document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=156679>Question 156679</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have to do a project about the associative property. I need example problems but I don't quite understand it well enough. I already have some simple problems but my teacher wants challenge problems too. Can you give me an example of a challenge problem for the associative property of addition and another for the associative property of multiplication so I can see how to make one. Thank you very much.\r<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 #115575 by </B><A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><B>Electrified_Levi(103)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><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=115575\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, Hope I can help<BR>\n" );
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document.write( "I have to do a project about the associative property. I need example problems but I don't quite understand it well enough. I already have some simple problems but my teacher wants challenge problems too. Can you give me an example of a challenge problem for the associative property of addition and another for the associative property of multiplication so I can see how to make one. Thank you very much. <BR>\n" );
document.write( "Troy<BR>\n" );
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document.write( "I think of associative property as \" how you arrange the parentheses, associative = \"arrange\"(parentheses),(both associative, and arrange start with \"a\" )<BR>\n" );
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document.write( "Here are some examples of associative property<BR>\n" );
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document.write( "Example: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285+%2B+3%29+%2B+7+=+5+%2B+%283+%2B+7%29+ ALIGN=MIDDLE  ALT=\"+%285+%2B+3%29+%2B+7+=+5+%2B+%283+%2B+7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%288%29+%2B+7+=+5+%2B+%2810%29+ ALIGN=MIDDLE  ALT=\"+%288%29+%2B+7+=+5+%2B+%2810%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15+=+15+ ALIGN=MIDDLE  ALT=\"+15+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Example: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%286+-+4%29+%2B+3+=+6+%2B+%28-4%2B3%29+ ALIGN=MIDDLE  ALT=\"+%286+-+4%29+%2B+3+=+6+%2B+%28-4%2B3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282%29+%2B+3+=+6+%2B+%28-1%29+ ALIGN=MIDDLE  ALT=\"+%282%29+%2B+3+=+6+%2B+%28-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+=+6+-1+ ALIGN=MIDDLE  ALT=\"+5+=+6+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+=+5+ ALIGN=MIDDLE  ALT=\"+5+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6-4+ ALIGN=MIDDLE  ALT=\"+6-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same thing as saying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+%2B+%28-4%29+ ALIGN=MIDDLE  ALT=\"+6+%2B+%28-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "Example: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+8x%29+%2B+10x+=+x+%2B+%288x+%2B+10x%29+ ALIGN=MIDDLE  ALT=\"+%28x+%2B+8x%29+%2B+10x+=+x+%2B+%288x+%2B+10x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%289x%29+%2B+10x+=+x+%2B+%2818x%29+ ALIGN=MIDDLE  ALT=\"+%289x%29+%2B+10x+=+x+%2B+%2818x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+19x+=+19x+ ALIGN=MIDDLE  ALT=\"+19x+=+19x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now lets use multiplication in the associative property<BR>\n" );
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document.write( "Example: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282+%2A+6%29+%2A+7+=+2+%2A+%286+%2A+7%29+ ALIGN=MIDDLE  ALT=\"+%282+%2A+6%29+%2A+7+=+2+%2A+%286+%2A+7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2812%29+%2A+7+=+2+%2A+%2842%29+ ALIGN=MIDDLE  ALT=\"+%2812%29+%2A+7+=+2+%2A+%2842%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+84+=+84+ ALIGN=MIDDLE  ALT=\"+84+=+84+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Example: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2A+4%29+%2A+y+=+x+%2A+%284+%2A+y%29+ ALIGN=MIDDLE  ALT=\"+%28x+%2A+4%29+%2A+y+=+x+%2A+%284+%2A+y%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%284x%29+%2A+y+=+x+%2A+%284y%29+ ALIGN=MIDDLE  ALT=\"+%284x%29+%2A+y+=+x+%2A+%284y%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4xy+=+4xy+ ALIGN=MIDDLE  ALT=\"+4xy+=+4xy+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Example: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E2+%2A+5%29+%2A+y%5E3+=+x%5E2+%2A+%285+%2A+y%5E3%29+ ALIGN=MIDDLE  ALT=\"+%28x%5E2+%2A+5%29+%2A+y%5E3+=+x%5E2+%2A+%285+%2A+y%5E3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285x%5E2%29+%2A+y%5E3+=+x%5E2+%2A+%285y%5E3%29+ ALIGN=MIDDLE  ALT=\"+%285x%5E2%29+%2A+y%5E3+=+x%5E2+%2A+%285y%5E3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x%5E2y%5E3+=+5x%5E2y%5E3+ ALIGN=MIDDLE  ALT=\"+5x%5E2y%5E3+=+5x%5E2y%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Here is a challenging one for multiplication<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28a%5E12+%2A+%2812b%29%5E3%29%2A+%288c%29%5E4+=+a%5E12+%2A+%28+%2812b%29%5E16+%2A+%288c%29%5E10%29+ ALIGN=MIDDLE   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=+%28a%5E12+%2A+1728b%5E3%29%2A+4096c%5E4+=+a%5E12+%2A+%28+1728b%5E3+%2A+4096c%5E4%29+ ALIGN=MIDDLE  ALT=\"+%28a%5E12+%2A+1728b%5E3%29%2A+4096c%5E4+=+a%5E12+%2A+%28+1728b%5E3+%2A+4096c%5E4%29+\"   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=+%281728a%5E12b%5E3%29%2A+4096c%5E4+=+a%5E12+%2A+%28+7077888b%5E3c%5E4%29+ ALIGN=MIDDLE  ALT=\"+%281728a%5E12b%5E3%29%2A+4096c%5E4+=+a%5E12+%2A+%28+7077888b%5E3c%5E4%29+\"   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=+7077888a%5E12b%5E3c%5E4+=+7077888a%5E12b%5E3c%5E4+ ALIGN=MIDDLE  ALT=\"+7077888a%5E12b%5E3c%5E4+=+7077888a%5E12b%5E3c%5E4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you are trying to use just numbers, here is another multiplication using associative property<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28%286%29%284%29%29%5E2+%2A+%28%283%29%2812%29%29%5E3%29+%2A+%28%285%29%284%29%29%5E4+=+%28%286%29%284%29%29%5E2+%2A+%28%28%283%29%2812%29%29%5E3+%2A+%28%285%29%284%29%29%5E4%29+ ALIGN=MIDDLE   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=+%28%2824%29%5E2+%2A+%2836%29%5E3%29+%2A+%2820%29%5E4+=+%2824%29%5E2+%2A+%28%2836%29%5E3+%2A+%2820%29%5E4%29+ ALIGN=MIDDLE   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=+%28576+%2A+46656%29+%2A+160000+=+576+%2A+%2846656+%2A+160000%29+ ALIGN=MIDDLE  ALT=\"+%28576+%2A+46656%29+%2A+160000+=+576+%2A+%2846656+%2A+160000%29+\"   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=+%2826873856%29+%2A+160000+=+576+%2A+%287464960000%29+ ALIGN=MIDDLE  ALT=\"+%2826873856%29+%2A+160000+=+576+%2A+%287464960000%29+\"   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=+4299816960000+=+4299816960000+ ALIGN=MIDDLE  ALT=\"+4299816960000+=+4299816960000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can always use smaller numbers, if that was too hard<BR>\n" );
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document.write( "A challenging problem using addition and associative problems is<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28%288%29%287%29%29%5E2+%2B+%28%285%29%283%29%29%5E3%29+%2B+%28%284%29%289%29%29%5E3+=+%28%288%29%287%29%29%5E2+%2B+%28%28%285%29%283%29%29%5E3+%2B+%28%284%29%289%29%29%5E3%29+ ALIGN=MIDDLE   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=+%28%2856%29%5E2+%2B+%2815%29%5E3%29+%2B+%2836%29%5E3+=+%2856%29%5E2+%2B+%28%2815%29%5E3+%2B+%2836%29%5E3%29+ ALIGN=MIDDLE   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=+%283136+%2B+3375%29+%2B+46656+=+3136+%2B+%283375+%2B+46656%29+ ALIGN=MIDDLE  ALT=\"+%283136+%2B+3375%29+%2B+46656+=+3136+%2B+%283375+%2B+46656%29+\"   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=+%286511%29+%2B+46656+=+3136+%2B+%2850031%29+ ALIGN=MIDDLE  ALT=\"+%286511%29+%2B+46656+=+3136+%2B+%2850031%29+\"   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=+53167+=+53167+ ALIGN=MIDDLE  ALT=\"+53167+=+53167+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can also do more than three numbers<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2B2%29%2B3%2B4%2B5%2B6%2B7%2B8+=+1%2B%282%2B3%29%2B4%2B5%2B6%2B7%2B8+=+1%2B2%2B3%2B4%2B5%2B%286%2B7%29%2B8+ ALIGN=MIDDLE   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=+%283%29%2B3%2B4%2B5%2B6%2B7%2B8+=+1%2B%285%29%2B4%2B5%2B6%2B7%2B8+=+1%2B2%2B3%2B4%2B5%2B%2813%29%2B8+ ALIGN=MIDDLE   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=+%283%29%2B33+=+%285%29+%2B+31+=+%2813%29%2B23+ ALIGN=MIDDLE  ALT=\"+%283%29%2B33+=+%285%29+%2B+31+=+%2813%29%2B23+\"   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=+36+=+36+=+36+ ALIGN=MIDDLE  ALT=\"+36+=+36+=+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can also do more than two numbers in side the parentheses<BR>\n" );
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document.write( "Lets use multiplication<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282%2A3%2A5%29%2A7%2A11%2A13%2A15%2A20+=+2%2A3%2A5%2A%287%2A11%2A13%29%2A15%2A20+=+2%2A3%2A5%2A7%2A%2811%2A13%2A15%29%2A20+ ALIGN=MIDDLE   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=+%2830%29%2A7%2A11%2A13%2A15%2A20+=+2%2A3%2A5%2A%281001%29%2A15%2A20+=+2%2A3%2A5%2A7%2A%282145%29%2A20+ ALIGN=MIDDLE   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=+%2830%29%2A+300300+=+%281001%29%2A9000+=+%282145%29%2A+4200+ ALIGN=MIDDLE  ALT=\"+%2830%29%2A+300300+=+%281001%29%2A9000+=+%282145%29%2A+4200+\"   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=+9009000=+9009000=+9009000 ALIGN=MIDDLE  ALT=\"+9009000=+9009000=+9009000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope I helped, Levi </SPAN>\n" );
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