"Seven more than eleven times a number, plus the quotient of y and z."

To represent the phrase "7 more than 11 times a number increased by the quotient of y and z" with an algebraic expression, you need to break down the statement into smaller parts and translate it into mathematical operators and terms.

Let's define the "number" mentioned in the phrase as a variable, such as 'x'. Now, we can construct the expression step by step:

1. "11 times a number" would be 11 times 'x', or 11x. 2. "increased by the quotient of y and z" means you need to add the result of dividing 'y' by 'z' to the previous product. The quotient of 'y' and 'z' is represented as y/z. 3. "7 more than" indicates you need to add 7 to the entire sum of the above two parts.

So, you first multiply 'x' by 11, then add the result of y/z, and finally add 7 to the sum. Combining all these parts, the algebraic expression is:

11x + (y/z) + 7