Evaluate :
$17.5 imes3-21\div7-3 imes12.5$

Q: Evaluate : $17.5\times3-21\div7-3\times12.5$

To evaluate the expression $17.5 \times 3 - 21 \div 7 - 3 \times 12.5$, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Let's break down the expression step by step: 1. **Multiplication and Division**: - First, calculate $17.5 \times 3$: \[ 17.5 \times 3 = 52.5 \] - Next, calculate $21 \div 7$: \[ 21 \div 7 = 3 \] - Then, calculate $3 \times 12.5$: \[ 3 \times 12.5 = 37.5 \] 2. **Subtraction**: - Substitute the results back into the expression: \[ 52.5 - 3 - 37.5 \] - Perform the subtraction from left to right: \[ 52.5 - 3 = 49.5 \] \[ 49.5 - 37.5 = 12 \] Thus, the final result of the expression is 12, which corresponds to Option 2. **Explanation of Incorrect Options**: - **Option 1 (52.5)**: This option might mistakenly consider only the first multiplication $17.5 \times 3$ without completing the entire expression. However, it does not account for the subsequent division and subtraction operations. - **Option 3 (120)**: This option is incorrect as it does not align with any logical step in the calculation of the given expression. It might be a result of a misunderstanding or miscalculation of the operations involved. - **Option 4 (50)**: This option could result from an error in the subtraction process, possibly by incorrectly subtracting the results of the division and multiplication. However, it does not match the correct evaluation of the expression. Therefore, the correct answer is indeed Option 2, which is 12, as demonstrated by the step-by-step calculation above.

Question

Accepted Answer

To evaluate the expression $17.5 \times 3 - 21 \div 7 - 3 \times 12.5$, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Let's break down the expression step by step:

1. **Multiplication and Division**: 
   - First, calculate $17.5 \times 3$:
     $$
     17.5 \times 3 = 52.5
     $$
   - Next, calculate $21 \div 7$:
     $$
     21 \div 7 = 3
     $$
   - Then, calculate $3 \times 12.5$:
     $$
     3 \times 12.5 = 37.5
     $$

2. **Subtraction**:
   - Substitute the results back into the expression:
     $$
     52.5 - 3 - 37.5
     $$
   - Perform the subtraction from left to right:
     $$
     52.5 - 3 = 49.5
     $$
     $$
     49.5 - 37.5 = 12
     $$

Thus, the final result of the expression is 12, which corresponds to Option 2.

**Explanation of Incorrect Options**:

- **Option 1 (52.5)**: This option might mistakenly consider only the first multiplication $17.5 \times 3$ without completing the entire expression. However, it does not account for the subsequent division and subtraction operations.

- **Option 3 (120)**: This option is incorrect as it does not align with any logical step in the calculation of the given expression. It might be a result of a misunderstanding or miscalculation of the operations involved.

- **Option 4 (50)**: This option could result from an error in the subtraction process, possibly by incorrectly subtracting the results of the division and multiplication. However, it does not match the correct evaluation of the expression.

Therefore, the correct answer is indeed Option 2, which is 12, as demonstrated by the step-by-step calculation above.