Problem 5 · 1989 AJHSME
Medium
Arithmetic & Operations
order-of-operations
−15 + 9 × (6 ÷ 3) =
Show answer
Answer: D — 3.
Show hints
Hint 1 of 3
You can't just sweep left to right — multiplication and the parentheses outrank addition and must happen first.
Still stuck? Show hint 2 →
Hint 2 of 3
Order of operations: parentheses, then × and ÷, then + and −. The +(−15) waits until the very end.
Still stuck? Show hint 3 →
Hint 3 of 3
After the multiplication you'll add a positive number to −15, which moves you up the number line toward zero and past it.
Show solution
Approach: resolve parentheses and × before the +
- Parentheses first: 6 ÷ 3 = 2. Multiplication next, since × outranks + : 9 × 2 = 18.
- Only now does the addition happen. Starting at −15 and adding 18 walks 18 steps up the number line: −15 + 18 = 3.
- Trap to avoid: reading left to right would give (−15 + 9) × … and a wrong negative answer like −12. The order of operations, not the reading order, decides what combines first.
Mark:
· log in to save