Solution: Convert $2 \frac{1}{2}$ to an improper fraction: $\frac{5}{2}$. Subtract $\frac{3}{4}$: $\frac{5}{2} - \frac{3}{4} = \frac{10}{4} - \frac{3}{4} = \frac{7}{4}$. The remaining storage is $\frac{7}{4}$ terabytes, which is $\boxed{\dfrac{7}{4}}$ of the total.

["How to Convert $2 \frac{1}{2}$ to an Improper Fraction and Subtract $\frac{3}{4}$: A Step-by-Step Explanation", "Understanding how to convert mixed numbers into improper fractions is essential in mathematics and helps simplify complex arithmetic problems. In this guide, we’ll explore the conversion of $2 \frac{1}{2}$ to its equivalent improper fraction, perform the subtraction of $\frac{3}{4}$, and interpret the result as remaining storage — demonstrating practical math in real-world contexts.", "---", "### Step 1: Convert $2 \frac{1}{2}$ to an Improper Fraction", "Mixed numbers consist of a whole number and a proper fraction. To convert $2 \frac{1}{2}$ into an improper fraction:", "1. Multiply the whole number by the denominator:\n $2 \ imes 2 = 4$\n2. Add the numerator:\n $4 + 1 = 5$\n3. Place the result over the denominator:\n $\frac{5}{2}$", "✅ So, $2 \frac{1}{2} = \frac{5}{2}$", "---", "### Step 2: Subtract $\frac{3}{4}$ from $\frac{5}{2}$", "Subtracting fractions requires a common denominator. Here’s how to proceed:", "- Convert $\frac{5}{2}$ to a fraction with denominator 4:\n $\frac{5}{2} = \frac{5 \ imes 2}{2 \ imes 2} = \frac{10}{4}$", "- Now subtract:\n $\frac{10}{4} - \frac{3}{4} = \frac{7}{4}$", "✅ Therefore,\n$$\n\frac{5}{2} - \frac{3}{4} = \frac{7}{4}\n$$", "---", "### Step 3: Interpret the Result — Remaining Storage", "The result, $\frac{7}{4}$ terabytes, represents the remaining digital storage after a subtraction operation — a common scenario in computing and data management.", "This fraction can also be expressed as a mixed number:\n$$\n\frac{7}{4} = 1 \frac{3}{4}\n$$\nSo, there are 1 and 3/4 terabytes left — equivalent to $\frac{7}{4}$ as an improper fraction.", "---", "### Final Answer:\n$$\n\frac{5}{2} - \frac{3}{4} = \frac{7}{4}\n$$\nThe remaining storage is $\boxed{\frac{7}{4}}$ terabytes — exactly $\frac{7}{4}$ of the total capacity.", "---", "### Why This Conversion Matters", "Working with improper fractions simplifies addition, subtraction, and calculations in fields like data science, engineering, and computing. Whether managing storage, processing data, or solving equations, mastering these conversions ensures accuracy and efficiency.", "---", "### Summary", "- $2 \frac{1}{2} = \frac{5}{2}$\n- $\frac{5}{2} - \frac{3}{4} = \frac{7}{4}$\n- Remaining storage: $\boxed{\frac{7}{4}}$ terabytes", "Next time you need to subtract fractions or work with mixed numbers, convert to improper fractions first — it makes the math cleaner and faster!", "---", "Keywords: convert $2 \frac{1}{2}$ to improper fraction, subtract fractions, improper fraction calculation, $\frac{5}{2} - \frac{3}{4} = \frac{7}{4}$, remaining storage, improper fraction example, math tutorial", "Meta Description: Convert $2 \frac{1}{2}$ to $\frac{5}{2}$, subtract $\frac{3}{4}$ to get $\frac{7}{4}$, and learn how this improper fraction applies in real-world storage calculations. Perfect for students and data professionals."]