Introduction / Context:
This computation chains percentages and fractions with a final multiplication by 10000. Converting percents to decimals and simplifying stepwise keeps arithmetic clean.
Given Data / Assumptions:
- Expression: 12 * (26/100) * (5/78) * (38/100) * (7/152) * 10000.
- All operations are multiplications; order can be regrouped for easier cancellation.
Concept / Approach:
Convert percents to fractions, then cancel common factors before multiplying. Look for simplifications like 10000 with denominators 100 and 152/78 factors.
Step-by-Step Solution:
Rewrite: 12 * (26/100) * (5/78) * (38/100) * (7/152) * 10000.First, combine the percent denominators with 10000: (100 * 100) in denominator cancels to 100 with 10000, leaving a factor 100.Now compute (7/152) * 100 = 700/152 = 25 * (28/152) = 25 * (7/38) = 175/38.Multiply remaining fractions: (26 * 5 * 38) / 78 = (26 * 5 * 38) / (2 * 39).Since 38 = 2 * 19 and 26 = 2 * 13, numerator = (2*13)*5*(2*19) = 4 * 13 * 5 * 19; divide by 2 in denominator ⇒ 2 * 13 * 5 * 19 / 39.39 = 3 * 13; cancel 13 ⇒ (2 * 5 * 19) / 3 = 190/3.Now: 12 * (190/3) * (175/38) = 4 * 190 * (175/38) (since 12/3 = 4).4 * 190 = 760. Then 760 * 175 / 38 = (760/38) * 175 = 20 * 175 = 3500.Finally divide by remaining 100 from earlier percent handling → 3500 / 100 = 35.Verification / Alternative check:
Numerical evaluation with decimals also yields 35 (e.g., 0.26 * 0.38 * 12 * 10000 * 5/78 * 7/152).
Why Other Options Are Wrong:
- 38, 41, 52, 28 are distractors near the true value but not equal to the exact simplification 35.
Common Pitfalls:
Forgetting to convert percents to fractions, or mismanaging cancellations with 10000 leading to a factor-of-10 error.
Final Answer:
35
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