document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=683768>Question 683768</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The operation * is defined on the set of real numbers by a*b=a+b+ab/2. Is the operation associative </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #466385 by </B><A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><B>tommyt3rd(5050)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=tommyt3rd><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=466385\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we check that (a*b)*c = a*(b*c)\r<BR>\n" );
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document.write( "(a*b)*c = (a+b+ab/2)*c = \r<BR>\n" );
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document.write( "a+b+ab/2 +c + ((a+b+ab/2)c)/2=\r<BR>\n" );
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document.write( "a*(b*c) = a*(b+c+bc/2) =\r<BR>\n" );
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document.write( "a+(b+c+bc/2)+(a((b+c+bc/2))/2\r<BR>\n" );
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document.write( "comparing...\r<BR>\n" );
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document.write( "(a+b+ab/2 +c + ((a+b+ab/2)c)/2) - <BR>\n" );
document.write( "(a+(b+c+bc/2)+(a((b+c+bc/2))/2)\r<BR>\n" );
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document.write( "which is 0\r<BR>\n" );
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document.write( "the operation is associative\r<BR>\n" );
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document.write( ":) </SPAN>\n" );
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