To solve the expression \( 45 \times 16 - \frac{17}{45} \times 15 + 28 \), we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

1. First, perform the multiplications and divisions:
\[
45 \times 16 = 720
\]
\[
\frac{17}{45} \times 15 = \frac{17 \times 15}{45} = \frac{255}{45} = 5.6667 \text{ (approximately)}
\]

2. Next, substitute these values back into the expression:
\[
720 - 5.6667 + 28
\]

3. Perform the subtraction and addition from left to right:
\[
720 - 5.6667 = 714.3333
\]
\[
714.3333 + 28 = 742.3333
\]

So, the value of the expression \( 45 \times 16 - \frac{17}{45} \times 15 + 28 \) is approximately \( 742.3333 \).