document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=365466>Question 365466</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the order to follow when working a math problem. For instance 5-3÷3= WHAT </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #260544 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=260544\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the order is:\r<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "\r\n" );
document.write( "you work from left to right.\r\n" );
document.write( "expressions within the inner set of parentheses are done first.\r\n" );
document.write( "expressions within the outer set of parentheses are done next.\r\n" );
document.write( "an expression without any parentheses has an implied set of parentheses that surrounds the whole problem.\r\n" );
document.write( "within each set of parentheses:\r\n" );
document.write( "     radicals and exponents are processed first from left to right.\r\n" );
document.write( "     multiplication and division are processed second from left to right.\r\n" );
document.write( "     addition and subtraction are processed third from left to right.\r\n" );
document.write( "\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in your problem, your expression is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5-3/3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "there are no inner parentheses to process first.<BR>\n" );
document.write( "an outer set of parentheses is implied which would make your equation look like:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(5-3/3)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have no radicals or exponents so these do not have to be done.<BR>\n" );
document.write( "you have a division so that is done next to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "( 5 - (3/3) ) = (5 - 1)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have a subtraction, so you process that next to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(5 - 1) = (4)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the outer set of parentheses does not have to be shown, so your answer is 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "looking back at your original problem, if you inserted parentheses where required, it would have looked like this:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(5 - (3/3)).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the inner set of parentheses would have been processed first to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(5 - 1).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the outer set of parentheses would have been processed next to get 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the parentheses can alter the order of operations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in your example, it was implied that:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5 - 3/3 was the same as (5 - (3/3))\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to alter the order of operations, you would put the parentheses surrounding the operations you wanted to be performed first.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in this case, if you wanted to subtract the 3 from the 5 before dividing by 3, then you would have had to use parentheses as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "((5-3)/3)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now the inner set of parentheses is still done first, but in this case it is the subtraction.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you would get (2/3) which becomes 2/3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "without any parentheses at all, the order of operations is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "exponents and radicals first from left to right.<BR>\n" );
document.write( "multiplication and division second from left to right.<BR>\n" );
document.write( "addition and subtraction third from left to right.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is the same order as shown above for within each set of parentheses.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "process from left to right means that, if the order of the operations is the same, then you do the leftmost operations before doing the rightmost operations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5 - 3 / 3 + 7 + 8/4 + 8 + 3^2 would be processed as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3^2 would be processed first to get 9<BR>\n" );
document.write( "3/2 would be processed next to get 1<BR>\n" );
document.write( "8/4 would be processed next to get 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your formula would become:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5 - 1 + 7 + 2 + 8 + 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5-1 would be processed next to get 4<BR>\n" );
document.write( "4+7 would be processed next to get 11<BR>\n" );
document.write( "11+2 would be processed next to get 13<BR>\n" );
document.write( "13 + 8 would be processed next to get 21<BR>\n" );
document.write( "21 + 9 would be processed next to get 30.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );