document.write( "Question 412244: If 2 is added to the numerator of a fraction, the resulting fraction is 2/3. If 1 is subtracted from the denominator, the resulting fraction is 1/2. What is the original fraction? \n" ); document.write( "
Algebra.Com's Answer #289589 by mananth(16946)\"\" \"About 
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If 2 is added to the numerator of a fraction, the resulting fraction is 2/3. If 1 is subtracted from the denominator, the resulting fraction is 1/2. What is the original fraction? \r
\n" ); document.write( "\n" ); document.write( "let x be in the numerator
\n" ); document.write( "y denominator
\n" ); document.write( "x/y fraction
\n" ); document.write( "x+2/y = 2/3
\n" ); document.write( "cross multiply
\n" ); document.write( "3(x+2)=2y
\n" ); document.write( "3x+6=2y
\n" ); document.write( "3x-2y=-6........1
\n" ); document.write( "...
\n" ); document.write( "x/(y-1)=1/2
\n" ); document.write( "cross multiply
\n" ); document.write( "2x=y-1
\n" ); document.write( "2x-y=-1..........2\r
\n" ); document.write( "\n" ); document.write( "multiply (2) by -2
\n" ); document.write( "-4x+2y=+2
\n" ); document.write( "add to (1)
\n" ); document.write( "-x=-4
\n" ); document.write( "x=4 numerator\r
\n" ); document.write( "\n" ); document.write( "plug value ofy in (2)
\n" ); document.write( "y=9\r
\n" ); document.write( "\n" ); document.write( "4/9 is the fraction \n" ); document.write( "
\n" );