1. **B**rackets (Parentheses): First, calculate `(2 + 3) = 5`. The expression becomes: `15 - [10 ÷ 5 × 2] + 4²` 2. **O**rders (Exponents): Next, calculate `4² = 16`. The expression becomes: `15 - [10 ÷ 5 × 2] + 16` 3. **B**rackets (Square brackets): Now, evaluate the operations inside `[ ]` from left to right. * **D**ivision: `10 ÷ 5 = 2`. * **M**ultiplication: `2 × 2 = 4`. The expression becomes: `15 - 4 + 16` 4. **A**ddition and **S**ubtraction: Finally, perform addition and subtraction from left to right. * **S**ubtraction: `15 - 4 = 11`. * **A**ddition: `11 + 16 = 27`. Why others are wrong: B — This result occurs if multiplication is incorrectly performed before division within the square brackets (e.g., `10 ÷ (5 × 2)` which gives `10 ÷ 10 = 1`, leading to `15 - 1 + 16 = 30`). C — This result occurs if addition is incorrectly performed before subtraction at the final step (e.g., `15 - (4 + 16)` instead of `(15 - 4) + 16`). D — This result occurs if the exponent `4²` is incorrectly calculated as `4 × 2 = 8` instead of `4 × 4 = 16`.

Step 1: Perform operations inside the brackets. (12 - 9) = 3 The expression becomes: 50 - 4 × 3 + 15 ÷ 5 Step 2: Perform multiplication and division from left to right. 4 × 3 = 12 15 ÷ 5 = 3 The expression becomes: 50 - 12 + 3 Step 3: Perform addition and subtraction from left to right. 50 - 12 = 38 38 + 3 = 41 Why others are wrong: A — This result (35) is obtained by performing addition (12 + 3 = 15) before subtraction (50 - 15) in the final step, incorrectly ignoring the left-to-right rule for addition and subtraction. B — Correct answer. C — This result (50) is obtained by incorrectly ignoring the multiplication `4 × (12 - 9)`, effectively calculating `50 - (12 - 9) + (15 ÷ 5) = 50 - 3 + 3 = 50`. D — This result (-4) is obtained by incorrectly interpreting `4 × (12 - 9)` as `4 × 12 - 9`, leading to `50 - 48 - 9 + 3 = 2 - 9 + 3 = -7 + 3 = -4`.

1. **Brackets (B)**: Evaluate the operation inside the brackets first. `(6 - 2) = 4` The expression becomes: `24 ÷ 4 × 3 + 5 - 1` 2. **Division and Multiplication (DM)**: Perform division and multiplication from left to right. First, `24 ÷ 4 = 6`. The expression becomes: `6 × 3 + 5 - 1` Next, `6 × 3 = 18`. The expression becomes: `18 + 5 - 1` 3. **Addition and Subtraction (AS)**: Perform addition and subtraction from left to right. First, `18 + 5 = 23`. The expression becomes: `23 - 1` Finally, `23 - 1 = 22`. Why others are wrong: A — This is the correct answer. The options are incorrect, let me fix it in the final output. The correct answer here is 22. Let's fix the options and re-evaluate. Correct answer should be 22. A. 6 B. 2 C. 47 D. 13 I made a mistake in selecting the correct answer in my thought process. My explanation clearly leads to 22. I need to update the Correct answer line to D (assuming 22 is D) or update options to include 22. Let's make 22 option A. A. 22 B. 6 C. 47 D. 13 Correct answer: A. Explanation (why this): 1. **Brackets (B)**: Evaluate the operation inside the brackets first. `(6 - 2) = 4` The expression becomes: `24 ÷ 4 × 3 + 5 - 1` 2. **Division and Multiplication (DM)**: Perform division and multiplication from left to right. First, `24 ÷ 4 = 6`. The expression becomes: `6 × 3 + 5 - 1` Next, `6 × 3 = 18`. The expression becomes: `18 + 5 - 1` 3. **Addition and Subtraction (AS)**: Perform addition and subtraction from left to right. First, `18 + 5 = 23`. The expression becomes: `23 - 1` Finally, `23 - 1 = 22`. Why the others are wrong: A — [The provided options are incorrect. I need to re-evaluate the previous incorrect option reasoning] Let's re-generate the 'Why others are wrong' part based on the new order of options and the intended incorrect calculations. Original thought for errors: * Incorrect Path 1: Multiplication before Division (even though D is to the left) -> `6` * Incorrect Path 2: Ignoring brackets (doing all operations left to right initially) -> `2` * Incorrect Path 3: Addition before Multiplication/Division -> `47` * Incorrect Path 4: Mistake in bracket operation (e.g., `6+2=8`) -> `13` So, if correct answer is 22 (Option A): B. 6 (Incorrect path 1) C. 47 (Incorrect path 3) D. 13 (Incorrect path 4) This looks consistent now. The initial error in my thought was just selecting 'A' as the correct answer and then having to re-align. With 22 being option A, it flows correctly. Consider the following mathematical expression: What is the value of the expression: `24 ÷ (6 - 2) × 3 + 5 - 1`? A. 22 B. 6 C. 47 D. 13 Correct answer: A Explanation (why this): 1. **Brackets (B)**: Evaluate the operation inside the brackets first. `(6 - 2) = 4` The expression becomes: `24 ÷ 4 × 3 + 5 - 1` 2. **Division and Multiplication (DM)**: Perform division and multiplication from left to right. First, `24 ÷ 4 = 6`. The expression becomes: `6 × 3 + 5 - 1` Next, `6 × 3 = 18`. The expression becomes: `18 + 5 - 1` 3. **Addition and Subtraction (AS)**: Perform addition and subtraction from left to right. First, `18 + 5 = 23`. The expression becomes: `23 - 1` Finally, `23 - 1 = 22`. Why the others are wrong: B — This results from performing multiplication before division (`4 × 3 = 12`) when division comes first from left to right after evaluating the bracket (`24 ÷ 12 + 5 - 1 = 2 + 5 - 1 = 6`). C — This results from performing addition before multiplication after evaluating the bracket (`24 ÷ 4 × (3 + 5) - 1 = 24 ÷ 4 × 8 - 1 = 6 × 8 - 1 = 48 - 1 = 47`). D — This results from an error in evaluating the bracket, for example, by incorrectly adding 6 and 2 instead of subtracting (`24 ÷ (6 + 2) × 3 + 5 - 1 = 24 ÷ 8 × 3 + 5 - 1 = 3 × 3 + 5 - 1 = 9 + 5 - 1 = 14 - 1 = 13`).

1. **BODMAS/PEMDAS** is the order of operations: Brackets, Orders (powers/roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). 2. **Brackets**: First, evaluate the expression inside the brackets: `(10 - 7) = 3`. The expression becomes: `48 ÷ 6 + 2 × 3 - 5`. 3. **Division and Multiplication** (from left to right): * Perform the division: `48 ÷ 6 = 8`. The expression becomes: `8 + 2 × 3 - 5`. * Perform the multiplication: `2 × 3 = 6`. The expression becomes: `8 + 6 - 5`. 4. **Addition and Subtraction** (from left to right): * Perform the addition: `8 + 6 = 14`. The expression becomes: `14 - 5`. * Perform the subtraction: `14 - 5 = 9`. Why others are wrong: A — This result (13) is obtained by incorrectly performing addition `6 + 2` before division `48 ÷ 6`, leading to `48 ÷ 8 × 3 - 5 = 6 × 3 - 5 = 18 - 5 = 13`. B — This result (16) is obtained by incorrectly evaluating `2 × (10 - 7)` as `(2 × 10) - 7`, ignoring the priority of the subtraction inside the bracket. This would make the expression `48 ÷ 6 + 20 - 7 - 5 = 8 + 20 - 7 - 5 = 28 - 7 - 5 = 21 - 5 = 16`. C — This result (25) is obtained by performing operations strictly from left to right without fully respecting the order of multiplication/division over addition/subtraction. For example, `(48 ÷ 6) = 8`, then `8 + 2 = 10`, then `10 × 3 = 30`, then `30 - 5 = 25`.

1. **Brackets (B):** First, calculate the operation inside the parentheses: (7 - 4) = 3. The expression becomes: 24 ÷ 3 - 2 + 5 × 3. 2. **Division (D) and Multiplication (M):** Next, perform division and multiplication from left to right. 24 ÷ 3 = 8. 5 × 3 = 15. The expression becomes: 8 - 2 + 15. 3. **Addition (A) and Subtraction (S):** Finally, perform addition and subtraction from left to right. 8 - 2 = 6. 6 + 15 = 21. Therefore, the value of the expression is 21. Why others are wrong: A — This result (33) occurs if operations are performed strictly from left to right, ignoring the priority of multiplication/division over addition/subtraction. B — This result (-9) occurs if addition is performed before subtraction in the final step (i.e., 8 - (2 + 15)), violating the left-to-right rule for operations of equal priority. D — This result (37) occurs if the multiplication (5 × 7) is performed before the operation within the brackets (7 - 4), thereby ignoring the brackets' priority.