What number is one third of the way from $\frac14$ to $\frac34$?
$\textbf{(A)}\ \frac {1}{3} \qquad \textbf{(B)}\ \frac {5}{12} \qquad \textbf{(C)}\ \frac {1}{2} \qquad \textbf{(D)}\ \frac {7}{12} \qquad \textbf{(E)}\ \frac {2}{3}$
Solution 1
We can rewrite the two given fractions as $\frac 3{12}$ and $\frac 9{12}$. (We multiplied all numerators and denominators by $3$.)
Now it is obvious that the interval between them is divided into three parts by the fractions $\boxed{\frac 5{12}}$ and $\frac 7{12}$.

Solution 2
The number we seek can be obtained as a weighted average of the two endpoints, where the closer one has weight $2$ and the further one $1$. We compute:
\[\dfrac{ 2\cdot\frac 14 + 1\cdot\frac 34 }3 = \dfrac{ \frac 54 }3 = \boxed{\dfrac 5{12}}\]