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2011 CEMC Gauss (Grade 8) Problems/Problem 1

Problem

If $\frac{8}{12} = \frac{\framebox {}}{3}$, then the value represented by $\framebox {}$ is

$\text{ (A) }\ 24\qquad\text{ (B) }\ 1\qquad\text{ (C) }\ 12\qquad\text{ (D) }\ 2\qquad\text{ (E) }\ 4$

Solution

$\frac{12}{3} = 4$, meaning we can divide the numerator and denominator by $4$ to arrive at our answer.

$\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}$

Since the numerator is $2$, the answer is $\boxed {\textbf {(D) }2}$.

~anabel.disher

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