document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=972769>Question 972769</A>: <I><SPAN STYLE=\"word-break: break-all;\">  	<BR>\n" );
document.write( "The numerator of a fraction (which is in its simplest form) is 5 less than the denominator. If the numerator is multiplied by 2, and the denominator is increased by 16, then the fraction becomes smaller by 1<BR>\n" );
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document.write( "of it. Find the original fraction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #595166 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=595166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> original fraction is (x-5) / x\r<BR>\n" );
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document.write( "when you multiply the numerator by 2 and add 16 to the denominator, the original fraction is reduced by 1/3.\r<BR>\n" );
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document.write( "this means the original fraction is equal to 2/3 times what it was originally.\r<BR>\n" );
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document.write( "your equation is:\r<BR>\n" );
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document.write( "(x-5) * 2 divided by x + 16<BR>\n" );
document.write( "is equal to 2/3 * (x-5) / x\r<BR>\n" );
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document.write( " this is equivalent to:\r<BR>\n" );
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document.write( "(x-5) * 2 / (x + 16) = ((x-5) * 2) / 3x\r<BR>\n" );
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document.write( "multiply both sides of the equation by (x+16) and by (3x) and you get:\r<BR>\n" );
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document.write( "(x-5) * 2 * (3x) = (x-5) * 2 * (x+16) \r<BR>\n" );
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document.write( "divide both sides of this equation by (x-5) and you get:\r<BR>\n" );
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document.write( "2 * 3x = 2 * (x + 16)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "6x = 2x + 32\r<BR>\n" );
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document.write( "subtract 2x from both sides of this equation to get:\r<BR>\n" );
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document.write( "4x = 32\r<BR>\n" );
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document.write( "divide both sides of this equation by 4 to get:\r<BR>\n" );
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document.write( "x = 8\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "your original fraction is (8-5)/8 = 3/8\r<BR>\n" );
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document.write( "your final fraction is (3 * 2) / (8 + 16) = 6 / 24 = 1/4\r<BR>\n" );
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document.write( "your original fraction of 3/8 * 2/3 = 6/24 = 1/4.\r<BR>\n" );
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document.write( "this is the same as your original fraction being reduced by 1/3.\r<BR>\n" );
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document.write( "3/8 - 1/3 * 3/8 = 3/8 - 3/24 = 9/24 - 3/24 = 6/24 = 1/4.\r<BR>\n" );
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document.write( "the questions was what is the original fraction.\r<BR>\n" );
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document.write( "the answer is that the original fraction is 3/8.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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