document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110626>Question 110626</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the proportion.\r<BR>\n" );
document.write( "\n" );
document.write( "k/28=8/63 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80595 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=80595\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the proportion:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2F28=8%2F63 ALIGN=MIDDLE  ALT=\"k%2F28=8%2F63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can start the solution to proportion problems by using a process called  \"cross multiplying.\"<BR>\n" );
document.write( ".<BR>\n" );
document.write( "In this process you multiply the numerator of one side times the denominator of the other<BR>\n" );
document.write( "side, then write the equal sign, and follow that by multiplying the numerator of the other<BR>\n" );
document.write( "side by the denominator of the first side. A little difficult to describe, but actually <BR>\n" );
document.write( "pretty easy to do once you get the hang of it.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "In this problem we can begin by multiplying the k (a numerator) times the 63 (the denominator<BR>\n" );
document.write( "from the other side), then write the equal sign, and on the other side of the equal sign<BR>\n" );
document.write( "multiply the 8 (a numerator) times the 28 (denominator from the opposite side).<BR>\n" );
document.write( ".<BR>\n" );
document.write( "When you do that you have:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=63%2Ak+=+8%2A28 ALIGN=MIDDLE  ALT=\"63%2Ak+=+8%2A28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now you can solve for k by dividing both sides by 63 (the multiplier of k) to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+%288%2A28%29%2F63 ALIGN=MIDDLE  ALT=\"k+=+%288%2A28%29%2F63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice that 63 factors into 9 times 7. Therefore, you can replace the 63 with 9*7 and the<BR>\n" );
document.write( "problem then becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+%288%2A28%29%2F%289%2A7%29 ALIGN=MIDDLE  ALT=\"k+=+%288%2A28%29%2F%289%2A7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "And the 28 in the numerator factors into 7 times 4. So replace the 28 with 7*4 and the<BR>\n" );
document.write( "problem is then:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+%288%2A7%2A4%29%2F%289%2A7%29 ALIGN=MIDDLE  ALT=\"k+=+%288%2A7%2A4%29%2F%289%2A7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can then cancel the 7 in the numerator with the 7 in the denominator and you have:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+%288%2Across%287%29%2A4%29%2F%289%2Across%287%29%29+=+%288%2A4%29%2F9+ ALIGN=MIDDLE  ALT=\"k+=+%288%2Across%287%29%2A4%29%2F%289%2Across%287%29%29+=+%288%2A4%29%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Nothing else will cancel nicely, so multiply out the numerator and divide that product<BR>\n" );
document.write( "by the denominator to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+%288%2A4%29%2F9+=+32%2F9+=+3.555556 ALIGN=MIDDLE  ALT=\"k+=+%288%2A4%29%2F9+=+32%2F9+=+3.555556\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you. The cross process of cross multiplying is a convenient way to remember<BR>\n" );
document.write( "what to do to convert proportions to an ordinary algebraic equation. You might want to<BR>\n" );
document.write( "remember it.<BR>\n" );
document.write( ". </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );