2015 CEMC Gauss (Grade 8) Problems/Problem 10

Problem

The number represented by $\Box$ so that $\frac{1}{2} + \frac{1}{4} = \frac{\Box}{12}$ is

$\textbf{(A)}\ 3 \qquad\textbf{(B)}\ 12 \qquad\textbf{(C)}\ 9 \qquad\textbf{(D)}\ 6 \qquad\textbf{(E)}\ 15$

We can first convert the fractions into twelfths, and then add them:

$\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}$

$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$

Adding these, we have:

$\frac{1}{2} + \frac{1}{4} = \frac{6 + 3}{12} = \frac{9}{12}$

Since the box simply represents the numerator of the resulting fraction in terms of twelfths, the answer is $\boxed {\textbf {(C) } 9}$

~anabel.disher