document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252512>Question 252512</A>: <I><SPAN STYLE=\"word-break: break-all;\"> when N is divided by 5, the remainder is 3. what is the remainder when 7N is divided by 5? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184486 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=184486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since dividing N by 5 gives a remainder of 3, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%2F5=q%2B3%2F5 ALIGN=MIDDLE  ALT=\"N%2F5=q%2B3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > where 'q' is the quotient (which is some whole number). Multiplying everything by 5 gets us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=5q%2B3 ALIGN=MIDDLE  ALT=\"N=5q%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7N=7%285q%2B3%29=35q%2B21 ALIGN=MIDDLE  ALT=\"7N=7%285q%2B3%29=35q%2B21\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If we divide 7N by 5, we then get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7N%2F5=%2835q%2B21%29%2F5=%2835q%29%2F5%2B21%2F5=7q%2B21%2F5 ALIGN=MIDDLE  ALT=\"7N%2F5=%2835q%2B21%29%2F5=%2835q%29%2F5%2B21%2F5=7q%2B21%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7N%2F5=7q%2B21%2F5 ALIGN=MIDDLE  ALT=\"7N%2F5=7q%2B21%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The remainder is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2F5 ALIGN=MIDDLE  ALT=\"21%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but it's too big which means that we need to break it up. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2F5=%2820%2B1%29%2F5=20%2F5%2B1%2F5=4%2B1%2F5 ALIGN=MIDDLE  ALT=\"21%2F5=%2820%2B1%29%2F5=20%2F5%2B1%2F5=4%2B1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Since the fractional portion is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this tells us that the remainder is 1. \r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the remainder of dividing 7N by 5 is 1.\r<BR>\n" );
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document.write( "Note: Try some examples to give you an idea that it works. </SPAN>\n" );
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