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43-{-9+2}2exponent+18dividedinto6{-2}\r\n" );
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document.write( "Is this what you mean?\r\n" );
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document.write( " 6(-2) \r\n" );
document.write( "43 - (-9 + 2)2 + -----\r\n" );
document.write( " 18\r\n" );
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document.write( "The rules are remembered by the \"word\" \"PEMDAS\" which is to be\r\n" );
document.write( "thought of as four rules \"PE[MD][AS]\". The \"P\" is for \"parentheses\".\r\n" );
document.write( "The \"E\" is for \"Exponentials\". The \"M\" is for \"Multiplications\". \r\n" );
document.write( "The \"D\" is for \"Divisions\". The \"A\" is for \"Additions\". The \"S\" is\r\n" );
document.write( "for \"Subtractions\"\r\n" );
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document.write( "P---1. Go through left to right looking for the lowest level of parentheses\r\n" );
document.write( " with operations to do inside. Do the first one you come to and replace\r\n" );
document.write( " the parentheses with what you get. Keep repeating this step until no\r\n" );
document.write( " parentheses are left with operations to do inside.\r\n" );
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document.write( "E---2. Go through left to right looking for exponentials. Do the first one you\r\n" );
document.write( " come to and replace the exponential with what you get. Keep repeating\r\n" );
document.write( " this step until no exponentials are left. \r\n" );
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document.write( "MD--3. Go through left to right looking for both multiplications and divisions.\r\n" );
document.write( " Do the first multiplication or division you come to and replace the\r\n" );
document.write( " multiplication or division with the result you get. Keep repeating\r\n" );
document.write( " this step until no multiplications or divisions are left. \r\n" );
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document.write( "AS--4. Go through left to right looking for both additions and subtractions.\r\n" );
document.write( " Do the first addition or subtraction you come to and replace the\r\n" );
document.write( " additiontion or subtraction with the result you get. Keep repeating\r\n" );
document.write( " this step until no additions or subtractions are left. You should end up\r\n" );
document.write( " with only a number. \r\n" );
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document.write( "If what you mean is\r\n" );
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document.write( " 6(-2) \r\n" );
document.write( "43 - (-9 + 2)2 + -----\r\n" );
document.write( " 18\r\n" );
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document.write( "then go through looking for parentheses first to see if anything can be done\r\n" );
document.write( "there.\r\n" );
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document.write( "The first parenthetical expression we see is (-9+2), so we combine -9 and 2\r\n" );
document.write( "to get -7, so we replace (-9+2) by (-7)\r\n" );
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document.write( " 6(-2) \r\n" );
document.write( "43 - (-7)2 + -----\r\n" );
document.write( " 18\r\n" );
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document.write( "There are no more parenthetical expressions with anything to be done inside\r\n" );
document.write( "them.\r\n" );
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document.write( "Next we go through looking for exponentials. The only exponential we see is\r\n" );
document.write( "(-7)2 which gives +49, so we replace (-7)2 by 49\r\n" );
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document.write( " 6(-2) \r\n" );
document.write( "43 - 49 + -----\r\n" );
document.write( " 18 \r\n" );
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document.write( "There are no more parentheses with operations inside, nor any more \r\n" );
document.write( "exponentials.\r\n" );
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document.write( "So next we go through looking for multiplications or divisions, and we do the\r\n" );
document.write( "first one we come to going left to right:\r\n" );
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document.write( "The first one of these we come to is the multiplication 6(-2), which gives -12,\r\n" );
document.write( "so we replace 6(-2) by -12\r\n" );
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document.write( " -12 \r\n" );
document.write( "43 - 49 + -----\r\n" );
document.write( " 18 \r\n" );
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document.write( "Next we go through again looking for multiplications or divisions, and we do\r\n" );
document.write( "the first one we come to going left to right:\r\n" );
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document.write( "The first one of these we come to is the division -12/18 which reduces to -2/3,\r\n" );
document.write( "so we replace the -12/18 by (-2/3)\r\n" );
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document.write( "43 - 49 + (-2/3)\r\n" );
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document.write( "Finally we do additions and subtractions left to right as we come to them:\r\n" );
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document.write( "Now we do 43 - 49 and replace that by -6\r\n" );
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document.write( "-6 + (-2/3)\r\n" );
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document.write( "To add two negative numbers we add their absolute values 6 and 2/3, getting\r\n" );
document.write( "6 2/3 or 20/3, and annex the negative sign, getting -20/3\r\n" );
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document.write( "This is the final answer: -20/3 \r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com \n" );
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