document.write( "Question 846331: Two thirds of a cake is left from a birthday party. Ginny decides to give 3/4 of the remaining cake to joe. What part of the entire cake will joe receive? \n" ); document.write( "

Algebra.Com's Answer #509724 by KMST(5347) $\"\"$ $\"About$

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Joe will get $\"3%2F4\"$ of $\"2%2F3\"$ of the cake.
\n" ); document.write( "When you want to find $\"3%2F4\"$ of something (like $\"3%2F4\"$ of 48 apples),
\n" ); document.write( "you multiply times $\"3%2F4\"$ ,
\n" ); document.write( "and the same goes if you are trying to find $\"3%2F4\"$ of $\"2%2F3\"$ of a cake.
\n" ); document.write( "

\n" ); document.write( "Joe will get 1/2 of the cake.
\n" ); document.write( "
\n" ); document.write( "ANOTHER WAY:
\n" ); document.write( "Since we have thirds and fourths,
\n" ); document.write( " $\"12\"$ could be a common denominator,
\n" ); document.write( "so let's think of twelfths.
\n" ); document.write( "Supposed that the cake came conveniently cut into $\"12\"$ equal slices.
\n" ); document.write( "Each slice is $\"1%2F12\"$ of the cake.
\n" ); document.write( "If you have $\"2%2F3\"$ of the cake left, you have $\"8\"$ slices left,
\n" ); document.write( "because $\"4\"$ slices would be $\"1%2F3\"$ of the cake,
\n" ); document.write( "and $\"8\"$ slices is twice $\"4\"$ slices.
\n" ); document.write( "To figure those $\"8\"$ slices, out of the original $\"12\"$ ,
\n" ); document.write( "you divided by $\"3\"$ to get $\"1%2F3\"$ ,
\n" ); document.write( "and then multiplied times $\"2\"$ to get $\"2%2F3\"$ of the original $\"12\"$ slices.
\n" ); document.write( "That is $\"12%2A%282%2F3%29=12%2A2%2F3=%2812%2F3%29%2A2=8\"$ .
\n" ); document.write( "You are multiplying times $\"2%2F3\"$ when you
\n" ); document.write( "first divide by $\"3\"$ and then multiply times $\"2\"$ , or
\n" ); document.write( "when you multiply times $\"2\"$ and then divide by $\"3\"$ .
\n" ); document.write( "It's all the same.
\n" ); document.write( "Now, $\"1%2F4\"$ of those $\"8\"$ slices left would be $\"2\"$ slices,
\n" ); document.write( "and $\"3%2F4\"$ of those $\"8\"$ slices left would be $\"6\"$ slices that you give to Joe.
\n" ); document.write( "Since the whole cake was $\"12\"$ slices, those $\"6\"$ slices are half of the cake. \n" ); document.write( "

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