Final answer:
The English phrase 'the quotient of g times the difference of a and b, and r' translates to the algebraic expression g(a - b) / r, which involves subtraction and division.
Step-by-step explanation:
To translate the English phrase "the quotient of g times the difference of a and b, and r" into an algebraic expression, we need to identify the operations described. The key terms here are quotient, which implies division, and difference, which indicates subtraction. Therefore, this phrase describes dividing the product of g and the difference between a and b by r.
The difference of a and b is represented as (a - b). We then multiply this by g to get g(a - b). Finally, we divide this product by r, leading to the algebraic expression:
g(a - b) / r