By using which sequence of mathematical operators will the expression 18 ? 6 ? 9 ? 27 become a correct equation?

Introduction / Context:
In this question, you are given an expression with three blanks for operators and four numerical options for which operators should go in which position. The goal is to select the sequence of operators so that the resulting mathematical sentence becomes a correct equation. This tests understanding of operator precedence and basic arithmetic.

Given Data / Assumptions:

- The incomplete expression is: 18 ? 6 ? 9 ? 27.
- Each option provides three operators in order, to fill the three question marks.
- We must form a true equation by using one of the sequences.
- Standard precedence rules (multiplication and division before addition and subtraction) apply after substitution.

Concept / Approach:
We treat each option as a proposed pattern for the three blanks. For each option, we substitute the given operators in order and evaluate the left-hand side. If the expression simplifies to 27, and the final symbol is "=", we have a valid equation. Systematic trial of each option with careful arithmetic is efficient here.

Step-by-Step Solution:
Test option B: "÷, × and =". Substitute the operators into 18 ? 6 ? 9 ? 27. We get: 18 ÷ 6 × 9 = 27. Now evaluate the left-hand side using precedence. First compute 18 ÷ 6 = 3. Then compute 3 × 9 = 27. So the left-hand side equals 27, which matches the right-hand side 27. Thus, 18 ÷ 6 × 9 = 27 is a correct equation.

Verification / Alternative check:
Check another option briefly to confirm it fails. For example, option A suggests "×, ÷ and =". That would give 18 × 6 ÷ 9 = 27. Evaluating, 18 × 6 = 108 and 108 ÷ 9 = 12, so we would have 12 = 27, which is false. Similar issues arise for options C and D, where the left-hand sides do not simplify to 27.

Why Other Options Are Wrong:

- Option A produces 18 × 6 ÷ 9 = 27, which simplifies to 12 = 27, not correct.
- Option C yields 18 × 6 + 9 = 27, which becomes 108 + 9 = 117, again false.
- Option D gives 18 + 6 − 9 = 27, which simplifies to 15 = 27, also incorrect.

Thus, only option B satisfies the equation.

Common Pitfalls:
Some learners might ignore operator precedence and evaluate strictly from left to right, which could temporarily make wrong options seem plausible. Others may misplace the equality sign, forgetting that it must compare two sides, not act as an operator. Remember to apply division and multiplication before addition or subtraction when checking each possibility.

Final Answer:
The correct sequence of operators is "÷, × and =", so the valid equation is 18 ÷ 6 × 9 = 27. The correct choice is ÷, × and =.