document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137879>Question 1137879</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many fractions of the form a/b are there, where a and b have no common factors<BR>\n" );
document.write( "larger than 1, such that b = a + 6 and a/b < 2017/2023?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755749 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=755749\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ans <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28+2022+%29+ ALIGN=MIDDLE  ALT=\"+highlight%28+2022+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Workout:<BR>\n" );
document.write( "(Assumes a and b are any integers):<br><BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%3E=0+ ALIGN=MIDDLE  ALT=\"+a%3E=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<br>\r<BR>\n" );
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document.write( "   a/(a+6) < 2017/2023<BR>\n" );
document.write( "     2023a  < 2017(a+6)<BR>\n" );
document.write( "     2023a  < 2017a + 12102<BR>\n" );
document.write( "        6a  < 12102<BR>\n" );
document.write( "         a  < 2017<br>\r<BR>\n" );
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document.write( "So that gives the 2017 fractions  0/6, 1/7, ..., 2016/2022<br>\r<BR>\n" );
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document.write( "Now for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%3C0+ ALIGN=MIDDLE  ALT=\"+a%3C0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "     -1/5, -2/4, -3/3, -4/2 and -5/1  are all < 2017/2023<BR>\n" );
document.write( "This is an additional 5 fractions. <br>\r<BR>\n" );
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document.write( "Continuing with negative integers:<BR>\n" );
document.write( " -6/0  is undefined<BR>\n" );
document.write( " -7/-1  is  7  > 2017/2023<br>\r<BR>\n" );
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document.write( "For all other negative integers a/(a+6) > 1 > 2017/2023  (the magnitude of (a) is greater than (a+6) for all these numbers) <br>\r<BR>\n" );
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document.write( "  2017 + 5 = 2022\r<BR>\n" );
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