document.write( "Question 656308: the numerator of a certain fraction is 5 times the denominator. if 6 is added to both the numerator and the denominator, the resulting fraction is equivalent to 2. what was the original fraction? \n" ); document.write( "

Algebra.Com's Answer #409476 by KMST(5328) $\"\"$ $\"About$

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Let $\"x\"$ be the denominator.
\n" ); document.write( "Then, the numerator is $\"5x\"$ , and the fraction is $\"5x%2Fx\"$ , which is equivalent to $\"5\"$ .
\n" ); document.write( " $\"5x%2Fx=5\"$
\n" ); document.write( "If you add $\"6\"$ to both the numerator and the denominator, the resulting fraction is
\n" ); document.write( " $\"%285x%2B6%29%2F%28x%2B6%29\"$
\n" ); document.write( "That fraction is equivalent to $\"2\"$ , so we can write
\n" ); document.write( " $\"%285x%2B6%29%2F%28x%2B6%29=2\"$
\n" ); document.write( "Multiplying both sides of the equal sign times $\"%28x%2B6%29\"$ we get
\n" ); document.write( " $\"%28%285x%2B6%29%2F%28x%2B6%29%29%2A%28x%2B6%29=2%2A%28x%2B6%29\"$ --> $\"5x%2B6=2%28x%2B6%29\"$ --> $\"5x%2B6=2x%2B2%2A6\"$ --> $\"5x%2B6=2x%2B12\"$
\n" ); document.write( "Subtracting $\"2x\"$ from both sides we get
\n" ); document.write( " $\"5x%2B6-2x=2x%2B12-2x\"$ --> $\"3x%2B6=12\"$
\n" ); document.write( "Subtracting $\"6\"$ from both sides we get
\n" ); document.write( " $\"3x%2B6-6=12-6\"$ --> $\"3x=6\"$
\n" ); document.write( "Dividing both sides by 3 we get
\n" ); document.write( " $\"3x%2F3=6%2F3\"$ --> $\"x=2\"$
\n" ); document.write( "So the original fraction was
\n" ); document.write( " $\"5x%2Fx=5%2A2%2F2\"$
\n" ); document.write( "or $\"highlight%2810%2F2%29\"$ \n" ); document.write( "

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