The expression is: [50 ÷ (1/4 of 8) - 3 × (15 - 7)] + (2.5 × 4 - 10) Step 1: Solve operations within the innermost brackets. (1/4 of 8) = (1/4) × 8 = 2 (15 - 7) = 8 (2.5 × 4) = 10 The expression becomes: [50 ÷ 2 - 3 × 8] + (10 - 10) Step 2: Perform division and multiplication within the main brackets. 50 ÷ 2 = 25 3 × 8 = 24 10 - 10 = 0 The expression becomes: [25 - 24] + 0 Step 3: Perform subtraction within the remaining main bracket. 25 - 24 = 1 The expression becomes: 1 + 0 Step 4: Perform the final addition. 1 + 0 = 1 Why others are wrong: A — This option results from incorrectly prioritising division before evaluating '1/4 of 8' as a single 'of' operation within the bracket (e.g., treating it as 50 ÷ 1/4 × 8). B — This option results from incorrectly applying multiplication before the subtraction within the (15 - 7) bracket, leading to (3 × 15) - 7. C — This option involves multiple BODMAS violations, including misinterpreting 'of' and completely ignoring bracket priority for (15-7).

1. Start with the innermost parentheses: (8 ÷ 2) = 4. The expression becomes: 25 - [ (12 + 4) × 0.5 - (3 of 10) ] + (-4)² 2. Next, complete the addition within the parentheses: (12 + 4) = 16. The expression becomes: 25 - [ 16 × 0.5 - (3 of 10) ] + (-4)² 3. Perform the 'of' operation: (3 of 10) = 3 × 10 = 30. The expression becomes: 25 - [ 16 × 0.5 - 30 ] + (-4)² 4. Perform the multiplication within the main bracket: 16 × 0.5 = 8. The expression becomes: 25 - [ 8 - 30 ] + (-4)² 5. Perform the subtraction within the main bracket: 8 - 30 = -22. The expression becomes: 25 - [-22] + (-4)² 6. Evaluate the exponent: (-4)² = 16. The expression becomes: 25 - [-22] + 16 7. Simplify the subtraction of a negative number: 25 - [-22] = 25 + 22 = 47. The expression becomes: 47 + 16 8. Perform the final addition: 47 + 16 = 63. Why others are wrong: B — This result (31) is obtained if (-4)² is incorrectly calculated as -16, leading to 25 + 22 - 16 = 31. C — This result (19) is obtained if 25 - [-22] is incorrectly calculated as 25 - 22, leading to 3 + (-4)² = 3 + 16 = 19. D — This result (66) is obtained if the order of operations within (12 + 8 ÷ 2) is done incorrectly as (12 + 8) ÷ 2 = 10, leading to 25 - [10 × 0.5 - 30] + 16 = 25 - [5 - 30] + 16 = 25 - [-25] + 16 = 50 + 16 = 66.

The expression is [ ( 3/4 + 1/2 of 2/3 ) ÷ 7/8 ] - 5/6 × 12. Follow the BODMAS/PEMDAS rule: Brackets/Parentheses, Orders (of/Exponents), Division/Multiplication (left to right), Addition/Subtraction (left to right). Step 1: Solve the "of" operation inside the inner parenthesis. 1/2 of 2/3 = 1/2 × 2/3 = 2/6 = 1/3. The expression becomes: [ ( 3/4 + 1/3 ) ÷ 7/8 ] - 5/6 × 12. Step 2: Solve the addition inside the inner parenthesis. 3/4 + 1/3 = (3×3)/(4×3) + (1×4)/(3×4) = 9/12 + 4/12 = 13/12. The expression becomes: [ (13/12) ÷ 7/8 ] - 5/6 × 12. Step 3: Solve the division inside the square brackets. 13/12 ÷ 7/8 = 13/12 × 8/7 = (13 × 8) / (12 × 7). Simplify by dividing 8 and 12 by their common factor 4: (13 × 2) / (3 × 7) = 26/21. The expression becomes: 26/21 - 5/6 × 12. Step 4: Solve the multiplication. 5/6 × 12 = 5 × (12/6) = 5 × 2 = 10. The expression becomes: 26/21 - 10. Step 5: Solve the final subtraction. 26/21 - 10 = 26/21 - 210/21 = (26 - 210) / 21 = -184/21. Why others are wrong: B — This result (184/21) would be obtained if the final subtraction was done in reverse (10 - 26/21) or if a sign error occurred. C — This result (-190/21) would be obtained if the order of operations within the inner parenthesis was incorrectly evaluated as (3/4 + 1/2) first, then 'of' 2/3. D — This result (-188/21) would be obtained if there was an arithmetic error in calculating '1/2 of 2/3' as 1/6 instead of 1/3.

1. Evaluate the innermost parenthesis: (1.2 + 0.8) = 2 2. Evaluate the fraction division within the curly braces: (3/5) ÷ (2/15) = (3/5) × (15/2) = 45/10 = 4.5 3. Evaluate the expression inside the curly braces: {4.5 - 4} = 0.5 4. Evaluate the expression inside the square brackets: [2 × 0.5] = 1 5. Calculate 25% of the result from step 4: 25% of 1 = 0.25 × 1 = 0.25 6. Perform the final addition: 0.25 + 10 = 10.25 Why others are wrong: A — This result occurs if (3/5) ÷ (2/15) is incorrectly calculated as (3/5) × (2/15) = 6/75 = 0.08, leading to 25% of [2 × {0.08 - 4}] + 10 = 25% of [2 × -3.92] + 10 = 25% of [-7.84] + 10 = -1.96 + 10 = 8.04. B — This result occurs if '25%' is treated as the number '25' directly, leading to 25 × [ (1.2 + 0.8) × { (3/5) ÷ (2/15) - 4 } ] + 10 = 25 × [2 × {4.5 - 4}] + 10 = 25 × [2 × 0.5] + 10 = 25 × 1 + 10 = 35. D — This result occurs if (1.2 + 0.8) is incorrectly calculated as (1.2 × 0.8) = 0.96, leading to 25% of [0.96 × {4.5 - 4}] + 10 = 25% of [0.96 × 0.5] + 10 = 25% of [0.48] + 10 = 0.12 + 10 = 10.12.

Step 1: Solve the operations within the innermost parentheses/brackets. (3/4 + 1/2) = (3/4 + 2/4) = 5/4 (5/6 - 1/3) = (5/6 - 2/6) = 3/6 = 1/2 Step 2: Apply the 'of' operation (which implies multiplication with higher precedence than standard multiplication/division). 5/4 of 16 = (5/4) × 16 = 5 × 4 = 20 Step 3: Perform the multiplication in the second bracket. (1/2) × 12 = 6 Step 4: Substitute these results back into the expression. The expression becomes: 20 ÷ 6 - 5 Step 5: Perform the division. 20 ÷ 6 = 20/6 = 10/3 Step 6: Perform the subtraction. 10/3 - 5 = 10/3 - 15/3 = -5/3 Why others are wrong: A — Correct answer derived by following the BODMAS/PEMDAS order of operations correctly. B — This could result from an incorrect calculation of the division (e.g., if (20-5)÷6 was done or a sign error with 5/3). C — This value (10/3) is the result of 20 ÷ 6, indicating that the final subtraction of 5 was omitted. D — This result (20) would be obtained if the subtraction (6-5) was incorrectly performed before division, i.e., 20 ÷ (6-5) = 20 ÷ 1 = 20.