Order of operations with implied square Evaluate (69 − 14 × 3 + 2) / [9 × 5 − (5)^2].

Introduction / Context:This expression combines multiplication, subtraction, addition, and an implied square. Correct evaluation depends on strict application of precedence: powers, then multiplication/division, then addition/subtraction, all left to right.

Given Data / Assumptions:

• Numerator: 69 − 14 × 3 + 2.
• Denominator: 9 × 5 − (5)^2.
• Assume (5)^2 denotes 25.

Concept / Approach:Compute products and powers first, then combine with additions/subtractions. After reducing numerator and denominator, perform the final division, simplifying to decimal if appropriate.

Step-by-Step Solution:Numerator: 14 × 3 = 42; then 69 − 42 + 2 = 27 + 2 = 29.Denominator: 9 × 5 = 45; (5)^2 = 25; then 45 − 25 = 20.Value = 29 / 20 = 1.45.

Verification / Alternative check:Convert to fraction and mixed number: 29/20 = 1 and 9/20 = 1.45; arithmetic is consistent.

Why Other Options Are Wrong:2.75, 26.5, and 265 are orders of magnitude off; 1.2 reflects miscomputing the numerator or denominator.

Common Pitfalls:Treating (5)^2 as 10; adding before doing the product 14 × 3; forgetting the final +2 in the numerator.

Final Answer:1.45