Difficulty: Easy
Correct Answer: 207/32
Explanation:
Introduction / Context:This question checks precision with multiplying and dividing rational numbers. The fastest path is to convert the entire expression to a product by multiplying with the reciprocal of the divisor, then cancel common factors.
Given Data / Assumptions:
Concept / Approach:Division by a fraction equals multiplication by its reciprocal. Cancel shared factors before multiplying across to avoid large intermediate numbers.
Step-by-Step Solution:
Rewrite division: (5/8) * (23/5) * (9/4).Cancel 5 in (5/8) with the 5 in (23/5), yielding (23/8) * (9/4).Multiply numerators: 23 * 9 = 207.Multiply denominators: 8 * 4 = 32.Result = 207/32 (already in lowest terms).Verification / Alternative check:As a decimal: 207/32 = 6.46875. Computing each step numerically also gives 6.46875, confirming the fraction.
Why Other Options Are Wrong:9/4 and 27/8 reflect partial multiplication errors; 23/32 comes from inverting the wrong factor; 13/10 is unrelated.
Common Pitfalls:Forgetting to flip the last fraction, canceling across addition (not allowed), or prematurely rounding decimals. Keep everything fractional until the end.
Final Answer:207/32
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