document.write( "Question 305634: What is the reasoning behind the division of fractions? For example, what does it mean to divide 1/2 by 2/3? Note: I'm not looking for the algorithm or the rule for generating the correct answer but rather the explanation of what it means. \n" ); document.write( "
Algebra.Com's Answer #218814 by richwmiller(17219)\"\" \"About 
You can put this solution on YOUR website!
Well let's take a slightly different problem that can be easily expressed in decimal format.
\n" ); document.write( "1/2 divided by 3/4
\n" ); document.write( ".50/.75
\n" ); document.write( "multiply by 100
\n" ); document.write( "50/75
\n" ); document.write( "factor out 25
\n" ); document.write( "2/3
\n" ); document.write( "What just happened.
\n" ); document.write( "We want to know how many times 3/4 can go into 1/2
\n" ); document.write( "Well it can't go a complete time because 3/4 is larger than 1/2
\n" ); document.write( "the ratio holds true for 50/75
\n" ); document.write( "How many times can 75 go into 50 it can't one whole time. It can go 2/3 of 1 time?\r
\n" ); document.write( "\n" ); document.write( "But what is interesting to me about this problem and yours is how we resolve the problem using fractions.
\n" ); document.write( "(1/2)/(2/3)=1/2*3/2=/3/4
\n" ); document.write( "and
\n" ); document.write( "(1/2) /(3/4) = 1/2*4/3=4/6=2/3 as we learned before.\r
\n" ); document.write( "\n" ); document.write( "We used the reciprocals to multiply rather than divide.
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