The expression is: 4/5 ÷ 2/3 of (15/8 - 1/4) + (2.5 + 1.5) × 3 - 7 Step 1: Solve the operations inside the parentheses (Brackets). (15/8 - 1/4) = (15/8 - 2/8) = 13/8 (2.5 + 1.5) = 4 The expression becomes: 4/5 ÷ 2/3 of 13/8 + 4 × 3 - 7 Step 2: Solve the 'of' operation. 2/3 of 13/8 = (2/3) × (13/8) = 26/24 = 13/12 The expression becomes: 4/5 ÷ 13/12 + 4 × 3 - 7 Step 3: Solve Division and Multiplication from left to right. Division: 4/5 ÷ 13/12 = 4/5 × 12/13 = 48/65 Multiplication: 4 × 3 = 12 The expression becomes: 48/65 + 12 - 7 Step 4: Solve Addition and Subtraction from left to right. 48/65 + 12 - 7 = 48/65 + 5 To add a fraction and an integer, convert the integer to a fraction with the same denominator: 5 = 5 × 65 / 65 = 325/65 48/65 + 325/65 = (48 + 325)/65 = 373/65 Why others are wrong: A — Correct answer. B — This results from incorrectly performing division before the 'of' operation. C — This results from an error in calculating the first bracket, specifically in the fraction subtraction. D — This results from omitting the final addition of '5' to the fraction 48/65.

1. Resolve `(3/4 of 16)`: `(3/4) × 16 = 12`. 2. Resolve `(12 ÷ 6)`: `2`. 3. Substitute these values back: `24 ÷ [ 12 - 2.5 × 2 ] + (5/8 - 1/4)`. 4. Resolve `2.5 × 2` inside the brackets: `5`. 5. Substitute back: `24 ÷ [ 12 - 5 ] + (5/8 - 1/4)`. 6. Resolve `12 - 5` inside the brackets: `7`. 7. Resolve `(5/8 - 1/4)`: `(5/8 - 2/8) = 3/8`. 8. Substitute back: `24 ÷ 7 + 3/8`. 9. Perform the division: `24/7`. 10. Perform the addition: `24/7 + 3/8`. 11. Find a common denominator (56): `(24 × 8) / (7 × 8) + (3 × 7) / (8 × 7)`. 12. Calculate: `192/56 + 21/56`. 13. Sum the fractions: `(192 + 21) / 56 = 213/56`. Why others are wrong: B — Incorrectly performed the final division after adding `7 + 3/8`. C — Incorrectly performed subtraction instead of addition in the final step (`24/7 - 3/8`). D — Made an error in the fraction subtraction `(5/8 - 1/4)`, potentially simplifying to `1/2` incorrectly.

The expression is [ 45 ÷ 3 × (7 + 2 of 5) - 3^2 ] + 18 ÷ 6 Step 1: Solve the operation 'of' inside the innermost parenthesis. (2 of 5 = 2 × 5 = 10) Expression becomes: [ 45 ÷ 3 × (7 + 10) - 3^2 ] + 18 ÷ 6 Step 2: Solve the addition inside the innermost parenthesis. (7 + 10 = 17) Expression becomes: [ 45 ÷ 3 × 17 - 3^2 ] + 18 ÷ 6 Step 3: Solve the exponent. (3^2 = 9) Expression becomes: [ 45 ÷ 3 × 17 - 9 ] + 18 ÷ 6 Step 4: Perform division and multiplication from left to right inside the main bracket. (45 ÷ 3 = 15) Expression becomes: [ 15 × 17 - 9 ] + 18 ÷ 6 Step 5: Perform multiplication inside the main bracket. (15 × 17 = 255) Expression becomes: [ 255 - 9 ] + 18 ÷ 6 Step 6: Perform subtraction inside the main bracket. (255 - 9 = 246) Expression becomes: 246 + 18 ÷ 6 Step 7: Perform division outside the bracket. (18 ÷ 6 = 3) Expression becomes: 246 + 3 Step 8: Perform the final addition. (246 + 3 = 249) The final answer is 249. Why others are wrong: B — Incorrectly performed addition before 'of' multiplication within the parentheses, treating `(7 + 2 of 5)` as `(7 + 2) × 5`. C — Incorrectly calculated the exponent `3^2` as `3 × 2` (resulting in 6 instead of 9). D — Incorrectly performed addition before division for the final operations outside the bracket.

The order of operations (BODMAS/PEMDAS) must be followed: Brackets, Orders (powers/roots, 'of'), Division/Multiplication (left to right), Addition/Subtraction (left to right). 1. **Solve operations inside the inner parentheses:** * `(0.5 ÷ 1/8)`: Convert 0.5 to a fraction (1/2). * (1/2 ÷ 1/8) = (1/2 × 8/1) = 8/2 = 4 * `(3/5 of 50)`: 'of' means multiplication. * (3/5 × 50) = (3 × 50) / 5 = 150 / 5 = 30 2. **Substitute these values back into the main bracket and solve:** * `[ 4 + 30 ] = 34` 3. **Perform multiplication outside the bracket:** * `34 × 2/17` * (34 × 2) / 17 = 68 / 17 = 4 4. **Perform the final subtraction:** * `4 - 1 = 3` Wait, I made a mistake in identifying the correct answer in my thought process. The correct answer should be `3`. Let me re-check the distractors and reassign the correct answer letter. Correct answer: [A/B/C/D] should be E if I had 5 options. Let's make 3 one of the options. My options were: A. 2.54 B. -30 C. 5.42 D. 5 My correct calculation is 3. I need to make `3` one of the options. Let's make Option D the correct answer: 3. And move `5` to A or C. New Options: A. 2.54 B. -30 C. 5.42 D. 3 Correct answer: D Explanation (why this): The order of operations (BODMAS/PEMDAS) must be followed: Brackets, Orders (powers/roots, 'of'), Division/Multiplication (left to right), Addition/Subtraction (left to right). 1. **Solve operations inside the inner parentheses:** * `(0.5 ÷ 1/8)`: Convert 0.5 to a fraction (1/2). * (1/2 ÷ 1/8) = (1/2 × 8/1) = 8/2 = 4 * `(3/5 of 50)`: 'of' means multiplication. * (3/5 × 50) = (3 × 50) / 5 = 150 / 5 = 30 2. **Substitute these values back into the main bracket and solve:** * `[ 4 + 30 ] = 34` 3. **Perform multiplication outside the bracket:** * `34 × 2/17` * (34 × 2) / 17 = 68 / 17 = 4 4. **Perform the final subtraction:** * `4 - 1 = 3` Why others are wrong: A — Incorrectly calculated `0.5 ÷ 1/8` as `0.5 × 1/8`. B — Performed subtraction `(2/17 - 1)` before multiplication `(34 × 2/17)`. C — Misinterpreted 'of' operation `(3/5 of 50)` as addition `(3/5 + 50)`. This looks good now. The output should be plain text, so I'll write it out exactly. --- One last check for the question statement. "Evaluate" is standard. The numbers are medium-difficult. No cultural specifics. The `Why the others are wrong` section lists a specific reason for A, B, C. For D (the correct answer), no reason is needed there. Final re-check. Looks compliant. Evaluate: `[ (0.5 ÷ 1/8) + (3/5 of 50) ] × 2/17 - 1` A. 2.54 B. -30 C. 5.42 D. 3 Correct answer: D Explanation (why this): 1. **Solve operations inside the inner parentheses first (BODMAS/PEMDAS - Brackets):** * `(0.5 ÷ 1/8)`: Convert 0.5 to a fraction (1/2). * (1/2 ÷ 1/8) = (1/2 × 8/1) = 8/2 = 4 * `(3/5 of 50)`: The word 'of' indicates multiplication (BODMAS/PEMDAS - Orders). * (3/5 × 50) = (3 × 50) / 5 = 150 / 5 = 30 2. **Substitute these values back into the main bracket and solve (BODMAS/PEMDAS - Brackets):** * `[ 4 + 30 ] = 34` 3. **Perform multiplication outside the bracket (BODMAS/PEMDAS - Multiplication):** * `34 × 2/17` = (34 × 2) / 17 = 68 / 17 = 4 4. **Perform the final subtraction (BODMAS/PEMDAS - Subtraction):** * `4 - 1 = 3` Why the others are wrong: A — This result would occur if `0.5 ÷ 1/8` was incorrectly calculated as `0.5 × 1/8`. B — This result would occur if the subtraction `(2/17 - 1)` was performed before the multiplication `(34 × 2/17)`. C — This result would occur if the 'of' operation in `(3/5 of 50)` was misinterpreted as addition `(3/5 + 50)`.

1. Solve the expression inside the innermost parenthesis: (5/6 of 18/5 - 1/2) * First, perform 'of' (multiplication): 5/6 × 18/5 = (5 × 18) / (6 × 5) = 18/6 = 3. * Now, perform subtraction: 3 - 1/2 = 6/2 - 1/2 = 5/2. * The expression becomes: [3/4 + (5/2) ÷ 7/8] × 2/3. 2. Next, solve the division within the square bracket: (5/2) ÷ 7/8. * (5/2) ÷ 7/8 = 5/2 × 8/7 = (5 × 8) / (2 × 7) = 40/14 = 20/7. * The expression becomes: [3/4 + 20/7] × 2/3. 3. Perform the addition within the square bracket: 3/4 + 20/7. * Find a common denominator, which is 28. * 3/4 = (3 × 7) / (4 × 7) = 21/28. * 20/7 = (20 × 4) / (7 × 4) = 80/28. * 21/28 + 80/28 = 101/28. * The expression becomes: 101/28 × 2/3. 4. Finally, perform the multiplication: 101/28 × 2/3. * (101 × 2) / (28 × 3) = 202 / 84. * Simplify the fraction by dividing both numerator and denominator by 2: 101/42. Why others are wrong: B — This result is obtained if division is performed before 'of' within the innermost parenthesis, i.e., (18/5 - 1/2) is calculated first, then 5/6 is multiplied by the result. C — This result occurs if addition (3/4 + 5/2) is performed before division (5/2 ÷ 7/8) within the main square bracket. D — This result is obtained if a calculation error is made, specifically if 3 - 1/2 is incorrectly taken as 2 instead of 5/2.