To solve the expression [tex]\( 8\left\lfloor \frac{1}{4} \right\rfloor \)[/tex], follow these steps:
1. Evaluate [tex]\(\frac{1}{4}\)[/tex]:
[tex]\(\frac{1}{4}\)[/tex] is a value that is equal to 0.25.
2. Apply the floor function [tex]\(\left\lfloor \cdot \right\rfloor\)[/tex]:
The floor function [tex]\(\left\lfloor x \right\rfloor\)[/tex] gives the greatest integer that is less than or equal to [tex]\(x\)[/tex]. For the value 0.25, the floor value is 0. Therefore, [tex]\(\left\lfloor \frac{1}{4} \right\rfloor = \left\lfloor 0.25 \right\rfloor = 0\)[/tex].
3. Multiply by 8:
After finding the floor value, multiply it by 8:
[tex]\[
8 \times 0 = 0
\][/tex]
Thus, the result of the expression [tex]\( 8\left\lfloor \frac{1}{4} \right\rfloor \)[/tex] is [tex]\( \boxed{0} \)[/tex].
