document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176320>Question 176320</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 6)  A student says that 3 divided by 0 is 0.  How do you respond? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131409 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=131409\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Division by zero is undefined. In other words, it is NOT allowed. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F0 ALIGN=MIDDLE  ALT=\"x%2F0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT allowed (where x is any number).\r<BR>\n" );
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document.write( "Why is this? First, we know that zero multiplied by ANY number is ALWAYS zero. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2Ax=0 ALIGN=MIDDLE  ALT=\"0%2Ax=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since 0 groups of something is nothing)\r<BR>\n" );
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document.write( "So we can easily say that 0*1=0\r<BR>\n" );
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document.write( "Now let's assume that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F0 ALIGN=MIDDLE  ALT=\"3%2F0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is possible. What would <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F0 ALIGN=MIDDLE  ALT=\"3%2F0\"   DISABLED_style= \"max-width:90%; height:auto;\" > be equal to? Let's say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F0=0 ALIGN=MIDDLE  ALT=\"3%2F0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (hypothetically of course)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F0=0 ALIGN=MIDDLE  ALT=\"3%2F0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the faulty equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=0%2A0 ALIGN=MIDDLE  ALT=\"3=0%2A0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 0 (ie move the zero in the denominator to the right side)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=0 ALIGN=MIDDLE  ALT=\"3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply. \r<BR>\n" );
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document.write( "Since this equation is false, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F0=0 ALIGN=MIDDLE  ALT=\"3%2F0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT true.\r<BR>\n" );
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document.write( "In general, the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F0=x ALIGN=MIDDLE  ALT=\"3%2F0=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > would become <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=0%2Ax ALIGN=MIDDLE  ALT=\"3=0%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > which would inevitably simplify to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=0 ALIGN=MIDDLE  ALT=\"3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is again false).  </SPAN>\n" );
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