document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196915>Question 1196915</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a is to b as c is to d;that is, a/b =c/d<BR>\n" );
document.write( "a) Show that b is to a as d is to c.<BR>\n" );
document.write( "b) Show that a-b is to b as c-d is to d.<BR>\n" );
document.write( "c) Show that a is to a+b as c is to c+d.<BR>\n" );
document.write( "d) Show that a+b is to c+d as b is to d. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830317 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=830317\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your are given that a/b = c/d.<BR>\n" );
document.write( "multiply both sides by b and both sides by d to get:<BR>\n" );
document.write( "ad = bc<BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "start with b/a = d/c<BR>\n" );
document.write( "multiply both sides by a and both sides by c to get:<BR>\n" );
document.write( "bc = ad<BR>\n" );
document.write( "switch sides to get:<BR>\n" );
document.write( "ad = bc<BR>\n" );
document.write( "this is same as you got with the given, so they're equivalent.<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "start with (a-b)/b = (c-d)/d<BR>\n" );
document.write( "multiply both sides by b and both sides by d to get:<BR>\n" );
document.write( "(a-b) * d = (c-d) * b<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "ad - bd = cb - db<BR>\n" );
document.write( "rearrange to get:<BR>\n" );
document.write( "ad - bd = bc - bd<BR>\n" );
document.write( "add bd to both sides to get:<BR>\n" );
document.write( "ad = bc<BR>\n" );
document.write( "this is the same as you got with the given so they're equivalent.<BR>\n" );
document.write( "(c)<BR>\n" );
document.write( "start with a/(a+b) = c/(c+d)<BR>\n" );
document.write( "multiply both sides by (a+b) and both sides by (c+d) to get:<BR>\n" );
document.write( "a * (c+d) = c * (a+b)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "ac + ad = ca + cb<BR>\n" );
document.write( "rearrange to get:<BR>\n" );
document.write( "ac + ad = ac + bc<BR>\n" );
document.write( "subtract ac from both sides to get:<BR>\n" );
document.write( "ad = bc<BR>\n" );
document.write( "this is the same as you got with the given so they're equivalent.<BR>\n" );
document.write( "(d)<BR>\n" );
document.write( "start with (a+b)/(c+d) = b/d<BR>\n" );
document.write( "multiply both sides by (c+d) and both sides by d to get:<BR>\n" );
document.write( "(a+b) * d = b * (c+d)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "ad + bd = bc + bd<BR>\n" );
document.write( "subtract bd from both sides to get:<BR>\n" );
document.write( "ad = bc<BR>\n" );
document.write( "this is the same as you got with the given to they're equivalent.\r<BR>\n" );
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document.write( "another way to show they're equivalent is to assign values to each variable so that a/b = c/d.<BR>\n" );
document.write( "if i assumed that a = 5 and b = 25, then a/b = 1/5<BR>\n" );
document.write( "i then multiply numerator and denominator by the same value to get another ratio.<BR>\n" );
document.write( "i used 7 and got c=35 and d=175<BR>\n" );
document.write( "when a = 5 and b = 25 and c = 35 and d = 175, a/b = c/d becomes 5/25 = 35/175 which becomes .2 = .2<BR>\n" );
document.write( "cross multiply to get ad = bc which becomes 5*175 = 25*35 which becomes 875 = 875.\r<BR>\n" );
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document.write( "i used excel to do the calculations for the given and for problems (a) through (d).<BR>\n" );
document.write( "the results from all options gave results from column C equal to results from column D and results from column E equal to results from column F.<BR>\n" );
document.write( "this confirmed that all equations given in problems (a) through (d) are equivalent to results from the given equation.\r<BR>\n" );
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document.write( "here are the excel results.<BR>\n" );
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document.write( " </SPAN>\n" );
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