document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164345>Question 1164345</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following list of numbers is closed under division? A. Rational Numbers B. Whole Numbers C. Perfect Squares D. Irrational Numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788713 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=788713\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Take any two rational numbers and divide one by the other.  Do you always get another rational number?\r<BR>\n" );
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document.write( "Hint:  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\"> be integers.  Then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{a}{b}\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{c}{d}\"> are rational numbers by definition.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{a}{b}\,\div\,\frac{c}{d}\ =\ \frac{a}{b}\,\cdot\,\frac{d}{c}\ =\ \frac{ad}{bc}\">\r<BR>\n" );
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document.write( "Now you have to decide whether <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large ad\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large bc\"> are integers or not.  If they are, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\frac{ad}{bc}\"> is rational and the rationals are closed under division, otherwise not.\r<BR>\n" );
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document.write( "Take any two whole numbers and divide one by the other. Do you always get another whole number?\r<BR>\n" );
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document.write( "Even though it doesn't make any difference for this particular question, I refuse to answer any question using the term \"whole numbers\" unless you define the term.  Some define the Whole Numbers as the positive Integers equivalent to one definition of the Natural Numbers.  Some define the set as the non-negative Integers equivalent to the other definition of the Natural Numbers. And some define the Whole Numbers as equivalent to the complete set of Integers.\r<BR>\n" );
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document.write( "Take any two perfect squares and divide one by the other. Do you always get another perfect square?\r<BR>\n" );
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document.write( "Hint:  Divide 4 by 25.\r<BR>\n" );
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document.write( "Take any two irrational numbers and divide one by the other.  Do you always get another irrational number?\r<BR>\n" );
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document.write( "Hint:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{\pi}{\pi}\ =\ ?\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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