First, calculate the total fraction of the paper completed: To add 3/5 and 1/4, find a common denominator, which is 20. Convert 3/5 to twentieths: (3 * 4) / (5 * 4) = 12/20 Convert 1/4 to twentieths: (1 * 5) / (4 * 5) = 5/20 Add the completed fractions: 12/20 + 5/20 = 17/20 The entire paper represents 1 whole, or 20/20. Subtract the completed fraction from the whole to find the remaining fraction: 20/20 - 17/20 = 3/20 Why others are wrong: A — This represents the total fraction of the paper that has been completed, not the fraction remaining. B — This could result from an incorrect calculation of the common denominator or a subtraction error. D — This results from incorrectly adding the numerators and denominators directly (3+1)/(5+4) without finding a common denominator.

1. First, determine the total fraction of the road section that has been paved. 2. This is the sum of the work done on Monday and Tuesday: 1/4 + 1/3. 3. To add these fractions, find a common denominator, which is 12. 4. Convert 1/4 to 3/12 and 1/3 to 4/12. 5. Add the converted fractions: 3/12 + 4/12 = 7/12. This is the portion completed. 6. The entire road section represents the whole, which can be expressed as 1 or 12/12. 7. Subtract the completed portion from the whole to find the remaining portion: 12/12 - 7/12 = 5/12. Why others are wrong: A — (Correct answer) B — This is the fraction of the road that has been completed, not the fraction remaining. C — This results from incorrectly adding the numerators (1+1=2) and denominators (4+3=7) directly, which is an invalid method for adding fractions. D — This results from an incorrect calculation or misapplication of fractional operations.

1. Initially, the total tray represents 1 whole. 2. After the morning sale, the fraction of muffins remaining is 1 - 2/5 = 3/5. 3. In the afternoon, 1/3 of the *remaining* muffins were sold. This means (1/3) * (3/5) = 1/5 of the original tray was sold in the afternoon. 4. The total fraction of muffins sold throughout the day is 2/5 (morning) + 1/5 (afternoon) = 3/5. 5. The fraction of muffins remaining unsold is 1 (whole) - 3/5 (total sold) = 2/5. Why others are wrong: A — Correct. B — This is the fraction of the *original* tray sold only in the afternoon, not the total remaining. C — This result occurs if one incorrectly assumes the afternoon sale was 1/3 of the *original* total, leading to 1 - (2/5 + 1/3). D — This is the total fraction of the *original* tray that was sold throughout the day, not the fraction remaining unsold.

The total flour supply can be represented as 1. After Monday, the flour remaining is 1 - 1/3 = 2/3. On Tuesday, 1/4 of the *remaining* flour was used, so 1/4 of 2/3 = (1 * 2) / (4 * 3) = 2/12 = 1/6 of the original supply. The total flour used by the end of Tuesday is the sum of Monday's use and Tuesday's use: 1/3 + 1/6. To add these fractions, find a common denominator, which is 6: 2/6 + 1/6 = 3/6 = 1/2. The fraction of the original flour supply left is 1 (total) - 1/2 (total used) = 1/2. Why others are wrong: B — This would be correct if the total used was 7/12 (e.g., if 1/4 was taken from the *original* amount on Tuesday, not the remainder). C — This represents the total flour used if 1/4 was taken from the *original* amount on Tuesday, rather than from the remainder. D — This is the amount of flour left *after Monday* only, not accounting for Tuesday's usage.

1. The initial fraction of water in the tank is 3/4. 2. The fraction of water used is 1/8. 3. The fraction of water added is 1/16. 4. To combine these fractions, find a common denominator for 4, 8, and 16, which is 16. 5. Convert all fractions to have the denominator 16: 3/4 = (3 * 4) / (4 * 4) = 12/16 1/8 = (1 * 2) / (8 * 2) = 2/16 1/16 remains 1/16. 6. Calculate the current fraction of water: Initial - Used + Added. 7. Substitute the equivalent fractions: 12/16 - 2/16 + 1/16. 8. Perform the operations: (12 - 2 + 1) / 16 = (10 + 1) / 16 = 11/16. Why others are wrong: A — (Correct Answer) B — This fraction (5/8) simplifies from 10/16, which would result if the final addition of 1/16 was omitted (12/16 - 2/16). C — This fraction (13/16) could result from errors like adding 1/8 instead of subtracting it, or making an error in calculation (e.g., 12/16 + 1/16, ignoring the subtraction). D — This fraction (9/16) could result if both 1/8 and 1/16 were subtracted from 3/4, or if there were calculation errors in the sequence of operations.