document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=945571>Question 945571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rectangular cards, 2cm by 3cm, are cut from a rectangular sheet 24cm by 36cm. What is the greatest number of cards that can be cut from the sheet?\r<BR>\n" );
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document.write( "Sorry, I am not sure of the topic, so I chose Area and Surface Area. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #576763 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=576763\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> THE EXPECTED SHOW-YOUR-WORK WAY:<BR>\n" );
document.write( "Steps 1 and 2:<BR>\n" );
document.write( "Sharpen your pencil, or take out the calculator, and<BR>\n" );
document.write( "in any order make the following two area calculations.<BR>\n" );
document.write( "A) Calculate the surface area (in square centimeters) of one card.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282cm%29%2A%283cm%29=6cm%5E2 ALIGN=MIDDLE  ALT=\"%282cm%29%2A%283cm%29=6cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B) Calculate the surface area (in square centimeters) of the rectangular sheet 24cm by 36cm.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2824cm%29%2A%2836cm%29=864cm%5E2 ALIGN=MIDDLE  ALT=\"%2824cm%29%2A%2836cm%29=864cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Step 3:<BR>\n" );
document.write( "Divide the surface area of the rectangular sheet by the surface area of one card.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=864cm%5E2%2F6cm%5E2=highlight%28144%29 ALIGN=MIDDLE  ALT=\"864cm%5E2%2F6cm%5E2=highlight%28144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "THE SMART AND FAST WAY TO DO IT FOR A TIMED TEST:<BR>\n" );
document.write( "It is possible to visualize and quickly calculate the result in your head<BR>\n" );
document.write( "(no calculator needed) as follows.<BR>\n" );
document.write( "Since both length are divisible by both card dimensions, there are several ways to cut the cards without any waste.<BR>\n" );
document.write( "If you are doing it at home, you may want make cut through one of the edges every 3-cm, parallel to the other edge, making strips.<BR>\n" );
document.write( "Then, stacking the strips, you may cut 2-cm sections through the stack to make the cards. Or you may cut every 2-cm first.<BR>\n" );
document.write( "If making cards is your business, you probably have a machine with criss-cross sharp edges that comes down over the 24cm by 36cm sheet and makes the cross-cuts all at the same time.<BR>\n" );
document.write( "The end result may look like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-1.5%2C37.5%2C-1%2C25%2C%0D%0Aline%280%2C0%2C36%2C0%29%2Cline%280%2C24%2C36%2C24%29%2C%0D%0Aline%280%2C0%2C0%2C24%29%2Cline%2836%2C0%2C36%2C24%29%2C%0D%0Agreen%28line%283%2C0%2C3%2C24%29%29%2C%0D%0Agreen%28line%286%2C0%2C6%2C24%29%29%2Cgreen%28line%289%2C0%2C9%2C24%29%29%2C%0D%0Agreen%28line%2812%2C0%2C12%2C24%29%29%2Cgreen%28line%2815%2C0%2C15%2C24%29%29%2C%0D%0Agreen%28line%2818%2C0%2C18%2C24%29%29%2Cgreen%28line%2821%2C0%2C21%2C24%29%29%2C%0D%0Agreen%28line%2824%2C0%2C24%2C24%29%29%2Cgreen%28line%2827%2C0%2C27%2C24%29%29%2C%0D%0Agreen%28line%2830%2C0%2C30%2C24%29%29%2Cgreen%28line%2833%2C0%2C33%2C24%29%29%2C%0D%0Ared%28line%280%2C2%2C36%2C2%29%29%2Cred%28line%280%2C4%2C36%2C4%29%29%2C%0D%0Ared%28line%280%2C6%2C36%2C6%29%29%2Cred%28line%280%2C8%2C36%2C8%29%29%2C%0D%0Ared%28line%280%2C10%2C36%2C10%29%29%2Cred%28line%280%2C12%2C36%2C12%29%29%2C%0D%0Ared%28line%280%2C14%2C36%2C14%29%29%2Cred%28line%280%2C16%2C36%2C16%29%29%2C%0D%0Ared%28line%280%2C18%2C36%2C18%29%29%2Cred%28line%280%2C20%2C36%2C20%29%29%2C%0D%0Ared%28line%280%2C22%2C36%2C22%29%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ,or like this <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-1.5%2C37.5%2C-1%2C25%2C%0D%0Aline%280%2C0%2C36%2C0%29%2Cline%280%2C24%2C36%2C24%29%2C%0D%0Aline%280%2C0%2C0%2C24%29%2Cline%2836%2C0%2C36%2C24%29%2C%0D%0Agreen%28line%282%2C0%2C2%2C24%29%29%2Cgreen%28line%284%2C0%2C4%2C24%29%29%2C%0D%0Agreen%28line%286%2C0%2C6%2C24%29%29%2Cgreen%28line%288%2C0%2C8%2C24%29%29%2C%0D%0Agreen%28line%2812%2C0%2C12%2C24%29%29%2Cgreen%28line%2810%2C0%2C10%2C24%29%29%2C%0D%0Agreen%28line%2814%2C0%2C14%2C24%29%29%2Cgreen%28line%2816%2C0%2C16%2C24%29%29%2C%0D%0Agreen%28line%2818%2C0%2C18%2C24%29%29%2Cgreen%28line%2820%2C0%2C20%2C24%29%29%2C%0D%0Agreen%28line%2822%2C0%2C22%2C24%29%29%2Cgreen%28line%2824%2C0%2C24%2C24%29%29%2C%0D%0Agreen%28line%2826%2C0%2C26%2C24%29%29%2Cgreen%28line%2828%2C0%2C28%2C24%29%29%2C%0D%0Agreen%28line%2832%2C0%2C32%2C24%29%29%2Cgreen%28line%2834%2C0%2C34%2C24%29%29%2C%0D%0Agreen%28line%2830%2C0%2C30%2C24%29%29%2C%0D%0Ared%28line%280%2C3%2C36%2C3%29%29%2Cred%28line%280%2C9%2C36%2C9%29%29%2C%0D%0Ared%28line%280%2C6%2C36%2C6%29%29%2Cred%28line%280%2C12%2C36%2C12%29%29%2C%0D%0Ared%28line%280%2C15%2C36%2C15%29%29%2Cred%28line%280%2C18%2C36%2C18%29%29%2C%0D%0Ared%28line%280%2C21%2C36%2C21%29%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " <BR>\n" );
document.write( "In either case, quick mental math gives you the answer.<BR>\n" );
document.write( "For the first picture,<BR>\n" );
document.write( "cutting the long, 36-cm edge at 3-cm intervals,<BR>\n" );
document.write( "and cutting the short, 24-cm edge at 2-cm intervals,<BR>\n" );
document.write( "you would be calculating<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2836cm%2F%223+cm%22%29%2A%2824cm%2F%222+cm%22%29=12%2A12=highlight%28144%29 ALIGN=MIDDLE  ALT=\"+%2836cm%2F%223+cm%22%29%2A%2824cm%2F%222+cm%22%29=12%2A12=highlight%28144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
document.write( "\n" );
document.write( "For the second picture,<BR>\n" );
document.write( "cutting the long, 36-cm edge at 2-cm intervals,<BR>\n" );
document.write( "and he short, 24-cm edge at 3-cm intervals,<BR>\n" );
document.write( "you would be calculating<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2836cm%2F%222+cm%22%29%2A%2824cm%2F%223+cm%22%29=18%2A8=2%2A9%2A8=2%2A72=highlight%28144%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );