document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=487933>Question 487933</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you differentiate the properties associative,communitive, and distributive  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #333199 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=333199\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The \"Commutative Laws\" say you can swap numbers over and still get the same answer ...\r<BR>\n" );
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document.write( "... when you add (a + b  =  b + a)  or when you multiply (a * b  =  b * a)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Commutative ALIGN=MIDDLE  ALT=\"Commutative\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Laws ALIGN=MIDDLE  ALT=\"+Laws\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <BR>\n" );
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document.write( "a + b  =  b + a<BR>\n" );
document.write( "a * b  =  b * a\r<BR>\n" );
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document.write( "The \"Associative Laws\" say that it doesn't matter how you group the numbers (i.e. which you calculate first) ...\r<BR>\n" );
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document.write( "... when you add (a + b) + c  =  a + (b + c)  or when you multiply (a * b) * c  =  a * (b *c)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Associative ALIGN=MIDDLE  ALT=\"Associative\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Laws ALIGN=MIDDLE  ALT=\"+Laws\"   DISABLED_style= \"max-width:90%; height:auto;\" >: 	<BR>\n" );
document.write( "(a + b) + c  =  a + (b + c)<BR>\n" );
document.write( "(a * b) * c  =  a * (b * c)\r<BR>\n" );
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document.write( "The \"Distributive Law\" is the BEST one of all, but needs careful attention.\r<BR>\n" );
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document.write( "This is what it lets you do:\r<BR>\n" );
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document.write( "3*(2+4)\r<BR>\n" );
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document.write( "the 3* can be \"distributed\" across the 2+4, into 3*2 and 3*4\r<BR>\n" );
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document.write( "the \"Distributive Law\" says:\r<BR>\n" );
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document.write( "you get the same answer when you:\r<BR>\n" );
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document.write( "    multiply a number by a group of numbers added together, or<BR>\n" );
document.write( "    do each multiply separately then add them\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Distributive ALIGN=MIDDLE  ALT=\"Distributive\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Law ALIGN=MIDDLE  ALT=\"Law\"   DISABLED_style= \"max-width:90%; height:auto;\" >: \r<BR>\n" );
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document.write( "a * (b + c)  =  a * b  +  a * c\r<BR>\n" );
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document.write( "These laws are to do with adding or multiplying, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > dividing or subtracting.\r<BR>\n" );
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document.write( "The Commutative Law <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=does ALIGN=MIDDLE  ALT=\"does\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+not ALIGN=MIDDLE  ALT=\"+not\"   DISABLED_style= \"max-width:90%; height:auto;\" > work for division:\r<BR>\n" );
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document.write( "Example:\r<BR>\n" );
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document.write( "    12 / 3 = 4, but<BR>\n" );
document.write( "    3 / 12 = ¼\r<BR>\n" );
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document.write( "The Associative Law <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=does ALIGN=MIDDLE  ALT=\"does\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+not ALIGN=MIDDLE  ALT=\"+not\"   DISABLED_style= \"max-width:90%; height:auto;\" > work for subtraction:\r<BR>\n" );
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document.write( "Example:\r<BR>\n" );
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document.write( "    (9 – 4) – 3 = 5 – 3 = 2, but<BR>\n" );
document.write( "    9 – (4 – 3) = 9 – 1 = 8\r<BR>\n" );
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document.write( " The Distributive Law <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=does ALIGN=MIDDLE  ALT=\"does\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+not ALIGN=MIDDLE  ALT=\"+not\"   DISABLED_style= \"max-width:90%; height:auto;\" > work for division:\r<BR>\n" );
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document.write( "Example:\r<BR>\n" );
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document.write( "    24 / (4 + 8) = 24 / 12 = 2, but<BR>\n" );
document.write( "    24 / 4 + 24 / 8 = 6 + 3 = 9\r<BR>\n" );
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