2004 CEMC Gauss (Grade 8) Problems/Problem 2

Problem

The value of $\frac{1}{2} + \frac{3}{4} - \frac{5}{8}$ is

$\textbf{(A)}\ \frac{9}{14} \qquad\textbf{(B)}\ 0 \qquad\textbf{(C)}\ \frac{5}{8} \qquad\textbf{(D)}\ \frac{1}{4} \qquad\textbf{(E)}\ \frac{7}{8}$

We can first use a common denominator, and then find the value of the expression.

We can see that $2 = 2$ , $4 = 2^{2}$ , and $8 = 2^{3}$ . We then see that $8$ is the common denominator, so we have:

$\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}$

$\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$

$\frac{5}{8} = \frac{5 \times 1}{8 \times 1} = \frac{5}{8}$

Thus:

$\frac{1}{2} + \frac{3}{4} - \frac{5}{8} = \frac{4}{8} + \frac{6}{8} - \frac{5}{8} = \frac{4 + 6 - 5}{8}$

$=\frac{10 - 5}{8} = \boxed {\textbf {(C) } \frac{5}{8}}$

~anabel.disher

2004 CEMC Gauss (Grade 8) (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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CEMC Gauss (Grade 8)