2012 AMC 8 Problems/Problem 4

Problem

Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat?

$\textbf{(A)}\hspace{.05in}\frac{1}{24}\qquad\textbf{(B)}\hspace{.05in}\frac{1}{12}\qquad\textbf{(C)}\hspace{.05in}\frac{1}{8}\qquad\textbf{(D)}\hspace{.05in}\frac{1}{6}\qquad\textbf{(E)}\hspace{.05in}\frac{1}{4}$

Solution 1

Peter ate $1 + \frac{1}{2} = \frac{3}{2}$ slices. The pizza has $12$ slices total. Taking the ratio of the amount of slices Peter ate to the amount of slices in the pizza, we find that Peter ate $\dfrac{\frac{3}{2}\text{ slices}}{12\text{ slices}} = \boxed{\textbf{(C)}\ \frac{1}{8}}$ of the pizza.

Solution 2

Another way of doing this question is adding the slices separately. When Peter splits a slice of pizza into two, the equation is 1/2 of 1/12. The answer for the split half a piece, is 1/24. Adding by 1/12 is the answer which is 1/8 of the pizza. ~SmartGrowth

2012 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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All AJHSME/AMC 8 Problems and Solutions

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2012 AMC 8 Problems/Problem 4

Contents

Problem

Solution 1

Solution 2

See Also