1988 AMC 8 Problem 15

Attempt Problem 15 of the 1988 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 1988 AMC 8 solutions, or check the answer key.

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

15.

What is the reciprocal of (12+13)?\left(\dfrac{1}{2} + \dfrac{1}{3}\right)?
16\dfrac{1}{6}
25\dfrac{2}{5}
65\dfrac{6}{5}
52\dfrac{5}{2}
55
Answer: C
Concepts:fraction
Small hint:
First add the fractions using a common denominator of 66
Big hint:
The reciprocal flips the numerator and denominator
Solution:
Adding, 12+13=36+26=56.\dfrac{1}{2} + \dfrac{1}{3} = \dfrac{3}{6} + \dfrac{2}{6} = \dfrac{5}{6}.
The reciprocal of 56\dfrac{5}{6} is 65.\dfrac{6}{5}.
Thus, the correct answer is C .
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