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# Floor and Ceiling Functions

Floor functions map a real number x to the largest integer less than or equal to x. You can probably guess what the ceiling function does.

# Fractional Part Function

What is $$\left\{\sqrt{71}\right\}\times\left(\sqrt{71}+8\right)?$$

Note: $$\{x\}$$ denotes the fractional part function.

What is $$\{21.11\}?$$

Note: $$\{x\}$$ denotes the fractional part function.

If $$0<x<50,$$ how many solutions are there to $\{x\}=0.9?$

Note: $$\{x\}$$ denotes the fractional part function.

What is $$\{15.15\}+\{-15.15\}?$$

Note: $$\{x\}$$ denotes the fractional part function.

What is $$\left\{\frac{85}{6}\right\}?$$

Note: $$\{x\}$$ denotes the fractional part function.

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