document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=616252>Question 616252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am havig difficulty determining the value of a determinant when there are fractions. Is there a short, easy way for me to evaluate? For example: \r<BR>\n" );
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document.write( "|3/4    3/4|<BR>\n" );
document.write( "|1/16  -1/8|\r<BR>\n" );
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document.write( "I know the following: <BR>\n" );
document.write( "(3/4)(-1/8)-(1/16)(3/4) = -3/32-3/64 = -9/64<BR>\n" );
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document.write( "what I cant explain is the numberator. Where is the -9 coming from? Please help!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #387586 by </B><A HREF=/tutors/aboutme.mpl?userid=dragonwalker><B>dragonwalker(73)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dragonwalker><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=387586\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (3/4)(-1/8)-(1/16)(3/4) = -3/32-3/64 = -9/64\r<BR>\n" );
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document.write( "Look at the denominator of the final two parts.\r<BR>\n" );
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document.write( "Notice you have -3/32 but then -3/64  and the result is -9/64\r<BR>\n" );
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document.write( "If you just use -3 -3 to figure out the final numerator then you are not accounting for the size that each numerator represents.\r<BR>\n" );
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document.write( "Picture a fraction as pieces of pie fitting into a pie pan. The denominator tells you how many slices fit into the pan. The bigger the denominator the smaller each piece of pie is. \r<BR>\n" );
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document.write( "So if you have a fraction that has a denominator of 64 each unit of a numerator represents a smaller size than if the denominator is 32 (64 pieces of pie fitting in a pie pan rather than 32)\r<BR>\n" );
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document.write( "Before adding or subtracting the numerators you need to make the denominators the same size.\r<BR>\n" );
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document.write( "The easiest way is to see if the smaller denominator(s) fit in the largest denominator. In this case 32 fits into 64 twice.\r<BR>\n" );
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document.write( "However if you change 3/32's denominator to 64 you have to take into account that each numerator has to represent a smaller piece. In fact in this case they have to be half the size so that 64 pieces could fit into a whole pie (or a whole number). So if you cut three pieces of pie into half each you will get twice as many pieces so you would now have 6 pieces of pie.\r<BR>\n" );
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document.write( "The easiest way to remember this is if you are multiplying the denominator by a certain number, the numerator has to be multiplied by the same number to keep the fraction the same size.\r<BR>\n" );
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document.write( "So -3/32 becomes -6/64\r<BR>\n" );
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document.write( "Now if you type the formula again you get:\r<BR>\n" );
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document.write( "-6/64 - 3/64 = -9/64 </SPAN>\n" );
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