Final answer:
The algebraic expression that represents 'the weight of the trout multiplied by 7' is (7w), as it signifies the weight being multiplied by the number 7.
Step-by-step explanation:
If (w) is the weight of a trout, the algebraic expression representing the phrase 'the weight of the trout multiplied by 7' is (7w). This is because when you multiply a number (in this case, the weight of the trout) by another number (7), you simply put the two numbers next to each other in algebraic notation, signifying multiplication.