Simplify: 25 − (18 − 4 × 9 ÷ 3)

Correct — A. The stem is an image and reads: Simplify 25 − (18 − 4 × 9 ÷ 3).

Open the bracket last. Inside it, × and ÷ are settled before the subtraction:
4 × 9 = 36
36 ÷ 3 = 12

Now the subtraction inside the bracket:
18 − 12 = 6

Then the outer subtraction:
25 − 6 = 19 → option (a)

Why the others are wrong

• (b)
  33 — 33 needs the bracket to come to −8, so 4 × 9 ÷ 3 would have to be 26. Every reading of that product-and-quotient gives 12.
• (c)
  -31 — −31 needs the bracket to come to 56. The bracket is 18 minus a positive quantity, so it can never exceed 18, let alone reach 56.
• (d)
  -17 — −17 is what you get by doing 18 − 4 first: (18 − 4) × 9 ÷ 3 = 42, then 25 − 42. Multiplication and division outrank subtraction, so 4 × 9 ÷ 3 must go first.

Brackets are opened first, but the same hierarchy applies inside them. Within 18 − 4 × 9 ÷ 3 the product and the quotient are resolved before the minus sign.

× and ÷ share one rank and are worked left to right; + and − share the rank below. Here that ordering costs nothing either way: 4 × 9 ÷ 3 and 4 × (9 ÷ 3) both give 12.

So the only real decision in this question is refusing to do 18 − 4 first, even though those two numbers sit next to each other.

Key facts

• Inside 18 − 4 × 9 ÷ 3 the product and quotient come first, giving 18 − 12 = 6.
• × and ÷ have equal rank and are taken left to right, so 4 × 9 ÷ 3 equals 12 either way.
• A minus sign in front of a bracket applies to the bracket's finished value, not to its first term.
• 25 − 6 = 19, which is option (a).

Common traps

• Doing 18 − 4 first because it is written first.
• Carrying the outer minus onto both bracket terms without flipping the second sign, giving 25 − 18 − 12 = −5.
• Rushing the arithmetic and reading 4 × 9 ÷ 3 as 4 ÷ 9 × 3.

No directly related past PYQ was found.