1. Convert decimals to fractions for consistency: 1.25 = 5/4 and 0.5 = 1/2. 2. The expression becomes: [3/4 + (5/4 ÷ 5/4) - 1/2] × 8 3. Solve the innermost parenthesis first: (5/4 ÷ 5/4) = 1. 4. The expression is now: [3/4 + 1 - 1/2] × 8 5. Perform addition and subtraction within the bracket from left to right: 3/4 + 1 = 3/4 + 4/4 = 7/4 6. The expression becomes: [7/4 - 1/2] × 8 7. Continue with subtraction within the bracket: 7/4 - 1/2 = 7/4 - 2/4 = 5/4 8. The expression is now: [5/4] × 8 9. Perform the final multiplication: 5/4 × 8 = (5 × 8) / 4 = 40 / 4 = 10 Why others are wrong: B — This result (12) occurs if the operations inside the bracket are incorrectly performed from left to right (treating `1.25 ÷ 5/4` as a later step), such as `(0.75 + 1.25 - 0.5) × 8 = (2 - 0.5) × 8 = 1.5 × 8 = 12`. C — This result (8.8) occurs if addition (`3/4 + 1.25`) is incorrectly performed before division (`1.25 ÷ 5/4`) inside the main bracket, i.e., `((0.75 + 1.25) ÷ 1.25 - 0.5) × 8 = (2 ÷ 1.25 - 0.5) × 8 = (1.6 - 0.5) × 8 = 1.1 × 8 = 8.8`. D — This result (14) occurs from an arithmetic error in the subtraction step, specifically if `7/4 - 1/2` was incorrectly calculated as `7/4 + 1/2 = 9/4` or `(7-1)/4 = 6/4`, or `7/4 - 1/2` was mistakenly evaluated as `(7+2)/4 = 9/4` or some other fraction that resulted in 14. For example, if `5/4` was incorrectly calculated as `7/4`, then `7/4 × 8 = 14`.

1. **Solve the innermost parentheses**: * `(0.5 + 3/4)`: Convert 0.5 to 1/2. `1/2 + 3/4 = 2/4 + 3/4 = 5/4`. * `(25% of 60)`: Convert 25% to 1/4. `1/4 × 60 = 15`. The expression becomes: `[ { (5/4) × 15 } ÷ 1.25 ] - 10`. 2. **Solve the multiplication within curly braces**: * `(5/4) × 15 = 75/4`. The expression becomes: `[ (75/4) ÷ 1.25 ] - 10`. 3. **Solve the division within square brackets**: * Convert 1.25 to a fraction: `1.25 = 5/4`. * `(75/4) ÷ (5/4) = 75/4 × 4/5 = 75/5 = 15`. The expression becomes: `15 - 10`. 4. **Perform the final subtraction**: * `15 - 10 = 5`. Why others are wrong: A — This result (50) could be obtained by incorrectly ignoring '25%' in '25% of 60' and just multiplying by 60, i.e., `[ { (1.25) × 60 } ÷ 1.25 ] - 10 = [ 75 ÷ 1.25 ] - 10 = 60 - 10 = 50`. B — This result (12) could be obtained by misinterpreting '3/4' as '4/3' in the initial addition: `(0.5 + 4/3) = (1/2 + 4/3) = (3/6 + 8/6) = 11/6`. Then, `[ { (11/6) × 15 } ÷ 1.25 ] - 10 = [ {55/2} ÷ 5/4 ] - 10 = [ 55/2 × 4/5 ] - 10 = [ 22 ] - 10 = 12`. C — This result (75) could be obtained by misinterpreting '25% of 60' as '25 + 60 = 85'. Then, `[ { (1.25) × 85 } ÷ 1.25 ] - 10 = [ 85 ] - 10 = 75`.

1. Solve the innermost parenthesis: (5 + 3) = 8. 2. Substitute this back into the expression: `[ { 8 × 4 - 16 } ÷ 2 ] of 6 + (27 - 3^3)` 3. Perform the multiplication within the curly braces: 8 × 4 = 32. 4. Perform the subtraction within the curly braces: {32 - 16} = 16. 5. Substitute this back: `[ 16 ÷ 2 ] of 6 + (27 - 3^3)` 6. Perform the division within the square brackets: [16 ÷ 2] = 8. 7. Substitute this back: `8 of 6 + (27 - 3^3)` 8. Solve the 'of' operation, which implies multiplication: 8 × 6 = 48. 9. Solve the exponent in the second parenthesis: 3^3 = 27. 10. Solve the subtraction in the second parenthesis: (27 - 27) = 0. 11. Finally, add the remaining terms: 48 + 0 = 48. Why others are wrong: A — This result is obtained by incorrectly performing subtraction before multiplication within the first bracket, e.g., calculating `(4 - 16)` before `(8 × 4)`. B — This result is obtained by incorrectly calculating the exponent `3^3` as `3 × 3 = 9` instead of `3 × 3 × 3 = 27`. C — This result is obtained by incorrectly performing the division `(16 ÷ 2)` as an addition `(16 + 2)`.

1. First, solve the operations inside the parentheses: (3/4 + 1/2) = (3/4 + 2/4) = 5/4 (2.5 - 1.75) = 0.75 = 3/4 2. Substitute these results back into the expression: [ 5/4 ÷ 5/8 ] × 3/4 3. Next, perform the division inside the square brackets: 5/4 ÷ 5/8 = 5/4 × 8/5 = 8/4 = 2 4. Finally, perform the multiplication: 2 × 3/4 = 6/4 = 3/2 = 1.5 Why others are wrong: A — This result would occur from an arithmetic error during the division or final multiplication. C — This value might arise from incorrect fraction simplification or an error in converting to decimals at an intermediate step. D — This would be the result if the second bracket (2.5 - 1.75) was incorrectly taken as 1, or if the final multiplication was omitted.

The expression is 3/4 + [ (1/2 of 8/3) ÷ (4/5 - 1/10) ] × 2/3 - 1/6. Follow the BODMAS/PEMDAS order of operations: Brackets, Orders (powers/roots), Division/Multiplication (from left to right), Addition/Subtraction (from left to right). 1. Solve the 'of' operation inside the innermost bracket: 1/2 of 8/3 = (1/2) × (8/3) = 8/6 = 4/3 2. Solve the subtraction inside the second innermost bracket: 4/5 - 1/10 = 8/10 - 1/10 = 7/10 3. Substitute these values back into the expression: 3/4 + [ (4/3) ÷ (7/10) ] × 2/3 - 1/6 4. Solve the division inside the square brackets: (4/3) ÷ (7/10) = (4/3) × (10/7) = 40/21 5. Substitute this value back: 3/4 + 40/21 × 2/3 - 1/6 6. Perform the multiplication: 40/21 × 2/3 = 80/63 7. Substitute back: 3/4 + 80/63 - 1/6 8. Find the Lowest Common Multiple (LCM) of the denominators (4, 63, 6). LCM(4, 63, 6) = 252 9. Convert fractions to have the common denominator: 3/4 = (3 × 63) / (4 × 63) = 189/252 80/63 = (80 × 4) / (63 × 4) = 320/252 1/6 = (1 × 42) / (6 × 42) = 42/252 10. Perform addition and subtraction from left to right: 189/252 + 320/252 - 42/252 = (189 + 320 - 42) / 252 = (509 - 42) / 252 = 467/252 Why others are wrong: A — This result is obtained by incorrectly calculating (4/5 - 1/10) as 3/5. B — This result is obtained by incorrectly omitting the multiplication by 2/3 after solving the square brackets. D — This result is obtained by incorrectly interpreting "1/2 of 8/3" as (1/2 + 8/3).