1986 AMC 8 Problem 6

Attempt Problem 6 of the 1986 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1986 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

6.

What is the value of the following expression?
21−23\frac{2}{1 - \frac{2}{3}}
−3-3
−43-\dfrac43
23\dfrac23
22
66
Answer: E
Concepts:fractionorder of operations
Small hint:
First simplify the denominator 1−231 - \dfrac23
Big hint:
Dividing by 13\dfrac13 is the same as multiplying by 33
Solution:
The denominator is 1−23=13,1 - \dfrac23 = \dfrac13, so the expression is 213=2×3=6.\dfrac{2}{\frac{1}{3}} = 2 \times 3 = 6.
Thus, the correct answer is E .
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