Final answer:
The expression that is equal to the quotient of a number and 8 is 'n divided by 8', or 'n/8'. 'n x 8' refers to multiplication, and 'n - 8' and 'n + 8' represent subtraction and addition, which are not the same as division by 8.
Step-by-step explanation:
When we talk about the quotient of a number and 8, we are referring to the operation of dividing that number by 8. This can be represented as n divided by 8, written as n/8 or as a fraction ⅛. In contrast, the expression n x 8 stands for multiplication of n by 8, which is the opposite operation.
The expressions n - 8 and n + 8 represent subtraction and addition respectively, and do not give the quotient of a number and 8.
Multiplication and division are related in that they are inverse operations.
This means that dividing by a number is the same as multiplying by its reciprocal.
Therefore, dividing by 8 is equivalent to multiplying by the reciprocal of 8, which is 1/8 or 0.125. Understanding the relationship between these operations is important as they can provide different methods to arrive at the same answer.