To determine which algebraic expression represents "the difference of 54 and a number," let's break down the phrase step by step:
1. Difference: The term "difference" in algebra refers to the result of subtracting one number from another.
2. 54 and a number: In this context, 54 is a constant value, and "a number" is typically represented by a variable, say [tex]\( n \)[/tex].
Given these two parts, we want to find the expression that correctly represents "the difference of 54 and a number." This means we need to subtract the variable [tex]\( n \)[/tex] from 54.
Examining the options:
1. [tex]\( 54 - n \)[/tex]:
- This expression directly represents subtracting the variable [tex]\( n \)[/tex] from 54, which matches our requirement.
2. [tex]\( \frac{54}{n} \)[/tex]:
- This expression represents dividing 54 by the variable [tex]\( n \)[/tex]. Division is not the same as finding the difference, so this is incorrect.
3. [tex]\( 54n \)[/tex]:
- This expression represents multiplying 54 by the variable [tex]\( n \)[/tex]. Multiplication is not the same as finding the difference, so this is incorrect.
4. [tex]\( 54 + n \)[/tex]:
- This expression represents adding the variable [tex]\( n \)[/tex] to 54. Addition is not the same as finding the difference, so this is incorrect.
Based on the analysis, the correct algebraic expression that represents "the difference of 54 and a number" is:
[tex]\[ 54 - n \][/tex]
