document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=566235>Question 566235</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that the sum of any pair of rational numbers is a rational number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #366153 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=366153\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let p = a/b and q = c/d be two rational numbers, where a, b, c, d are integers.\r<BR>\n" );
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document.write( "Now add them:\r<BR>\n" );
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document.write( "p + q\r<BR>\n" );
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document.write( "a/b + c/d\r<BR>\n" );
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document.write( "(ad)/(bd)+(bc)/(bd)\r<BR>\n" );
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document.write( "(ad+bc)/(bd)\r<BR>\n" );
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document.write( "So p + q = (ad+bc)/(bd), which is a rational number (the numerator and denominator are both integers since integer addition and multiplication are both closed operations)\r<BR>\n" );
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document.write( "So this proves that the sum of any pair of rational numbers is a rational number. </SPAN>\n" );
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