Compute the fractional expression with correct order of operations: Evaluate 1 3/5 − (2/3 ÷ 12/13) + (7/5 × 1/3). Express the final result as a single simplified fraction.

Introduction / Context:
This simplification tests mastery of mixed numbers, fraction division and multiplication, and adding/subtracting with unlike denominators. The key is to convert the mixed number to an improper fraction, respect operation order, and reduce at the end for a neat, exact answer.

Given Data / Assumptions:

• Treat “×” as multiplication and “÷” as division.
• Expression: 1 3/5 − (2/3 ÷ 12/13) + (7/5 × 1/3).
• Final output should be a single simplified fraction.

Concept / Approach:
Use the rule a ÷ b = a * (1/b) for fractions. Do products and divisions before the outer additions/subtractions when grouped. Convert the mixed number 1 3/5 into an improper fraction to combine results over a common denominator.

Step-by-Step Solution:
Convert 1 3/5 = (5*1 + 3)/5 = 8/5.Evaluate division: 2/3 ÷ 12/13 = (2/3) * (13/12) = 26/36 = 13/18.Evaluate product: 7/5 × 1/3 = 7/15.Assemble: 8/5 − 13/18 + 7/15.Common denominator 90: 8/5 = 144/90, 13/18 = 65/90, 7/15 = 42/90.Compute: 144/90 − 65/90 + 42/90 = (144 − 65 + 42)/90 = 121/90.

Verification / Alternative check:
Reduce along the way if possible. None of 8/5, 13/18, or 7/15 further reduce together to a simpler path than using 90, and 121/90 is already in lowest terms (121 = 11^2, denominator 90 = 2 * 3^2 * 5, no common factor).

Why Other Options Are Wrong:
131/90 results from adding an extra 10/90; 19/30 and 11/30 come from incorrect common denominators; 30 ignores fraction arithmetic and order of operations.

Common Pitfalls:
Forgetting to invert the second fraction during division; treating 1 3/5 as 1 + 3/5 but then mixing denominators incorrectly; skipping the common denominator step.

Final Answer:
121/90