document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=560295>Question 560295</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what does it mean to equate the cross product? <BR>\n" );
document.write( "hat size           head circumference          head circumference<BR>\n" );
document.write( "7 7/8                  24                         61<BR>\n" );
document.write( "7 1/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #363841 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=363841\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> THE PROBLEM<BR>\n" );
document.write( "The hat size, head circumference in inches, and head circumference in centimeters are in direct proportion.<BR>\n" );
document.write( "They tell you that a hat size of 7 7/8 will fit a head circumference of 24 inches or 61 centimeters.<BR>\n" );
document.write( "You want to know the head circumference in inches (x), and in centimeters (y) corresponding to a hat size of 7 1/2.<BR>\n" );
document.write( "WHAT IS MEANT BY CROSS PRODUCTS<BR>\n" );
document.write( "To find the head circumference in inches (x) corresponding to a hat size of 7 1/2 you would write the proportion<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F7%267%2F8 ALIGN=MIDDLE  ALT=\"24%2F7%267%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F7%261%2F2 ALIGN=MIDDLE  ALT=\"x%2F7%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To get to an equivalent equation without denominators, you would multiply both sides of the equal sign by the denominators<BR>\n" );
document.write( "By doing that, and simplifying, you would get a simpler equation with one product equated (stated as equal) to another product:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%287%261%2F2%29=x%287%267%2F8%29 ALIGN=MIDDLE  ALT=\"24%287%261%2F2%29=x%287%267%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The equated products involve numbers that were placed crisscross from each other in the original equation. That's why they are called \"cross products\".<BR>\n" );
document.write( "When you are solving the problem, you can just say that the cross products are equal, and save yourself any further explanations and intermediate steps.<BR>\n" );
document.write( "THE SOLUTION<BR>\n" );
document.write( "For the circumference in centimeters (x), we write<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F7%267%2F8 ALIGN=MIDDLE  ALT=\"24%2F7%267%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F7%261%2F2 ALIGN=MIDDLE  ALT=\"x%2F7%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equating cross products we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%287%261%2F2%29=x%287%267%2F8%29 ALIGN=MIDDLE  ALT=\"24%287%261%2F2%29=x%287%267%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We write the mixed numbers as improper fractions to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2815%2F2%29=%2863%2F8%29x ALIGN=MIDDLE  ALT=\"24%2815%2F2%29=%2863%2F8%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180=%2863%2F8%29x ALIGN=MIDDLE  ALT=\"180=%2863%2F8%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F63 ALIGN=MIDDLE  ALT=\"8%2F63\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%288%2F63%29=%288%2F63%29%2863%2F8%29x ALIGN=MIDDLE  ALT=\"180%288%2F63%29=%288%2F63%29%2863%2F8%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=160%2F7=x ALIGN=MIDDLE  ALT=\"160%2F7=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which could be expressed as the mixed number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%266%2F7 ALIGN=MIDDLE  ALT=\"22%266%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or it could be approximated as the decimal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22.86 ALIGN=MIDDLE  ALT=\"22.86\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "However, since it's a circumference measurement in inches, a more appropriate answer would be 23 inches.<BR>\n" );
document.write( "For the circumference in centimeters (x), we write<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=61%2F7%267%2F8 ALIGN=MIDDLE  ALT=\"61%2F7%267%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F7%261%2F2 ALIGN=MIDDLE  ALT=\"y%2F7%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equating cross products we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=61%287%261%2F2%29=y%287%267%2F8%29 ALIGN=MIDDLE  ALT=\"61%287%261%2F2%29=y%287%267%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=61%2815%2F2%29=y%2863%2F8%29 ALIGN=MIDDLE  ALT=\"61%2815%2F2%29=y%2863%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=61%288%2F63%29%2815%2F2%29 ALIGN=MIDDLE  ALT=\"y=61%288%2F63%29%2815%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=61%2A8%2A15%2F%2863%2A2%29 ALIGN=MIDDLE  ALT=\"y=61%2A8%2A15%2F%2863%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which simplifies to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=61%2A5%2F21 ALIGN=MIDDLE  ALT=\"y=61%2A5%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and calculates to approximately 58 centimeters. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );