document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=534254>Question 534254</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is a reciprocal </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #351419 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=351419\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The reciprocal is a number that, when multiplied by the original number, yields 1.<BR>\n" );
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document.write( "In simplest terms, the reciprocal of the number 'x' is 1/x.<BR>\n" );
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document.write( "The reciprocal of a fraction is the fraction \"upside\" down.<BR>\n" );
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document.write( "Say you have a fraction 'a/b'.  The reciprocal is 'b/a'.<BR>\n" );
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document.write( "As you can imagine, reciprocals can be defined for functions, too.<BR>\n" );
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document.write( "Let's say you have 'x +1'.  The reciprocal is 1/(x+1).<BR>\n" );
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document.write( "The reciprocal also is defined by exponents.<BR>\n" );
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document.write( "Given you have 'x', that is the same as saying you have 'x^1' because any number to the power 1 = itself.<BR>\n" );
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document.write( "We also know that any number raised to the 0th power = 1.<BR>\n" );
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document.write( "When we multiply the same number raised to powers you add the exponents.<BR>\n" );
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document.write( "As noted above, x = x^1<BR>\n" );
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document.write( "In general,<BR>\n" );
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document.write( "So you probably can guess the reciprocal of 'x^1'.<BR>\n" );
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document.write( "'y' has to = -1<BR>\n" );
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document.write( "This definition of the reciprocal also reveals that negative exponents can be shown as fractions.<BR>\n" );
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document.write( "That's a lot to cover in one answer, but I hope it gives you feel for the definition and usefulness of the reciprocal.<BR>\n" );
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