10. Joel is \( 2 \frac{1}{2} \) inches shorter than Carlos. Carlos is \( 1 \frac{1}{4} \) inches taller than Dan. If Dan is \( 58 \frac{1}{4} \) inches tall, how many inches tall is Joel?

Let's break it down step by step! First, we need to determine Carlos's height. If Dan is \( 58 \frac{1}{4} \) inches tall and Carlos is \( 1 \frac{1}{4} \) inches taller than Dan, we add those heights together: \( 58 \frac{1}{4} + 1 \frac{1}{4} = 59 \frac{1}{2} \) inches. Now, we find Joel's height by subtracting \( 2 \frac{1}{2} \) inches from Carlos's height: \( 59 \frac{1}{2} - 2 \frac{1}{2} = 57 \) inches. So, Joel is 57 inches tall! Mathematically, always double-check conversions between whole numbers and fractions to avoid any miscalculations. A little attention can prevent common mistakes, like losing track of the fractional parts during additions or subtractions! This type of height comparison and relationships appears in various fields, including architecture, fashion design, or even sports. Knowing how different people's heights relate can be useful, whether you're designing a space that accommodates everyone or crafting an outfit that flatters various body types!