document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117353>Question 117353</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello out there,I need some help with some tough problems,the first one is,Simplify:15/30.The next one is,Simplify:9/k+8/k.The third one is,Simplify:8t/21-5t/21.And the last one is,Simplify:p/8+3p/8,thanks to whoever can help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85371 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=85371\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"Simplify:15/30\"\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=reduce_fraction.solver>Reducing Fractions Calculator</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>In order to reduce <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F30 ALIGN=MIDDLE  ALT=\"15%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the numerator and denominator must share a common factor. This common number must evenly divide into both of them without any remainder or decimal. <BR>\n" );
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document.write( "  In order to completely reduce the fraction, you must divide the numerator and the denominator by the greatest common factor (GCF). The GCF of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30 ALIGN=MIDDLE  ALT=\"30\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression= ALIGN=MIDDLE  ALT=\"\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: click <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/divisibility/find-greatest-common-factor.solver>here</a> if you need help with finding the GCF). So divide both the numerator and denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression= ALIGN=MIDDLE  ALT=\"\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "  In other words, to reduce the fraction you do this<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28numerator%2FGCF%29%2F%28denominator%2FGCF%29=Reduced_Fraction ALIGN=MIDDLE  ALT=\"%28numerator%2FGCF%29%2F%28denominator%2FGCF%29=Reduced_Fraction\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2F%29%2F%2830%2F%29 ALIGN=MIDDLE  ALT=\"%2815%2F%29%2F%2830%2F%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the numerator, denominator, and the GCF<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%2F%2830%2F%29 ALIGN=MIDDLE  ALT=\"%281%29%2F%2830%2F%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide 15 by  to get 1. This is now the new numerator.<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide 30 by  to get 2. This is now the new denominator.<BR>\n" );
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document.write( "  So  <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2F%29%2F%2830%2F%29=1%2F2 ALIGN=MIDDLE  ALT=\"%2815%2F%29%2F%2830%2F%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  This means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F30 ALIGN=MIDDLE  ALT=\"15%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" > reduces to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F30=1%2F2 ALIGN=MIDDLE  ALT=\"15%2F30=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "\"Simplify:9/k+8/k\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F%28k%29%2B8%2F%28k%29 ALIGN=MIDDLE  ALT=\"9%2F%28k%29%2B8%2F%28k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "Since the denominators are all equal, we can combine the numerators\r<BR>\n" );
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document.write( "Now combine like terms\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F%28k%29%2B8%2F%28k%29=%2817%29%2F%28k%29 ALIGN=MIDDLE  ALT=\"9%2F%28k%29%2B8%2F%28k%29=%2817%29%2F%28k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "#3\r<BR>\n" );
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document.write( "\"8t/21-5t/21\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8t%2F21-5t%2F21 ALIGN=MIDDLE  ALT=\"8t%2F21-5t%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "Since the denominators are all equal, we can combine the numerators\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8t%2F21-5t%2F21=%288-5t%29%2F%2821%29 ALIGN=MIDDLE  ALT=\"8t%2F21-5t%2F21=%288-5t%29%2F%2821%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "\"Simplify:p/8+3p/8\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2F%288%29%2B3p%2F%288%29 ALIGN=MIDDLE  ALT=\"p%2F%288%29%2B3p%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "Since the denominators are all equal, we can combine the numerators\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%2B3p%29%2F%288%29 ALIGN=MIDDLE  ALT=\"%28p%2B3p%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   \r<BR>\n" );
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document.write( "Now combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%29%2F%282%29 ALIGN=MIDDLE  ALT=\"%28p%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2F%288%29%2B3p%2F%288%29=%28p%29%2F%282%29 ALIGN=MIDDLE  ALT=\"p%2F%288%29%2B3p%2F%288%29=%28p%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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