Final answer:
The expression for 'The quotient of three times x and seven' is written as \(\frac{3x}{7}\) which denotes the division of 3x by 7.
Step-by-step explanation:
The correct expression for the statement "The quotient of three times x and seven" is \(\frac{3x}{7}\). To understand this, let's break it down. The word quotient indicates division, three times x means 3x, and and seven refers to the number 7. By combining these components and following the order of operations, we construct the expression \(\frac{3x}{7}\), where 3x is the numerator (the dividend) and 7 is the denominator (the divisor).