document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159720>Question 1159720</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #782776 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=782776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A solution using logical reasoning and a bit of trial and error with simple arithmetic....<br><BR>\n" );
document.write( "When the denominator is decreased by 7, the fraction becomes 1.  That means the denominator is 7 more than the numerator.  So the fraction is of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2F%28n%2B7%29 ALIGN=MIDDLE  ALT=\"n%2F%28n%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "When the numerator is increased by 3, the fraction becomes (equivalent to) 3/4.  So the fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B3%29%2F%28n%2B7%29 ALIGN=MIDDLE  ALT=\"%28n%2B3%29%2F%28n%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to 3/4.<br><BR>\n" );
document.write( "From there you can solve the problem algebraically:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B3%29%2F%28n%2B7%29+=+3%2F4 ALIGN=MIDDLE  ALT=\"%28n%2B3%29%2F%28n%2B7%29+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28n%2B7%29+=+4%28n%2B3%29 ALIGN=MIDDLE  ALT=\"3%28n%2B7%29+=+4%28n%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%2B21+=+4n%2B12 ALIGN=MIDDLE  ALT=\"3n%2B21+=+4n%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+9 ALIGN=MIDDLE  ALT=\"n+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The original fraction is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2F%28n%2B7%29+=+9%2F16 ALIGN=MIDDLE  ALT=\"n%2F%28n%2B7%29+=+9%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If you have excellent number sense, you can also work the last part of the problem informally.  You know the fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B3%29%2F%28n%2B7%29 ALIGN=MIDDLE  ALT=\"%28n%2B3%29%2F%28n%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to 3/4.  In the fraction 3/4, the difference between numerator and denominator is 1; you want the difference to be 4 (the difference between n+3 and n+7).<br><BR>\n" );
document.write( "So the fraction after you increase the numerator by 3 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A4%29%2F%284%2A4%29+=+12%2F16 ALIGN=MIDDLE  ALT=\"%283%2A4%29%2F%284%2A4%29+=+12%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >; and that makes the original fraction 9/16.<br><BR>\n" );
document.write( " </SPAN>\n" );
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