In the following arithmetic expression, apply the correct order of operations and determine the value that should replace the question mark (?). 452 + 312 ÷ 13 = 34 × ?

Introduction / Context:
This question tests application of the order of operations, commonly known as BODMAS or PEMDAS, in an equation that relates an arithmetic expression to a product involving an unknown multiplier. The learner must correctly evaluate the left hand side and then solve for the missing value on the right hand side.

Given Data / Assumptions:
- Expression: 452 + 312 ÷ 13 = 34 × ? - Division must be carried out before addition. - The symbol × denotes multiplication.

Concept / Approach:
According to the order of operations, division is performed before addition, and multiplication is handled once both sides of the equation are simplified. After evaluating the left side completely, the result is equated to 34 times the unknown number. Solving this simple linear equation gives the required value of the question mark.

Step-by-Step Solution:
Step 1: Evaluate the division on the left side: 312 ÷ 13. Step 2: Perform the division: 312 ÷ 13 = 24. Step 3: Add this result to 452: 452 + 24 = 476. Step 4: Now the equation becomes 476 = 34 × ?. Step 5: Solve for the unknown: ? = 476 ÷ 34. Step 6: Compute 476 ÷ 34 = 14.

Verification / Alternative check:
To verify, substitute 14 back into the equation. Compute 34 × 14, which equals 476. The left side is also 452 + (312 ÷ 13) = 452 + 24 = 476. Since both sides give the same result, the value 14 correctly satisfies the equation.

Why Other Options Are Wrong:
- Option 12 would give 34 × 12 = 408, which does not match the left side value 476. - Option 16 would give 34 × 16 = 544, larger than the left side result. - Option 18 would produce 34 × 18 = 612, which is again not equal to 476.

Common Pitfalls:
Some learners mistakenly add first and divide later, which gives an incorrect value for the left side. Others may perform the division but then miscalculate the final division when solving for the unknown. Careful, stepwise use of the order of operations is crucial in such problems.

Final Answer:
The value of the question mark is 14, so the correct option is 14.