Solve the equation. \[ \begin{array}{l}k+\frac{1}{8}=11 \frac{1}{4} \\ k=\square \\ \text { (Type a whole number, fraction, or mixed number.) }\end{array} \]

To solve the equation \( k + \frac{1}{8} = 11 \frac{1}{4} \), first convert the mixed number \( 11 \frac{1}{4} \) into an improper fraction. \[ 11 \frac{1}{4} = \frac{(11 \times 4) + 1}{4} = \frac{44 + 1}{4} = \frac{45}{4} \] Now, rewrite the equation: \[ k + \frac{1}{8} = \frac{45}{4} \] Next, subtract \( \frac{1}{8} \) from both sides: \[ k = \frac{45}{4} - \frac{1}{8} \] To perform this subtraction, find a common denominator, which is 8: Convert \( \frac{45}{4} \) to have the same denominator: \[ \frac{45}{4} = \frac{45 \times 2}{4 \times 2} = \frac{90}{8} \] Now perform the subtraction: \[ k = \frac{90}{8} - \frac{1}{8} = \frac{90 - 1}{8} = \frac{89}{8} \] Therefore, the solution is: \[ k = \frac{89}{8} \] You can also express \( \frac{89}{8} \) as a mixed number: \[ \frac{89}{8} = 11 \frac{1}{8} \] So, the final answer can be written as either: \[ k = \frac{89}{8} \quad \text{or} \quad k = 11 \frac{1}{8} \]