document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119917>Question 119917</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please explain the difference between Distrributive, Associative and communitative properties.  When i am doing my homework, and asked to do a question involving one of the properites, i cannot figure out which is the correct one.  If there is some formula for remembering the correct solutions, please let me know. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87886 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=87886\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I don't know of any \"formula\" for remembering these definitions but a thorough understanding of them is essential if you want to apply them correctly.<BR>\n" );
document.write( "\"Distributive Property\" has to do with multiplying each number inside the parenthese by the number that is outside of the parentheses. <BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%284%2B2%29+=+3%2A4%2B3%2A2 ALIGN=MIDDLE  ALT=\"3%284%2B2%29+=+3%2A4%2B3%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2B6+=+18 ALIGN=MIDDLE  ALT=\"12%2B6+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Notice that the 3 outside the parentheses multiplies each term (number) inside the parenthese.<BR>\n" );
document.write( "Another example:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%286-4%29+=+5%2A6-5%2A4 ALIGN=MIDDLE  ALT=\"5%286-4%29+=+5%2A6-5%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30-20+=+10 ALIGN=MIDDLE  ALT=\"30-20+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Pay particular attention when the number outside the parentheses is negative.<BR>\n" );
document.write( "The result of multiplying a number by a negative number is a change in the sign.<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%287%2B3%29+=+%28-3%29%287%29%2B%28-3%29%283%29 ALIGN=MIDDLE  ALT=\"-3%287%2B3%29+=+%28-3%29%287%29%2B%28-3%29%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-21%2B%28-9%29+=+-30 ALIGN=MIDDLE  ALT=\"-21%2B%28-9%29+=+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "\"Associative Property\" has to do with grouping (associating).<BR>\n" );
document.write( "This property tells you that the way in which numbers are grouped (associated) when added or multiplied does not change the sum or product.<BR>\n" );
document.write( "Examples:<BR>\n" );
document.write( "\"Associative property of addition\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2B4%29%2B5+=+3%2B%284%2B5%29 ALIGN=MIDDLE  ALT=\"%283%2B4%29%2B5+=+3%2B%284%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2B5+=+3%2B9 ALIGN=MIDDLE  ALT=\"7%2B5+=+3%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Notice that it doesn't matter whether you add the 3 and the 4 first then the 5 or add the 4 and the 5 first then the 3, you will get the same result.<BR>\n" );
document.write( "\"Associative property of multiplication\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A4%29%2A5+=+3%2A%284%2A5%29 ALIGN=MIDDLE  ALT=\"%283%2A4%29%2A5+=+3%2A%284%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2A5+=+3%2A20 ALIGN=MIDDLE  ALT=\"12%2A5+=+3%2A20\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Here you'll see that it doesn't matter whether you multiply the 3*4 first then the 5 or multiply the 4*5 first then the 3, you get the same result.<BR>\n" );
document.write( "\"The Commutative Property\"  To \"commute\" means to change location or position.<BR>\n" );
document.write( "The commutative (notice the spelling, it's not \"communative\") Property tells you that the order in which numbers are add or multiplied does not change the sum or product.<BR>\n" );
document.write( "Examples:<BR>\n" );
document.write( "Comutative property of addition:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2B8+=+8%2B5 ALIGN=MIDDLE  ALT=\"5%2B8+=+8%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2B6%2B7+=+6%2B5%2B7 ALIGN=MIDDLE  ALT=\"5%2B6%2B7+=+6%2B5%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2B6%2B5+=+18 ALIGN=MIDDLE  ALT=\"7%2B6%2B5+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Commutative property of multiplication:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A4+=+4%2A3 ALIGN=MIDDLE  ALT=\"3%2A4+=+4%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A6%2A7+=+7%2A6%2A5 ALIGN=MIDDLE  ALT=\"5%2A6%2A7+=+7%2A6%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210 ALIGN=MIDDLE  ALT=\"210\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I hope this helps! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );