Mixed numbers to improper fractions; chained division and multiplication Evaluate exactly: 4 2/17 ÷ 1 2/5 * 2 2/33.

Introduction / Context:
Converting mixed numbers to improper fractions is essential before performing sequential division and multiplication. This exercise ensures you can manage multiple conversions and simplifications without losing accuracy.

Given Data / Assumptions:

• Expression: 4 2/17 ÷ 1 2/5 * 2 2/33.
• All operations are exact with rational numbers.
• No rounding should be used; simplify by cancellation where possible.

Concept / Approach:
Convert each mixed number to an improper fraction. Replace division by multiplication with the reciprocal. Then perform cancellations before multiplying to keep numbers small and avoid arithmetic errors. The final result should be reduced to lowest terms if any common factors remain.

Step-by-Step Solution:
Convert: 4 2/17 = 70/17 (since 4*17 + 2 = 70).Convert: 1 2/5 = 7/5; 2 2/33 = 68/33.Rewrite: (70/17) ÷ (7/5) * (68/33) = (70/17) * (5/7) * (68/33).Cancel 70/7 = 10: gives (10*5/17) * (68/33) = (50/17) * (68/33).Cancel 68/17 = 4: yields (50*4)/33 = 200/33.

Verification / Alternative check:
Decimal approximation: 200/33 ≈ 6.0606. Computing the original expression numerically (with adequate precision) produces the same value, confirming the rational arithmetic.

Why Other Options Are Wrong:
61/11 (~5.545) and 81/11 (~7.364) reflect partial cancellations or misplaced reciprocals.42/13 (~3.231) comes from incorrect conversions of mixed numbers.

Common Pitfalls:
Forgetting to invert the divisor; skipping the simplification 68/17 = 4; or mishandling the mixed-to-improper conversion, which often leads to off-by-one numerators.

Final Answer:
200/33