is equal to:

Correct — A. The bar drawn over 1⁄3 + 1⁄2 is a vinculum, and a vinculum is settled before any bracket.

Vinculum: 1⁄3 + 1⁄2 = 2⁄6 + 3⁄6 = 5⁄6
Round bracket: 5⁄6 − 5⁄6 = 0
Curly bracket: 4 × 0 = 0
Square bracket: 1 + 0 = 1

Finally 9 ÷ 1 = 9, which is option (a).

Why the others are wrong

• (b)
  Option (b) is 1, the value of the square bracket. That is a real intermediate step, but the 9 ÷ in front of it has not been carried out yet.
• (c)
  Option (c), 9⁄5, is what ignoring the bar gives: 5⁄6 − 1⁄3 + 1⁄2 read left to right is 1, then 4 × 1 = 4, 1 + 4 = 5 and 9 ÷ 5.
• (d)
  Option (d) is 0, the value inside the curly bracket. It disappears the moment the 1 + outside that bracket is applied.

The full order of operations is V-BODMAS: Vinculum, then Brackets, then Of, Division, Multiplication, Addition, Subtraction. The vinculum is the bar drawn over a group of terms and it outranks everything.

Once the bar is resolved to 5⁄6, the round bracket becomes 5⁄6 − 5⁄6 = 0, and a zero inside a product wipes out the curly bracket entirely.

Work outward one bracket at a time — round, then curly, then square — and write each value down rather than holding it in your head.

Key facts

• A vinculum is resolved before brackets — the order is Vinculum, Bracket, Of, Division, Multiplication, Addition, Subtraction.
• 1⁄3 + 1⁄2 = 5⁄6, exactly the quantity it is subtracted from, so the round bracket is 0.
• Any product containing that 0 is 0, so the square bracket is 1 and the whole expression is 9 ÷ 1.

Common traps

• Treating the bar as decoration and working 5⁄6 − 1⁄3 + 1⁄2 left to right, which yields 9⁄5.
• Stopping at the square bracket's value of 1 and never dividing 9 by it.
• Rushing the LCM and writing 1⁄3 + 1⁄2 as 2⁄5, which breaks the cancellation the item is built on.

No directly related past PYQ was found.