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Explanation:
Multiply the denominators to get 3*4 = 12. We'll use this value to set up the number of slices we start with.
If we started with 12 slices, then 1/3 of this is (1/3)*12 = 4 slices. So Carlos ate 4 slices. There are 12-4 = 8 slices left.
1/4 of that value is (1/4)*8 = 2 which is the number of slices given to his friend.
Divide the number of slices given to the friend (2) over the number we started with (12) to get 2/12 = 1/6
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Another approach:
If Carlos ate 1/3 of the full pie, then there are 2/3 of it left.
1/4 of this is (1/4)*(2/3) = (1*2)/(4*3) = 2/12 = 1/6 which represents the fractional amount of the original pie given to the friend.
