Difficulty: Easy
Correct Answer: 117/32
Explanation:
Introduction / Context:This question checks fluency with mixed numbers, improper fractions, and division of fractions. Success depends on consistent conversion and careful cancellation to avoid arithmetic bloat.
Given Data / Assumptions:
Concept / Approach:Convert 2 3/5 to an improper fraction: 2 3/5 = 13/5. Division by 4/9 is multiplication by its reciprocal 9/4. Multiply numerators and denominators and simplify if possible.
Step-by-Step Solution:
Rewrite: (5/8) × (13/5) ÷ (4/9) = (5/8) × (13/5) × (9/4).Cancel the common factor 5: (5/8) × (13/5) → (1/8) × 13.Multiply remaining: (13/8) × (9/4) = (13 × 9) / (8 × 4).Compute: 117 / 32. This is already in lowest terms.Verification / Alternative check:As a decimal, 117/32 = 3.65625. Back-multiplying confirms the same decimal from the original sequence, indicating no cancellation mistakes.
Why Other Options Are Wrong:213/27, 111/27, 223/32, and 321/32 arise from mixing the divide-by-reciprocal step or misapplying cancellation. None reduce to the correct value 117/32.
Common Pitfalls:Forgetting to invert 4/9 during division, leaving the mixed number unconverted, or dropping factors during cancellation.
Final Answer:117/32
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