1. First, perform the operation inside the parentheses: (7 - 3) = 4. 2. The expression becomes: 48 ÷ 4 × 4 + 5. 3. Next, perform division and multiplication from left to right as they have equal precedence. 4. Perform the division: 48 ÷ 4 = 12. 5. The expression becomes: 12 × 4 + 5. 6. Perform the multiplication: 12 × 4 = 48. 7. The expression becomes: 48 + 5. 8. Finally, perform the addition: 48 + 5 = 53. Why others are wrong: A — This result is obtained by incorrectly performing multiplication (4 × 4 = 16) before division when they are at the same level of precedence, leading to 48 ÷ 16 + 5 = 3 + 5 = 8. B — This result is obtained by incorrectly ignoring the parentheses and performing operations from left to right as if no parentheses were present: 48 ÷ 4 × 7 - 3 + 5 = 12 × 7 - 3 + 5 = 84 - 3 + 5 = 81 + 5 = 86. D — This result suggests a calculation error in the final addition (e.g., 48 + 5 = 50) or a mistake in an earlier step leading to an incorrect final sum.

Step 1: Perform the operation inside the parentheses first. (5/6 - 1/3) = (5/6 - 2/6) = 3/6 = 1/2 Step 2: Perform the division. 1/2 ÷ 1/2 = 1/2 × 2/1 = 1 Step 3: Perform the addition. 1 + 2/3 = 3/3 + 2/3 = 5/3 Why others are wrong: A — Results from an incorrect order of operations, specifically performing addition before division (e.g., 1/2 ÷ (1/2 + 2/3)). B — Results from an error in fraction division, specifically multiplying the fractions instead of inverting the divisor and multiplying (e.g., 1/2 ÷ 1/2 incorrectly calculated as 1/2 × 1/2 = 1/4). D — Results from an incorrect application of the order of operations, performing division before the operation within parentheses (e.g., 5/6 - (1/3 ÷ 1/2) + 2/3).

1. First, calculate the term inside the parentheses: (8/3 - 1/6) Find a common denominator, which is 6: (16/6 - 1/6) = 15/6 Simplify the fraction: 15/6 = 5/2 2. Next, calculate the exponent: (3/4)² (3/4)² = 3²/4² = 9/16 3. Now, perform the multiplication: (1/2) × (5/2) (1/2) × (5/2) = 5/4 4. Finally, perform the addition: 9/16 + 5/4 Find a common denominator, which is 16: 9/16 + (5×4)/(4×4) = 9/16 + 20/16 Add the fractions: (9 + 20)/16 = 29/16 Why others are wrong: A — Correct calculation. B — Incorrectly calculating (3/4)² as 3/2 instead of 9/16, leading to 3/2 + 5/4 = 6/4 + 5/4 = 11/4. C — Error in order of operations, specifically by calculating (1/2 × 8/3) first, then (4/3 - 1/6), or similar misapplication of the distributive property. (e.g., (3/4)^2 + (1/2 * 8/3) - 1/6 = 9/16 + 4/3 - 1/6 = 27/48 + 64/48 - 8/48 = 83/48). D — Incorrectly calculating (8/3 - 1/6) as 7/6 (by subtracting numerators without finding a common denominator for the 3 and 6, or similar error), leading to 9/16 + (1/2 × 7/6) = 9/16 + 7/12 = 27/48 + 28/48 = 55/48.

1. Perform division: `48 ÷ 6 = 8`. The expression becomes `8 + 2 × 3 - 7`. 2. Perform multiplication: `2 × 3 = 6`. The expression becomes `8 + 6 - 7`. 3. Perform addition from left to right: `8 + 6 = 14`. The expression becomes `14 - 7`. 4. Perform subtraction: `14 - 7 = 7`. Why others are wrong: A — This result is obtained by incorrectly performing addition (6+2) before division. B — This result is obtained by incorrectly performing subtraction (3-7) before multiplication. C — This result is obtained by incorrectly performing operations strictly from left to right, ignoring the hierarchy of multiplication/division over addition/subtraction.

1. Start with the innermost operation inside the parentheses: 20 / 5 = 4. 2. Continue inside the parentheses with addition: 10 + 4 = 14. 3. Next, perform the multiplication within the square brackets: 3 * 14 = 42. 4. Perform the division outside the square brackets: 42 / 2 = 21. 5. Finally, perform the subtraction: 50 - 21 = 29. Why others are wrong: A — This results from performing addition before division inside the parentheses (10 + 20) / 5 = 6. B — This results from forgetting to divide by 2 after simplifying the expression within the square brackets. C — This results from an error in the initial division (e.g., calculating 20 / 5 as 10 instead of 4). D — This option represents the correct simplification of the expression.