To determine which algebraic expression represents "the difference of 54 and a number," let's break down the meaning of the phrase "the difference of 54 and a number."
In mathematics, the word "difference" refers to the result of subtracting one quantity from another.
Given that we have a specific number, 54, and we want to find its difference with another number, [tex]\( n \)[/tex], our operation involves subtraction.
Let’s analyze the provided expressions:
1. [tex]\( 54 - n \)[/tex]: This expression shows 54 minus another number [tex]\( n \)[/tex]. This fits exactly with the concept of "the difference of 54 and a number."
2. [tex]\( \frac{54}{n} \)[/tex]: This expression shows 54 divided by another number [tex]\( n \)[/tex]. Division does not represent difference; hence, this expression is not what we are looking for.
3. [tex]\( 54n \)[/tex]: This expression indicates 54 multiplied by another number [tex]\( n \)[/tex]. Multiplication does not represent difference either.
4. [tex]\( 54 + n \)[/tex]: This expression shows 54 plus another number [tex]\( n \)[/tex]. Addition is not the operation we need to represent a difference.
Since the correct mathematical operation for "difference" is subtraction, the expression that represents "the difference of 54 and a number" is:
[tex]\[ 54 - n \][/tex]
Thus, the correct expression is:
[tex]\[ 54 - n \][/tex]
