document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120827>Question 120827</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When two negative numbers are multiplied the answer is postive.  For example,<BR>\n" );
document.write( "(-a x -b)=ab.  What is the best conceptual explanation for this? The rule says a negative multiplied by a negative is a postive.  What is the best way to explain why this rule is true?\r<BR>\n" );
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document.write( "I am stumped on the explanation. Thanks.<BR>\n" );
document.write( "Kenneth </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88617 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=88617\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Think of yourself standing on the number line at Zero.  You perform multiplications of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ab ALIGN=MIDDLE  ALT=\"a%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" > by taking <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > steps that are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > units long each.  (you need long legs if b is large).\r<BR>\n" );
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document.write( "Now, the signs on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > tell you the direction you are facing when you start and whether you walk forwards or backwards respectively.\r<BR>\n" );
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document.write( "Here's the rule:  if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive, you face to the right, and if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative, you face to the left.  Then, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive you walk forwards, in the direction that you are facing, but if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative, you walk backwards, away from the direction that you are facing.\r<BR>\n" );
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document.write( "Examples:  Multiply 2 times 3.  Face RIGHT and take 2 steps FORWARD, each step being 3 units.  You end up at positive 6.\r<BR>\n" );
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document.write( "Multiply -2 times 3.  Face LEFT and take 2 steps FORWARD, each step being 3 units.  You end up at negative 6.\r<BR>\n" );
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document.write( "Multiply 2 times -3.  Face RIGHT and take 2 steps BACKWARD, each step being 3 units.  You end up at negative 6.\r<BR>\n" );
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document.write( "Multiply -2 times -3.  Face LEFT and take 2 steps BACKWARD, each step being 3 units.  You end up at positive 6.\r<BR>\n" );
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document.write( "Hope that helps.<BR>\n" );
document.write( "John </SPAN>\n" );
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