Evaluate: 71/4 - [5/6 ÷ \1/3 - (1/2 × (3/4 - 1/4))\]

Question

Evaluate: 71/4 - [5/6 ÷ \1/3 - (1/2 × (3/4 - 1/4))\]

1. A. -31/4
2. B. 31/4
3. C. -23/4 (Correct answer)
4. D. 23/4

Correct Answer

Option C — -23/4

Detailed Solution & Explanation

The correct answer is $-2\dfrac{3}{4}$.

Key Points

• Work outward through the brackets.
• Innermost: $\tfrac{3}{4}-\tfrac{1}{4}=\tfrac{1}{2}$; then $\tfrac{1}{2}\times\tfrac{1}{2}=\tfrac{1}{4}$; then $\tfrac{1}{3}-\tfrac{1}{4}=\tfrac{1}{12}$; then $\tfrac{5}{6}\div\tfrac{1}{12}=\tfrac{5}{6}\times12=10$.
• Finally $7\tfrac{1}{4}-10=\tfrac{29}{4}-10=-\tfrac{11}{4}=-2\tfrac{3}{4}$.
• Nested BODMAS is safest resolved from the innermost bracket outward, one operation at a time; the sign flips negative only at the last subtraction.