1. The problem asks to write the phrase "the quotient of 18 and a number a" as a mathematical expression. 2. The word "quotient" means division, so the phrase refers to dividing 18 by the number $a$. 3. The expression for the quotient of 18 and $a$ is written as: $$\frac{18}{a}$$ 4. This expression means 18 divided by $a$, where $a$ is the variable representing the unknown number. 5. Important note: $a$ cannot be zero because division by zero is undefined. 6. Therefore, the expression is $$\frac{18}{a}$$ with the condition $a \neq 0$. Final answer: $$\frac{18}{a}$$