Nested division with decimals: Evaluate 0.15 ÷ (0.5 ÷ 15) by simplifying the inner division first and then completing the outer operation.
Aptitude
Decimal Fraction
Difficulty: Easy
Choose an option
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A4.5
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B45
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C0.03
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D0.45
Answer
Correct Answer: 4.5
Explanation
Introduction / Context:Nested divisions can be simplified by working from the inside out. This problem also reinforces that dividing by a fraction is equivalent to multiplying by its reciprocal, a crucial concept in decimal and fraction arithmetic alike.
Given Data / Assumptions:
- Expression: 0.15 ÷ (0.5 ÷ 15)
- All numbers are exact decimals.
Concept / Approach:First evaluate the inner operation 0.5 ÷ 15. Then divide 0.15 by that result. Alternatively, note that 0.5 ÷ 15 = 1/30, so the overall expression becomes 0.15 ÷ (1/30) = 0.15 × 30.
Step-by-Step Solution:
Inner: 0.5 ÷ 15 = 0.5 / 15 = 1/2 ÷ 15 = 1 / 30 ≈ 0.033333…Outer: 0.15 ÷ (1/30) = 0.15 × 30= 4.5Verification / Alternative check:
Compute directly as fractions: 0.15 = 15/100 = 3/20; then (3/20) ÷ (1/30) = (3/20) × 30 = 90/20 = 9/2 = 4.5.Why Other Options Are Wrong:
- 45: Treats 0.15 as 15, ignoring decimals.
- 0.03 or 0.45: Arise from inverting the wrong term or dropping a factor of 10.
Common Pitfalls:
- Performing outer division first, against order of operations.
- Misinterpreting 0.5 ÷ 15 as 0.5 × 15.
Final Answer:
4.5