Evaluate using precedence rules Compute the value of (7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5).

Introduction / Context:This problem demonstrates strict adherence to operator precedence (division before addition) inside both numerator and denominator. Mastery of BODMAS/PEMDAS prevents common mistakes.

Given Data / Assumptions:

• Expression: (7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5).
• No hidden parentheses beyond those shown.

Concept / Approach:Resolve the division terms first in both numerator and denominator. Then perform the additions, and finally divide the simplified numerator by the simplified denominator.

Step-by-Step Solution:Numerator: 7 + 7 + (7 ÷ 7) = 7 + 7 + 1 = 15.Denominator: 5 + 5 + (5 ÷ 5) = 5 + 5 + 1 = 11.Overall value = 15 / 11.

Verification / Alternative check:Convert to mixed numbers if desired: 15/11 = 1 and 4/11, but the fractional form is exact and preferred.

Why Other Options Are Wrong:1 would require numerator = denominator; 1/5 and 3/11 result from misplacing the division; 11/15 is the reciprocal, not the value.

Common Pitfalls:Adding before dividing; treating 7 ÷ 7 as 7; forgetting to compute the 5 ÷ 5 term in the denominator.

Final Answer:15 / 11