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ARITHMETIC OPERATIONS became the denotation of a multiple of 60.Another possible explanation comes from the coinage system.One talent and 10 mana may have been written,where the meant I talent,which is 60 mana.We do the same when we write $1.20 and mean 100 cents by the 1.The scheme for writing amounts of money may then have been taken over to arithmetic generally. 4.Arithmetic Operations In the Babylonian system the symbols for I and 10 were basic.Numbers from 1 to 59 were formed by combining fewer or more of these symbols.Hence the processes of addition and subtraction were merely a matter of adding or taking away symbols.To indicate addition the Babylonians joined numbers together as in,which indicates 16.Subtraction was often indicated by the symbol is 40-3.In astronomical texts of a later period the word appears,signifying addition. Multiplication of integers was also performed.To multiply by 37,say, would mean multiplying by 30,then by 7,and adding the results.The symbol for multiplication was ,pronounced a-rd.It meant“togo.” The Babylonians divided one whole number by another.Since to divide by an integer a is to multiply by the reciprocal 1/a,to this extent fractions were involved.The Babylonians converted the reciprocals to sexagesimal "decimals"and,except for the few mentioned above,did not use special symbols for fractions.They had tables showing how numbers of the form I/a, where a=235.could be written as terminating sexagesimal numbers. Some tables gave approximate values for 1/7,1/11,1/13,etc.,because these fractions led to infinite repeating sexagesimals.Where fractions involving denominators other than 2,3,or 5 occurred in the older problems,the same troublesome factors occurred in the numerator and were cancelled. The Babylonians relied entirely upon the tables of reciprocals.Their tables show,for example, igi2 gdl-bi 30 igi 8 gal-bi 7,30 igi 3 gdl-bi 20 igi 9 gal-bi 6,40 igi4 gal-bi15 igi 6 gal-bi 10 igi27l-bi2,13,20 obviously meaning 1/2 =30/60,1/3 =20/60,etc.The precise meanings of igi and gal-bi are not known.Sexagesimal fractions,that is,numbers less than 1,expressed in inverse powersf,60,etc.but with denominators merely understood,continued to be used by the Greeks Hipparchus and Ptolemy and in Renaissance Europe up to the sixteenth century,when they were replaced by decimals in base 10
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