Answer
$\frac{47}{32}$
Work Step by Step
First, the lowest common denominator of the three fractions that make up the length is found. 32 is the lowest number divisible by 2, 16 and 32, so it is the LCD.
Next, the fractions are multiplied so that their denominators are equal to the LCD. The first dimension, $\frac{1}{2}$ inches, is multiplied by 16, so that it is now equal to $\frac{16}{32}$, the second dimension, $\frac{11}{16}$, is multiplied by 2, so that it is now equal to $\frac{22}{32}$, and the third fraction, $\frac{9}{32}$, already has the LCD as its denominator, so it is not necessary to multiply it by anything.
The three new fractions we have, $\frac{16}{32}$, $\frac{22}{32}$ and $\frac{9}{32}$, are added together to get a sum of $\frac{47}{32}$. Therefore, the length marked in the diagram is equal to $\frac{47}{32}$.
