1. Initially, Sarah has 1 whole cake. 2. She gives 1/3 of the cake to her neighbor, so the remaining cake is 1 - 1/3 = 2/3 of the original cake. 3. She then eats 1/4 of the *remaining* cake. This means she eats (1/4) * (2/3) = 2/12 = 1/6 of the original cake. 4. The total fraction of cake consumed or given away is the sum of what the neighbor received and what Sarah ate: (1/3) + (1/6) = (2/6) + (1/6) = 3/6 = 1/2 of the original cake. 5. Therefore, the fraction of the original cake left is 1 - 1/2 = 1/2. Why others are wrong: A — This results from incorrectly assuming Sarah ate 1/4 of the *original* cake, not the remaining, i.e., 1 - 1/3 - 1/4. C — This results from various miscalculations, such as assuming Sarah ate 1/4 of the *neighbor's* portion, or incorrectly adding and subtracting fractions. D — This is the amount of cake left *before* Sarah ate her share, not the final remaining fraction.