To determine which algebraic expression represents the phrase "the product of 16 and the weight of the trout," let’s break down the phrase step by step:
1. Identify the variable:
- The phrase mentions the "weight of the trout," which we denote by the variable \( w \).
2. Identify the operation:
- The phrase specifies the "product" of two quantities. In mathematics, "product" means the result of multiplication.
3. Identify the quantities to be multiplied:
- We have two quantities: 16 and the weight of the trout (denoted by \( w \)).
4. Set up the multiplication:
- The product of 16 and the weight of the trout is written as \( 16 \times w \).
5. Write the algebraic expression:
- The multiplication of 16 and \( w \) can be written simply as \( 16w \).
Let's review the options:
A. \(\frac{w}{16}\): This represents the weight of the trout divided by 16, which is incorrect.
B. \(16W\): This represents 16 multiplied by the weight of the trout. Though it uses an uppercase \( W \), if we assume consistent notation (assuming \( W \) was a typo and should match the \( w \) in the question), this is correct.
C. \(w+16\): This represents the weight of the trout plus 16, which is incorrect.
D. \(w-16\): This represents the weight of the trout minus 16, which is incorrect.
Thus, the correct algebraic expression that represents "the product of 16 and the weight of the trout" is:
[tex]\[ \boxed{16w} \][/tex]
So, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
