(0.1667 × 0.8333 × 0.3333) / (0.2222 × 0.6667 × 0.1250) is approximately equal to:

Question

(0.1667 × 0.8333 × 0.3333) / (0.2222 × 0.6667 × 0.1250) is approximately equal to:

1. A. 2.5 (Correct answer)
2. B. 4.5
3. C. 0.5
4. D. 0.25

Correct Answer

Option A — 2.5

Detailed Solution & Explanation

The correct answer is 2.5.

Key Points

• Recognise each decimal as a familiar fraction:
  • 0.1667 ≈ 1/6, 0.8333 ≈ 5/6, 0.3333 ≈ 1/3
  • 0.2222 ≈ 2/9, 0.6667 ≈ 2/3, 0.1250 = 1/8
• Numerator = (1/6)(5/6)(1/3) = 5/108.
• Denominator = (2/9)(2/3)(1/8) = 4/216 = 1/54.
• Dividing: (5/108) × 54 = 5/2 = 2.5.

Additional Information

• Converting recurring decimals to fractions turns a messy six-factor multiplication into cancellation — the whole point of the question.
• The conversions worth instant recall: 0.1667 = 1/6, 0.2222 = 2/9, 0.3333 = 1/3, 0.6667 = 2/3, 0.8333 = 5/6, 0.125 = 1/8, 0.1111 = 1/9, 0.4444 = 4/9.
• A rough estimate confirms the scale: the numerator is about 0.046 and the denominator about 0.0185, so the ratio is near 2.5 — enough to pick the option without exact work.
• The word approximately signals that the decimals are rounded forms of exact fractions, which is the hint to convert.