To determine the correct algebraic expression for the phrase "the difference of the number of roses and 18 lilies," let's break down and analyze the phrase step by step:
1. Identifying the Variables:
- We are given that [tex]\( r \)[/tex] represents the number of roses.
- The number 18 represents the number of lilies.
2. Understanding the Phrase:
- The key term here is "difference." In mathematics, the word "difference" refers to the result of subtracting one number from another.
3. Formulating the Expression:
- According to the phrase, we need to find the difference between the number of roses ([tex]\( r \)[/tex]) and the number of lilies (18).
- To express this difference algebraically, we subtract the number of lilies from the number of roses.
4. Writing the Expression:
- The expression for the difference between [tex]\( r \)[/tex] (roses) and 18 (lilies) is written as:
[tex]\[
r - 18
\][/tex]
5. Checking the Answer Choices:
- Let's match this expression with the provided answer choices:
- A. [tex]\( r \cdot 18 \)[/tex] represents the product of the number of roses and 18, which is not correct.
- B. [tex]\( r + 18 \)[/tex] represents the sum of the number of roses and 18, which is not correct.
- C. [tex]\( r \div 18 \)[/tex] represents the quotient of the number of roses divided by 18, which is not correct.
- D. [tex]\( r - 18 \)[/tex] represents the difference between the number of roses and 18, which matches our formulated expression.
6. Conclusion:
- The correct algebraic expression for the phrase "the difference of the number of roses and 18 lilies" is:
[tex]\[
r - 18
\][/tex]
Therefore, the answer is [tex]\( \boxed{D} \)[/tex].
