document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=439478>Question 439478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having issues understanding how and when to \"reorder the operations\".  It appears when the reorder of operations is done that all expressions with a letter get moved to the right and all subtraction problems get changed to additions problems.  What are the rules of this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #303726 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=303726\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first something about the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ORDER ALIGN=MIDDLE  ALT=\"ORDER\"   DISABLED_style= \"max-width:90%; height:auto;\" > OF OPERATIONS RULES\r<BR>\n" );
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document.write( "When performing more than one operation on an algebraic expression, work out the operations and signs in the following order:\r<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=First ALIGN=MIDDLE  ALT=\"First\"   DISABLED_style= \"max-width:90%; height:auto;\" > calculate powers and roots.\r<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Then ALIGN=MIDDLE  ALT=\"Then\"   DISABLED_style= \"max-width:90%; height:auto;\" > perform all multiplication and division.\r<BR>\n" );
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document.write( "    Finally, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=finish ALIGN=MIDDLE  ALT=\"finish\"   DISABLED_style= \"max-width:90%; height:auto;\" > with addition and subtraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Order ALIGN=MIDDLE  ALT=\"Order\"   DISABLED_style= \"max-width:90%; height:auto;\" > of operations are a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=set ALIGN=MIDDLE  ALT=\"set\"   DISABLED_style= \"max-width:90%; height:auto;\" > of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rules ALIGN=MIDDLE  ALT=\"rules\"   DISABLED_style= \"max-width:90%; height:auto;\" > that mathematicians have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=agreed ALIGN=MIDDLE  ALT=\"agreed\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=follow ALIGN=MIDDLE  ALT=\"follow\"   DISABLED_style= \"max-width:90%; height:auto;\" > to avoid mass <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CONFUSION ALIGN=MIDDLE  ALT=\"CONFUSION\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=simplifying ALIGN=MIDDLE  ALT=\"simplifying\"   DISABLED_style= \"max-width:90%; height:auto;\" > mathematical expressions or equations.\r<BR>\n" );
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document.write( "easier way to remember the ORDER OF OPERATIONS RULES\r<BR>\n" );
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document.write( "For those of you that remember best with acronyms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Please ALIGN=MIDDLE  ALT=\"Please\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Excuse+ ALIGN=MIDDLE  ALT=\"+Excuse+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=My ALIGN=MIDDLE  ALT=\"My\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Dear ALIGN=MIDDLE  ALT=\"+Dear\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Aunt ALIGN=MIDDLE  ALT=\"+Aunt\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Sally ALIGN=MIDDLE  ALT=\"+Sally\"   DISABLED_style= \"max-width:90%; height:auto;\" > (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PEMDAS ALIGN=MIDDLE  ALT=\"PEMDAS\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "    Please ...=>...Parentheses\r<BR>\n" );
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document.write( "    Escuse...=>...Exponents\r<BR>\n" );
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document.write( "    My ...=>...Multiplication\r<BR>\n" );
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document.write( "    Dear ...=>...Division\r<BR>\n" );
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document.write( "    Aunt ...=>...Addition\r<BR>\n" );
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document.write( "    Sally ...=>...Subtraction\r<BR>\n" );
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document.write( "now, about the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RE-ORDER ALIGN=MIDDLE  ALT=\"RE-ORDER\"   DISABLED_style= \"max-width:90%; height:auto;\" > OF OPERATIONS RULES  \r<BR>\n" );
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document.write( "the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Associative ALIGN=MIDDLE  ALT=\"Associative\"   DISABLED_style= \"max-width:90%; height:auto;\" > Property, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=commutative ALIGN=MIDDLE  ALT=\"commutative\"   DISABLED_style= \"max-width:90%; height:auto;\" > property, and the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=distributive ALIGN=MIDDLE  ALT=\"distributive\"   DISABLED_style= \"max-width:90%; height:auto;\" > property-three basic properties of numbers- allow you to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=move ALIGN=MIDDLE  ALT=\"move\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+stuff ALIGN=MIDDLE  ALT=\"+stuff\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+around ALIGN=MIDDLE  ALT=\"+around\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=regroup ALIGN=MIDDLE  ALT=\"regroup\"   DISABLED_style= \"max-width:90%; height:auto;\" >, all <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=without ALIGN=MIDDLE  ALT=\"without\"   DISABLED_style= \"max-width:90%; height:auto;\" > affecting the result\r<BR>\n" );
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document.write( "the Associative Property-Use the associative property to change the grouping in an algebraic expression to make the work tidier or more convenient.\r<BR>\n" );
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document.write( "The commutative property makes working with algebraic expressions easier. The commutative property changes the order of some numbers in an operation to make the work tidier or more convenient — all without affecting the result.\r<BR>\n" );
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document.write( "Addition: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+=+b+%2B+a ALIGN=MIDDLE  ALT=\"a+%2B+b+=+b+%2B+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Example: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2B+5+=+9 ALIGN=MIDDLE  ALT=\"4+%2B+5+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%2B+4+=+9 ALIGN=MIDDLE  ALT=\"5+%2B+4+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2B+5+=+5+%2B+4 ALIGN=MIDDLE  ALT=\"4+%2B+5+=+5+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Reordering ALIGN=MIDDLE  ALT=\"Reordering\"   DISABLED_style= \"max-width:90%; height:auto;\" > the numbers <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=doesn%27t ALIGN=MIDDLE  ALT=\"doesn%27t\"   DISABLED_style= \"max-width:90%; height:auto;\" > affect the result.\r<BR>\n" );
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document.write( "Multiplication:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2A+b+=+b+%2A+a ALIGN=MIDDLE  ALT=\"a+%2A+b+=+b+%2A+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtraction: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%96+b+ ALIGN=MIDDLE  ALT=\"a+%96+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+%96+a+ ALIGN=MIDDLE  ALT=\"+b+%96+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >(except in a few special cases)\r<BR>\n" );
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document.write( "Example: (–5) – (+2) = (–7) and (+2) – (–5) = +7, so (–5) – (+2) is not equal to  (+2) – (–5)\r<BR>\n" );
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document.write( "Here, you see how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=subtraction ALIGN=MIDDLE  ALT=\"subtraction\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=doesn%27t ALIGN=MIDDLE  ALT=\"doesn%27t\"   DISABLED_style= \"max-width:90%; height:auto;\" > follow the commutative property.\r<BR>\n" );
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document.write( "Exception: If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the same number, then the subtraction appears to be commutative because switching the order doesn’t change the answer.\r<BR>\n" );
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document.write( "Example: 2 –2 = 0 and –2 + 2 = 0, so 2 –2 = –2 + 2\r<BR>\n" );
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document.write( "Division: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3Ab+not=+b+%F7+a ALIGN=MIDDLE  ALT=\"a+%3Ab+not=+b+%F7+a\"   DISABLED_style= \"max-width:90%; height:auto;\" > (except in a few special cases)\r<BR>\n" );
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document.write( "Example: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6%29+%3A+%28%2B1%29+=+-6 ALIGN=MIDDLE  ALT=\"%28-6%29+%3A+%28%2B1%29+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2B1%29+%3A+%28-6%29+=+-1%2F6 ALIGN=MIDDLE  ALT=\"%28%2B1%29+%3A+%28-6%29+=+-1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6%29+%F7+%28%2B1%29 ALIGN=MIDDLE  ALT=\"%28-6%29+%F7+%28%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2B1%29+%2F+-6%29 ALIGN=MIDDLE  ALT=\"%28%2B1%29+%2F+-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Division also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=doesn%27t ALIGN=MIDDLE  ALT=\"doesn%27t\"   DISABLED_style= \"max-width:90%; height:auto;\" > follow the commutative property.\r<BR>\n" );
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document.write( "Exception: If a and b are opposites, then you get –1 no matter which order you divide them in.\r<BR>\n" );
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document.write( "Example: 2 : –2 = –1 and –2:2 = –1, so 2:–2 = –2 :2\r<BR>\n" );
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document.write( " </SPAN>\n" );
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