To find a fraction of a fraction, you multiply the two fractions. Maya dedicates 3/4 of her total time to mathematics. She dedicates 2/3 of that mathematics time to geometry problems. So, the fraction of total study time dedicated to geometry is (2/3) * (3/4). Multiply the numerators: 2 * 3 = 6. Multiply the denominators: 3 * 4 = 12. This results in the fraction 6/12. Simplify the fraction: 6/12 simplifies to 1/2. Why others are wrong: A — Correct answer. B — This could result from calculating the remaining fraction (1 - 2/3 = 1/3) and then multiplying it by 3/4, misinterpreting the question's intent. C — This is an error made by adding the numerators (2+3) and denominators (3+4) directly, which is not a valid operation for multiplying fractions. D — This is the result of adding the two fractions (2/3 + 3/4 = 8/12 + 9/12 = 17/12), not multiplying them.

First, calculate the total fraction of the project completed: 2/5 + 1/3. To add these fractions, find a common denominator, which is 15. Convert 2/5 to an equivalent fraction with a denominator of 15: (2*3)/(5*3) = 6/15. Convert 1/3 to an equivalent fraction with a denominator of 15: (1*5)/(3*5) = 5/15. Add the equivalent fractions: 6/15 + 5/15 = 11/15. This is the total fraction of the project completed. To find the fraction remaining, subtract the completed portion from the whole project (which is 1, or 15/15). Remaining = 15/15 - 11/15 = 4/15. Why others are wrong: A — Correct. B — This represents the total fraction of the project that has been *completed*, not the fraction that remains. C — This results from incorrectly adding the numerators (2+1=3) and the denominators (5+3=8) directly, without finding a common denominator. D — This would be the result of subtracting 1/3 from 2/5 (6/15 - 5/15 = 1/15), which incorrectly finds the difference between the two completed parts instead of their sum and then subtracting from the whole.

1. The entire pizza represents 1 whole. 2. John consumed 1/4 of the pizza. 3. The fraction of pizza remaining after John's share is 1 - 1/4 = 3/4. 4. Mary then ate 1/2 of the *remaining* pizza. This means Mary ate 1/2 * (3/4) = 3/8 of the original pizza. 5. The total fraction of pizza consumed is John's share + Mary's share = 1/4 + 3/8. 6. To add these fractions, find a common denominator (8). 1/4 is equivalent to 2/8. 7. Total consumed = 2/8 + 3/8 = 5/8. 8. The fraction of the original pizza left is 1 (whole pizza) - 5/8 (consumed) = 3/8. Why others are wrong: A — This would represent 1 slice remaining, indicating a miscalculation of total consumed or remaining portion. B — This could be the fraction remaining if John ate 1/2 and Mary ate 1/4 of the total, or a misinterpretation of "half of the remaining". D — This would be the amount left if only 1/2 of the pizza was consumed in total, or if Mary was the only one to eat and consumed half.

The problem asks for 2/3 of the 3/4 cup of sugar. To find a fraction "of" another fraction, you multiply them. Multiply the numerators: 2 * 3 = 6. Multiply the denominators: 3 * 4 = 12. The product is 6/12. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 6. 6 ÷ 6 = 1. 12 ÷ 6 = 2. So, the simplified amount is 1/2 cup. Why others are wrong: B — This result is obtained by incorrectly adding the two fractions (3/4 + 2/3), not by finding a fraction "of" another. C — This result is obtained by incorrectly subtracting the two fractions (3/4 - 2/3), not by finding a fraction "of" another. D — This result comes from incorrectly adding the numerators and denominators (2+3)/(3+4), which is an incorrect operation for this problem.

Step 1: Calculate the total amount of sugar used. Total used = 3/4 kg + 1/2 kg To add these fractions, find a common denominator, which is 4. 1/2 kg can be written as 2/4 kg. Total used = 3/4 kg + 2/4 kg = 5/4 kg. Step 2: Convert the initial amount of sugar to an improper fraction with the common denominator. Initial amount = 3 1/2 kg. As an improper fraction, 3 1/2 = (3 * 2 + 1) / 2 = 7/2 kg. To have a denominator of 4, multiply the numerator and denominator by 2: 7/2 kg = 14/4 kg. Step 3: Subtract the total amount of sugar used from the initial amount. Remaining sugar = 14/4 kg - 5/4 kg = 9/4 kg. Step 4: Convert the result to a mixed number. 9/4 kg = 2 with a remainder of 1, so 2 1/4 kg. Why others are wrong: A — Correct answer. B — This is the total amount of sugar used (1 1/4 kg), not the amount remaining after subtraction from the initial supply. C — This result occurs if only the first amount (3/4 kg) was subtracted from the initial amount (3 1/2 kg - 3/4 kg = 2 3/4 kg), ignoring the second usage. D — This result could occur from an error in finding the common denominator for the sum of used fractions (e.g., mistakenly calculating 3/4 + 1/2 = 2/3, then subtracting this from 3 1/2).