Problem 2 · 1991 AJHSME
Easy
Arithmetic & Operations
order-of-operations
16 + 84 − 2 =
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Answer: C — 12.
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Hint 1 of 2
A long fraction bar is invisible parentheses: it says "finish ALL of the top and ALL of the bottom first, then divide." What are those two totals?
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Hint 2 of 2
Treat it as (16 + 8) ÷ (4 − 2) — the bar groups, so the add and the subtract both happen before the division.
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Approach: the fraction bar groups top and bottom — collapse each, then divide
- The bar acts like parentheses around the whole top and the whole bottom: top = 16 + 8 = 24, bottom = 4 − 2 = 2.
- Now divide the two totals: 24 ÷ 2 = 12.
- Trap to dodge: don't divide term-by-term (16÷4 + 8÷2 = 8) — the bar isn't shorthand for that. It groups everything above against everything below.
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