document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95014>Question 95014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Place parentheses to make the following equation true\r<BR>\n" );
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document.write( "13 - 4 x 5  / 2 +10 = 13 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69138 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=69138\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "13 - 4 x 5  / 2 +10 = 13<BR>\n" );
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document.write( "Let's replace the x with the multiplication symbol *. It doesn't change the problem, but<BR>\n" );
document.write( "it makes it a little easier to read because we won't confuse the x (meaning times) with the<BR>\n" );
document.write( "letter x which is often used as an unknown in algebra. So the given equation becomes:<BR>\n" );
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document.write( "13 - 4 * 5/2 +10 = 13<BR>\n" );
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document.write( "How about if we put parentheses around the middle term to set it apart as follows:<BR>\n" );
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document.write( "13 -((4*5)/2) + 10 = 13<BR>\n" );
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document.write( "The parentheses now make this problem in the textbook form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13+-%28%284%2A5%29%2F2%29+%2B+10+=+13 ALIGN=MIDDLE  ALT=\"13+-%28%284%2A5%29%2F2%29+%2B+10+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that the 4*5 is 20 and when you divide that by the 2 you get 10. This reduces<BR>\n" );
document.write( "the problem to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13+-+10+%2B+10+=+13 ALIGN=MIDDLE  ALT=\"13+-+10+%2B+10+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And the -10 and +10 cancel each other out, so the problem is reduced to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+13+=+13 ALIGN=MIDDLE  ALT=\"+13+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is a true statement, so by using the parentheses the way we did we made the given problem<BR>\n" );
document.write( "much easier to understand because it was then in the correct form.<BR>\n" );
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document.write( "The lesson here is that using parentheses can really help to clarify a problem. You see<BR>\n" );
document.write( "a lot of students in this forum write things such as:<BR>\n" );
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document.write( "2/x+7<BR>\n" );
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document.write( "According to the rules governing the order of operations, this means:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fx+%2B+7 ALIGN=MIDDLE  ALT=\"2%2Fx+%2B+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "but you wonder if they didn't mean to write 2/(x+7) which is completely different <BR>\n" );
document.write( "because it means:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28x%2B7%29 ALIGN=MIDDLE  ALT=\"2%2F%28x%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That lack of clarity causes some tutors to disregard the problem because they don't know<BR>\n" );
document.write( "which version they should work and they may just confuse the student by working the wrong<BR>\n" );
document.write( "one.<BR>\n" );
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document.write( "Hope this helps you to understand the importance of parentheses.  It sure doesn't hurt<BR>\n" );
document.write( "to use them to make sure you are communicating what you mean in a problem.<BR>\n" );
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