document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=52209>Question 52209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is \"solving equation and problems\" \"Transforming equations-multiplication and division\".\r<BR>\n" );
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document.write( "           1/2x=22 <BR>\n" );
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document.write( "  I read something about getting the reciprocal of 1/2 so i guess 2/1. i dunno. can some one help by explaining the WHOLE precess to me. I think these are fractions, bu it could be division. I feel so stupid. Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #34783 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=34783\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Whenever you see a fraction, division is going on<BR>\n" );
document.write( "Whenever you are asked to do a division, you can<BR>\n" );
document.write( "always express the division as a fraction<BR>\n" );
document.write( "OR, fractions are division and division is fractions<BR>\n" );
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document.write( "One of the best tools you can use when working with<BR>\n" );
document.write( "fractions is the rule:<BR>\n" );
document.write( " If you multiply the top and the bottom of a fraction<BR>\n" );
document.write( " by the same quantity, the fraction does not change<BR>\n" );
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document.write( "That's because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F5+=+13%2F13 ALIGN=MIDDLE  ALT=\"5%2F5+=+13%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%2Fy+=+759%2F759 ALIGN=MIDDLE  ALT=\"+y%2Fy+=+759%2F759\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1+=+6%2F6 ALIGN=MIDDLE  ALT=\"1%2F1+=+6%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "They are all equal to 1 exactly.<BR>\n" );
document.write( "So, if I have the fraction 1/3, all these are true<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F5%29%2A%281%2F3%29+=+%2813%2F13%29%2A%281%2F3%29+=+%28y%2Fy%29%2A%281%2F3%29+=+%28759%2F759%29%2A%281%2F3%29+=+%281%2F1%29%2A%281%2F3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "All of these are the exact same thing as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%2A%281%2F3%29 ALIGN=MIDDLE  ALT=\"%281%29%2A%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that<BR>\n" );
document.write( "is just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, what if you have the strange fraction that looks like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2F+%281%2F3%29 ALIGN=MIDDLE  ALT=\"1+%2F+%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >?<BR>\n" );
document.write( "This is the RECIPROCAL of 1/3<BR>\n" );
document.write( "just apply the rule I gave you, but choose the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Fn ALIGN=MIDDLE  ALT=\"n%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > carefully<BR>\n" );
document.write( "multiply this fraction by 3/3. One more useful fact: you can<BR>\n" );
document.write( "always write a number this way with out changing it:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+=+5%2F1 ALIGN=MIDDLE  ALT=\"5+=+5%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > because dividing by one doesn't change the number<BR>\n" );
document.write( "Back to the fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2F+%281%2F3%29 ALIGN=MIDDLE  ALT=\"1+%2F+%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply it by 3/3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F3%29%2A%281%2F%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"%283%2F3%29%2A%281%2F%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > take a deep breath. You haven't changed anything.<BR>\n" );
document.write( "It's still 1/3. Now just let the number on top associate with eachother and<BR>\n" );
document.write( "same for the bottom<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F3%29%2A%281%2F%281%2F3%29%29+=+%283%2A1%29+%2F+%28%283%29%2A%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"%283%2F3%29%2A%281%2F%281%2F3%29%29+=+%283%2A1%29+%2F+%28%283%29%2A%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > another deep breath. <BR>\n" );
document.write( "You still haven't changed anything<BR>\n" );
document.write( "Now you just have to realize that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%281%2F3%29+=+1 ALIGN=MIDDLE  ALT=\"3%2A%281%2F3%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Three thirds is one<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A1%29+%2F+%28%283%29%2A%281%2F3%29%29+=+%283%2A1%29+%2F+1 ALIGN=MIDDLE  ALT=\"%283%2A1%29+%2F+%28%283%29%2A%281%2F3%29%29+=+%283%2A1%29+%2F+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > You still haven't changed anything<BR>\n" );
document.write( "Now note that 3*1 = 3 just the same as 3/1 = 3 so,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A1%29+%2F+1+=+3+%2F+1 ALIGN=MIDDLE  ALT=\"%283%2A1%29+%2F+1+=+3+%2F+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F1+=+3 ALIGN=MIDDLE  ALT=\"3%2F1+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > You STILL haven't changed anything!<BR>\n" );
document.write( "So, going ALL the way back, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2F+%281%2F3%29+=+3 ALIGN=MIDDLE  ALT=\"1+%2F+%281%2F3%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > The reciprocal of 1/3 equals 3.<BR>\n" );
document.write( "Think in these tiny steps. Don't try to jerk your brain<BR>\n" );
document.write( "ahead too far (It hurts the brain). Hope I helped </SPAN>\n" );
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