1998 AMC 8 Problem 3

Attempt Problem 3 of the 1998 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 1998 AMC 8 solutions, or check the answer key.

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

3.

What is the value of the following expression? 38+7845\dfrac{\frac{3}{8}+\frac{7}{8}}{\frac{4}{5}}
11
2516 \dfrac{25}{16}
22
4320\dfrac{43}{20}
4716\dfrac{47}{16}
Answer: B
Concepts:fraction
Small hint:
Add the numerator fractions first.
Big hint:
Dividing by 45\frac{4}{5} means multiplying by 54.\frac{5}{4}.
Solution:
This evaluates to: 38+7845=5445=(54)2=2516.\begin{align*} \dfrac{\frac{3}{8}+\frac{7}{8}}{\frac{4}{5}} &= \dfrac{\frac{5}{4}}{\frac{4}{5}} \\ &=\left(\dfrac{5}{4}\right)^2 \\ &= \dfrac{25}{16}.\end{align*}
Thus, the correct answer is B .
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