Let's solve the expression step by step:

Given expression:  
\[
\left(\frac{80\% \times 7.5}{2}\right) - \frac{9}{5} + \frac{10}{\frac{1}{2}}
\]

### Step 1: Simplify \(80\% \times 7.5\)
\[
80\% = \frac{80}{100} = 0.8
\]
\[
0.8 \times 7.5 = 6
\]

### Step 2: Divide by 2
\[
\frac{6}{2} = 3
\]

So, the expression simplifies to:
\[
3 - \frac{9}{5} + \frac{10}{\frac{1}{2}}
\]

### Step 3: Simplify \(\frac{9}{5}\)
\[
\frac{9}{5} = 1.8
\]

### Step 4: Simplify \(\frac{10}{\frac{1}{2}}\)
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{10}{\frac{1}{2}} = 10 \times 2 = 20
\]

### Step 5: Substitute back into the expression
\[
3 - 1.8 + 20
\]

### Step 6: Perform the addition and subtraction
\[
3 - 1.8 = 1.2
\]
\[
1.2 + 20 = 21.2
\]

The final answer is:
\[
\boxed{21.2}
\]

Would you like more details or have any questions?

Here are 8 related questions:
1. How do you convert percentages to decimals?
2. What is the process for multiplying decimals?
3. How do you handle division by fractions?
4. What is the importance of the order of operations in solving expressions?
5. How would the answer change if the percentage were different?
6. Can you solve a similar expression with different numbers?
7. What is the reciprocal of a fraction, and how is it used?
8. Why is it necessary to simplify fractions before performing operations?

**Tip:** Always be cautious with the order of operations (PEMDAS/BODMAS) when solving complex expressions!

Learn how to solve the mathematical expression involving percentages, fractions, and order of operations step-by-step. This problem covers key concepts in percentages, fraction operations, and the importance of the order of operations (PEMDAS/BODMAS). Suitable for high school students.

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