document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697295>Question 697295</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 4 < a < 7 < b < 9, then which of the following best defines a/b?\r<BR>\n" );
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document.write( "I tried to look at it like a triangle, with (a) being 6 and (b) being 8, but I'm stuck after that. \r<BR>\n" );
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document.write( "a. 4/9 < a/b < 1<BR>\n" );
document.write( "b. 4/9 < a/b < 7/9<BR>\n" );
document.write( "c. 4/7 < a/b < 7/9<BR>\n" );
document.write( "d. 4/7 < a/b < 1<BR>\n" );
document.write( "e. 4/7 < a/b < 9/7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #429875 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+Parker><B>Edwin Parker(36)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+Parker><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=429875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is a counterexample to show<BR>\n" );
document.write( "that \r<BR>\n" );
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document.write( "b. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F9 ALIGN=MIDDLE  ALT=\"4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fb ALIGN=MIDDLE  ALT=\"a%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F9 ALIGN=MIDDLE  ALT=\"7%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "is not always true:\r<BR>\n" );
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document.write( "Suppose a = 6 and b = 7.5 \r<BR>\n" );
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document.write( "4 < a < 7 < b < 9 because 4 < 6 < 7 < 7.5 < 9 <BR>\n" );
document.write( "However <BR>\n" );
document.write( "a/b = 6/7.5 = .8 <BR>\n" );
document.write( "and <BR>\n" );
document.write( "7/9 = 0.7778 (rounded to 4 decimal places) \r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fb ALIGN=MIDDLE  ALT=\"a%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F9 ALIGN=MIDDLE  ALT=\"7%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and thus this is a case when choice b.<BR>\n" );
document.write( "is false.\r<BR>\n" );
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document.write( "The second response above gives a <BR>\n" );
document.write( "counterexample of choice c.\r<BR>\n" );
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document.write( "Here is a counterexample to show<BR>\n" );
document.write( "that \r<BR>\n" );
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document.write( "d. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F7 ALIGN=MIDDLE  ALT=\"4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fb ALIGN=MIDDLE  ALT=\"a%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > < 1\r<BR>\n" );
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document.write( "is not always true:\r<BR>\n" );
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document.write( "Suppose a = 4.2 and b = 8 \r<BR>\n" );
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document.write( "4 < a < 7 < b < 9 because 4 < 4.2 < 7 < 8 < 9 <BR>\n" );
document.write( "However <BR>\n" );
document.write( "a/b = 4.2/8 = .525 <BR>\n" );
document.write( "and <BR>\n" );
document.write( "4/7 = 0.5714 (rounded to 4 decimal places) \r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fb ALIGN=MIDDLE  ALT=\"a%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F7 ALIGN=MIDDLE  ALT=\"4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and thus this is a case when choice d.<BR>\n" );
document.write( "is false.\r<BR>\n" );
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document.write( "This is also a counterexample for choice e.\r<BR>\n" );
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document.write( "Edwin</pre> </SPAN>\n" );
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