document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=863607>Question 863607</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I explain to a 6th grader the process to figure out, \"64% of what number is 84\".\r<BR>\n" );
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document.write( "thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #520491 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=520491\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i would start with discussing the reversibility of operations, such as:\r<BR>\n" );
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document.write( "if 3 * 4 = 12, then 12 / 4 = 3 and 12 / 3 = 4<BR>\n" );
document.write( "this is a basic rule of reversibility of operations that states that, in general:<BR>\n" );
document.write( "if a * b = c, then b = c/a and a = c/b.\r<BR>\n" );
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document.write( "this rule of reversibility applies to all mathematical operations.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "if 4 + 3 = 7, then 7 - 4 = 3 and 7 - 3 = 4\r<BR>\n" );
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document.write( "etc.\r<BR>\n" );
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document.write( "you can demonstrate this rule by several examples, such as:\r<BR>\n" );
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document.write( "4 * 2 = 8<BR>\n" );
document.write( "8 / 4 = 2<BR>\n" );
document.write( "8 / 2 = 4\r<BR>\n" );
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document.write( "or:\r<BR>\n" );
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document.write( "20 * 5 = 100<BR>\n" );
document.write( "100 / 20 = 5<BR>\n" );
document.write( "100 / 5 = 20\r<BR>\n" );
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document.write( "you can then tell the student that the questions involves this same principle, because:\r<BR>\n" );
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document.write( "64% of a number is equal to .64 * the number.\r<BR>\n" );
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document.write( "this is another rule that the student should know in order to solve this problem.\r<BR>\n" );
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document.write( "now you can introduce the problem again such as:\r<BR>\n" );
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document.write( "64% of what number is equal to 84.\r<BR>\n" );
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document.write( "this is the same as:\r<BR>\n" );
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document.write( ".64 * what number is equal to 84.\r<BR>\n" );
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document.write( "by the reversibility of operations rule, this means that:\r<BR>\n" );
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document.write( "84 / .64 = the number\r<BR>\n" );
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document.write( "or:\r<BR>\n" );
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document.write( "84 / the number = .64\r<BR>\n" );
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document.write( "the student, by this time, should know how to divide 84 by .64.\r<BR>\n" );
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document.write( "for a problem as sophisticated as this one, however, i would resort to the calculator so the student doesn't get bogged down in the arithmetic.\r<BR>\n" );
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document.write( "after applyig the division, the studet should get:\r<BR>\n" );
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document.write( "84 /.64 = 132.25\r<BR>\n" );
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document.write( "now you can confirm for the student that this answer is good by applying the rule of reversibility to get:\r<BR>\n" );
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document.write( ".64 * 132.25 = 84\r<BR>\n" );
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document.write( "84 / .64 = 132.25\r<BR>\n" );
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document.write( "84 / 132.25 = .64\r<BR>\n" );
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document.write( "you can use your calculator again for this part.\r<BR>\n" );
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document.write( "if you want to show the student without using the calculator, then choose a simpler problem, such as:\r<BR>\n" );
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document.write( "50% of what number = 200\r<BR>\n" );
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document.write( "same deal applies\r<BR>\n" );
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document.write( "this means that .5 times what number = 200\r<BR>\n" );
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document.write( "this is true if and only if:\r<BR>\n" );
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document.write( "200 / .5 = the number or:\r<BR>\n" );
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document.write( "200 / the number = .5\r<BR>\n" );
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document.write( "you then divide 200 by .5 to get 200 / (1/2) which becomes 200 * (2/1) which becomes 400\r<BR>\n" );
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document.write( "400 is the number.\r<BR>\n" );
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document.write( "you confirm by applying the rule.\r<BR>\n" );
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document.write( ".5 * 400 = 200\r<BR>\n" );
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document.write( "200 / .5 = 400\r<BR>\n" );
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document.write( "200 / 400 = .5\r<BR>\n" );
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document.write( "the rule of reversibility is how the students check their work all the time so this should not be a novel idea to the student.\r<BR>\n" );
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document.write( "by now the student should have learned that 64% of a number is the same as .64 times the number.\r<BR>\n" );
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document.write( "if not, you may have to sped some time teaching about that concept.\r<BR>\n" );
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document.write( "at the end, you can show the student the short cut.\r<BR>\n" );
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document.write( "if 64% of a number is equal to 84, the you find the number by dividing 84 by .64.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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