1. **Innermost parenthesis and 'of' operator (Brackets - B/P):** * Calculate `1/3 of 18`: `(1/3) × 18 = 6` * Calculate `(72 ÷ 9 - 2)`: * First, division: `72 ÷ 9 = 8` * Then, subtraction: `8 - 2 = 6` 2. **Braces {} (Brackets - B/P):** * Substitute the results back into the braces: `{ 6 + 6 } = 12` 3. **Square brackets [] (Brackets - B/P):** * Now calculate the multiplication inside the square brackets: `[ 12 × 4 ] = 48` 4. **Main expression - Division (Division - D):** * Perform the division in the main expression: `48 ÷ 2 = 24` 5. **Main expression - Subtraction (Subtraction - S):** * Finally, perform the subtraction: `50 - 24 = 26` Why others are wrong: B — This results from incorrectly performing subtraction before division in the final step: `(50 - 48) ÷ 2 = 2 ÷ 2 = 1`. C — This results from incorrectly applying multiplication within the inner parenthesis, for example, treating `(72 ÷ 9 - 2) × 4` as `72 ÷ 9 - (2 × 4)`. D — This results from a basic arithmetic error, such as miscalculating `72 ÷ 9` as `7` instead of `8`.

1. Resolve 'of' within the innermost bracket: 3/4 of 16 = (3/4) * 16 = 12. 2. Resolve addition within the innermost bracket: 1/2 + 12 = 0.5 + 12 = 12.5. 3. Resolve division within the main curly bracket: 12.5 ÷ 5 = 2.5. 4. Resolve multiplication in the second part of the main curly bracket: 4.5 × 2 = 9. 5. Resolve addition within the main curly bracket: 2.5 + 9 = 11.5. 6. Resolve multiplication outside the main bracket: 3 × (2/3) = 2. 7. Perform the final subtraction: 11.5 – 2 = 9.5. Why others are wrong: A — Incorrectly grouping 1/2 and 3/4 before applying 'of', leading to ((1/2 + 3/4) of 16) = (5/4 of 16) = 20, then proceeding. B — This is the correct calculation following the standard order of operations (BODMAS/PEMDAS). C — Mistakenly evaluating `3 × (2/3)` as simply `3` (or miscalculating it as such), leading to `11.5 - 3 = 8.5`. D — Performing division prematurely inside the initial bracket (12 ÷ 5 first) before addition, leading to `(0.5 + 2.4) = 2.9`, then `2.9 + 9 - 2 = 9.9`.

1. Calculate the power: 2^3 = 8. 2. Evaluate the first parenthesis: ( 1/4 + 3/8 ) = ( 2/8 + 3/8 ) = 5/8. 3. Evaluate the second parenthesis: ( 0.625 - 1/8 ) Convert 0.625 to a fraction: 0.625 = 625/1000 = 5/8. Subtract: 5/8 - 1/8 = 4/8 = 1/2. 4. Substitute these values back into the expression: 8 × (5/8) ÷ (1/2) + 10. 5. Perform multiplication and division from left to right: 8 × (5/8) = 5. 5 ÷ (1/2) = 5 × 2 = 10. 6. Perform the final addition: 10 + 10 = 20. Why others are wrong: A — This result (12.5) occurs if the division `÷ (1/2)` is incorrectly performed as multiplication by `(1/2)`. B — This result (17.5) occurs if `2^3` is mistakenly calculated as `6` instead of `8`. D — This result (15) occurs if the division `÷ (1/2)` is completely ignored after multiplying `8 × (5/8)`.

First, evaluate the expression inside the parentheses: (1/2 + 2/3 of 3/4) Apply 'of' (multiplication) within the parentheses: 2/3 of 3/4 = (2/3) × (3/4) = 6/12 = 1/2 Now, add the fractions within the parentheses: 1/2 + 1/2 = 1 The expression simplifies to: 3 1/3 ÷ 1 - 1/5 × 10 Convert the mixed number to an improper fraction: 3 1/3 = (3×3 + 1)/3 = 10/3 The expression is now: 10/3 ÷ 1 - 1/5 × 10 Perform division and multiplication from left to right: Division: 10/3 ÷ 1 = 10/3 Multiplication: 1/5 × 10 = 10/5 = 2 The expression becomes: 10/3 - 2 Perform the subtraction: 10/3 - 2 = 10/3 - 6/3 = 4/3 Why others are wrong: A — This is the correct answer. B — This result (38/21) is obtained if (1/2 + 2/3) is calculated before (2/3 of 3/4) within the parentheses. C — This result (31/6) is obtained if the initial division (3 1/3 ÷ 1/2) is performed before evaluating the full parenthesis. D — This result (-6/23) is obtained if the 'of' operation is ignored and (1/2 + 2/3 + 3/4) is calculated within the parentheses.

1. **B**rackets First: * Inside the first set of parentheses: `3/4 of 4/9` means `3/4 × 4/9`. `3/4 × 4/9 = 12/36 = 1/3`. * Inside the second set of parentheses (within the square brackets): `5/6 - 1/3`. To subtract, find a common denominator (6). `1/3 = 2/6`. `5/6 - 2/6 = 3/6 = 1/2`. 2. **O**rders (of / exponents) is already covered by 'of' in step 1. 3. **D**ivision and **M**ultiplication (from left to right) within the square brackets: * The square bracket now contains `[ (1/2) ÷ 7/12 ] × 2/5`. * Perform division first: `1/2 ÷ 7/12 = 1/2 × 12/7 = 12/14 = 6/7`. * Now perform multiplication: `6/7 × 2/5 = 12/35`. 4. The expression simplifies to: `1/3 + 12/35 - 1/10`. 5. **A**ddition and **S**ubtraction (from left to right): * Find the Lowest Common Multiple (LCM) of the denominators 3, 35, and 10. LCM(3, 35, 10) = 2 × 3 × 5 × 7 = 210. * Convert each fraction to have a denominator of 210: `1/3 = (1 × 70) / (3 × 70) = 70/210`. `12/35 = (12 × 6) / (35 × 6) = 72/210`. `1/10 = (1 × 21) / (10 × 21) = 21/210`. * Perform the operations: `70/210 + 72/210 - 21/210 = (70 + 72 - 21) / 210 = (142 - 21) / 210 = 121/210`. Why others are wrong: A — Correct answer. B — Incorrect application of BODMAS within the brackets, specifically treating multiplication before division when they appear together from left to right, or misinterpreting the division by `7/12`. For example, if `(1/2) ÷ (7/12 × 2/5)` was calculated. C — Error in performing the division operation, possibly by multiplying instead of dividing (`1/2 × 7/12`) within the brackets. D — A minor arithmetic error in the final addition or subtraction step after correctly applying BODMAS for the fractions.