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 #366155 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=366155\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{a}{b}\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{c}{d}\"> be two rational numbers, where a,b,c,d are integers. Then,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}\">\r<BR>\n" );
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document.write( "Since integers are closed under addition and multiplication, the numerator and denominator will both be integers. Hence, the sum of two rational numbers is a rational number. We can also say that rational numbers are closed under addition. </SPAN>\n" );
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