Simplify 15.5 − [3 − {7 − (5 − (14.5 − 13.5))}].

Correct — A. Clear the brackets from the inside outwards, one at a time.

14.5 − 13.5 = 1
5 − 1 = 4
7 − 4 = 3
3 − 3 = 0

15.5 − 0 = 15.5 → option (a).

The entire square bracket collapses to zero, so the leading 15.5 survives untouched. An answer equal to the first number is not a sign that a step was skipped.

Why the others are wrong

• (b)
  13.5 — 13.5 drops a sign. Reading 7 − (5 − 1) as 7 − 5 − 1 = 1 gives 3 − 1 = 2, then 15.5 − 2. The minus governs the whole bracket, so the step is 7 − 4.
• (c)
  14.5 — 14.5 is 15.5 − 1, the innermost value taken straight off the front number. That 1 still has three brackets to pass through before it can reach the 15.5.
• (d)
  12.5 — 12.5 is 15.5 − 3, treating the square bracket as though it were just the 3. The braces inside cancel that 3 exactly, which is why the bracket is worth 0.

BODMAS fixes the order of the brackets themselves: innermost first, then outwards through ( ), { } and finally [ ].

Every operation in this expression is a subtraction, so the only thing that can go wrong is a sign. A minus in front of a bracket applies to everything inside it, and each cleared bracket carries its own sign out with it.

Four separate lines cost a few seconds and remove the risk entirely. Doing it in one line is where the mark goes.

Key facts

• Brackets are cleared innermost outwards: ( ), then { }, then [ ].
• A minus sign in front of a bracket applies to every term inside it.
• 15.5 − [3 − {7 − (5 − 1)}] = 15.5 − [3 − 3] = 15.5.

Common traps

• Reading 7 − (5 − 1) as 7 − 5 − 1.
• Working outside-in, which is the wrong direction for brackets.
• Distrusting an answer that equals the leading number and re-doing the sum until it changes.

No directly related past PYQ was found.