If # = ×, @ = -, and $ = +, then evaluate: 9 # 2 @ 3 $ 1

Concept: In order-of-operations problems (BODMAS/PEMDAS), operators are ranked: brackets, then multiplication/division, then addition/subtraction. Critically, when two operators share the SAME rank — such as addition and subtraction — there is no further hierarchy between them: they must be evaluated strictly in left-to-right sequence, exactly as they appear in the expression. Grouping same-rank operations out of order (e.g., doing every addition first, then every subtraction) is not a rule of BODMAS and produces a wrong result.

Step-by-step:

1. Replace each symbol with its operation: 9 # 2 @ 3 $ 1 becomes 9 × 2 − 3 + 1.

2. Perform the higher-precedence operation first: 9 × 2 = 18, so the expression reduces to 18 − 3 + 1.

3. Evaluate the remaining addition and subtraction strictly left to right: 18 − 3 = 15, then 15 + 1 = 16.

Cross-check: If addition were incorrectly grouped before subtraction — treating 3 + 1 = 4 first, then 18 − 4 — the result would be 14, but this violates the left-to-right rule for equal-precedence operators and is not a valid application of BODMAS. Evaluating strictly left to right confirms the expression equals 16.