6,
1/2*2/6=1/3*2/6+1/6*2/6
2/12=2/18+2/36
1/6=1/9+1/18
1/6+1/9+1/18=2/6
You would then convert the answer into Egyptian fractions.

Neugebauer Notation

The Egyptian notation system can be quite cumbersome for some numbers, especialy with writing fractions, for these instances Neugebaur Notation is usefull. This system simply expresses Egyptian fractions as Hindu Arabic numerals under a bar. For example,
=
15

Concept Reveiw

     Translate into Egyptian numerals:
1/2
4/5
3/7
9/12
4/6
     Translate into Neugebauer Notation:
1/356
5/425
7/49
3/7
2/30
     Translate into Hindu Arabic:





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