Evaluate: \(6 - [2/3 ÷ \1/6 + (1/2× (1 - 1/3))\]\)

Question

Evaluate: \(6 - [2/3 ÷ \1/6 + (1/2× (1 - 1/3))\]\)

1. A. \(14/3\) (Correct answer)
2. B. \(15/3\)
3. C. \(16/3\)
4. D. \(17/3\)

Correct Answer

Option A — \(14/3\)

Detailed Solution & Explanation

The correct answer is 14/3.

Key Points

• Work strictly outward from the innermost bracket:
  • 1 − 1/3 = 2/3
  • 1/2 × 2/3 = 1/3
  • 1/6 + 1/3 = 1/6 + 2/6 = 1/2
  • 2/3 ÷ 1/2 = 2/3 × 2/1 = 4/3
  • 6 − 4/3 = 18/3 − 4/3 = 14/3

Additional Information

• The bracket hierarchy is ( ) → { } → [ ], innermost first — the "B" of BODMAS, and the whole point of this question.
• Dividing by a fraction means multiplying by its reciprocal: a ÷ (b/c) = a × (c/b).
• Note that option B, 15/3, simplifies to 5 — options are sometimes left unsimplified to disguise a familiar value, so reduce every option mentally before comparing.
• Convert whole numbers to the common denominator before the final subtraction; writing 6 as 18/3 prevents the commonest slip here.

प्रश्न (हिन्दी में)

मूल्यांकन कीजिए: \(6 - [2/3 ÷ \1/6 + (1/2× (1 - 1/3))\]\)

1. A. \(14/3\)
2. B. \(15/3\)
3. C. \(16/3\)
4. D. \(17/3\)