1989 AMC 8 Problem 12

Attempt Problem 12 of the 1989 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 1989 AMC 8 solutions, or check the answer key.

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

12.

What is the value of
1−131−12?\frac{1 - \frac{1}{3}}{1 - \frac{1}{2}}?
13\dfrac{1}{3}
23\dfrac{2}{3}
34\dfrac{3}{4}
32\dfrac{3}{2}
43\dfrac{4}{3}
Answer: E
Concepts:fraction
Small hint:
Simplify the numerator and denominator separately
Big hint:
1−13=231 - \frac{1}{3} = \frac{2}{3} and 1−12=12;1 - \frac{1}{2} = \frac{1}{2}; then divide
Solution:
The numerator is 1−13=23,1 - \frac{1}{3} = \frac{2}{3}, and the denominator is 1−12=12.1 - \frac{1}{2} = \frac{1}{2}.
Dividing gives 23÷12=23×2=43.\frac{2}{3} \div \frac{1}{2} = \frac{2}{3} \times 2 = \frac{4}{3}.
Thus, the correct answer is E .
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