document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=77956>Question 77956</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the fractions 4567890123/780123456   and 4567890124/780123458 is greater. Give a algebric proof i.e. which avoids multiplications of the numbers involved. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #55845 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=55845\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If we let a=4567890123 and b=780123456 we have a first fraction of:\r<BR>\n" );
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document.write( "<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;\" >\r<BR>\n" );
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document.write( "Since the 2nd fraction has a numerator of 1 added to 4567890123 and a denominator of 2 added to 780123456 we have a 2nd fraction:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B1%29%2F%28b%2B2%29 ALIGN=MIDDLE  ALT=\"%28a%2B1%29%2F%28b%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So lets assume these two fractions are equal (they're not, but lets place a relation between them)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fb=%28a%2B1%29%2F%28b%2B2%29 ALIGN=MIDDLE  ALT=\"a%2Fb=%28a%2B1%29%2F%28b%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now cross multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28b%2B2%29=b%28a%2B1%29 ALIGN=MIDDLE  ALT=\"a%28b%2B2%29=b%28a%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab%2B2a=ab%2Bb ALIGN=MIDDLE  ALT=\"ab%2B2a=ab%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the left side has 2 \"a\" terms, the left side is larger (there are more larger terms on the left side). In other words, this is true:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fb%3E%28a%2B1%29%2F%28b%2B2%29 ALIGN=MIDDLE  ALT=\"a%2Fb%3E%28a%2B1%29%2F%28b%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Which means the first fraction is larger, ie\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4567890123%2F780123456%3E4567890124%2F780123458 ALIGN=MIDDLE  ALT=\"4567890123%2F780123456%3E4567890124%2F780123458\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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