To find an algebraic expression that represents "45 less than the product of 18 and a number," we need to follow a step-by-step approach.
1. Identify the Variable:
Let's denote the unknown number by [tex]\( n \)[/tex].
2. Determine the Product:
The product of 18 and the number [tex]\( n \)[/tex] is represented as [tex]\( 18n \)[/tex].
3. Subtract 45 from the Product:
To find an expression for "45 less than the product," we need to subtract 45 from [tex]\( 18n \)[/tex].
Combining these steps, we write the algebraic expression as:
[tex]\[ 18n - 45 \][/tex]
Now, let's compare this with the given options:
- Option A: [tex]\( 18n - 45 \)[/tex]
- Option B: [tex]\( 45 - 18n \)[/tex]
- Option C: [tex]\( 18(n - 45) \)[/tex] (which simplifies to [tex]\( 18n - 810 \)[/tex])
- Option D: [tex]\( n(18 - 45) \)[/tex] (which simplifies to [tex]\( n \cdot (-27) \)[/tex] or [tex]\( -27n \)[/tex])
Considering the correct formation and subtraction, the correct answer is:
[tex]\[ \boxed{18n - 45} \][/tex]
Thus, the correct option is:
Option A: [tex]\( 18n - 45 \)[/tex].
