Write an algebraic expression for the given quantity. Let $x$ represent the unknown value. one-eighth of a number reduced by eight times the same number What is the algebraic expression?

Step 1 ：The question is asking for an algebraic expression that represents 'one-eighth of a number reduced by eight times the same number'. In this case, the 'number' is represented by the variable $x$.

Step 2 ：Break down the phrase as follows:

Step 3 ：'one-eighth of a number' can be represented as $\frac{1}{8}x$ or $0.125x$.

Step 4 ：'reduced by' means subtraction.

Step 5 ：'eight times the same number' can be represented as $8x$.

Step 6 ：Putting it all together, the algebraic expression is $\frac{1}{8}x - 8x$.

Step 7 ：Simplify the expression to get $-7.875x$.

Step 8 ：Final Answer: The algebraic expression is $\boxed{-7.875x}$.