8. For any real number $x$, let $\lfloor x\rfloor$ be the largest integer less than or equal to $x$ and $x=x-\lfloor x\rfloor$. Let $a$ and $b$ be real numbers with $b \neq 0$ such that
$$
a=b\left\lfloor\frac{a}{b}\right\rfloor-b\left\{\frac{a}{b}\right\} .
$$

Which of the following statements is incorrect?
(A) If $b$ is an integer then $a$ is an integer;
(B) If $a$ is a non-zero integer then $b$ is an integer;
(C) If $b$ is a rational number then $a$ is a rational number;
(D) If $a$ is a non-zero rational number then $b$ is a rational number;
(E) If $b$ is an even number then $a$ is an even number.
8. Answer: (B).
Note that $a=b \cdot \frac{a}{b}=b\left(\left\lfloor\frac{a}{b}\right\rfloor+\left\{\frac{a}{b}\right\}\right)=b\left\lfloor\frac{a}{b}\right\rfloor+b\left\{\frac{a}{b}\right\}$.
It follows from $a=b\left\lfloor\frac{a}{b}\right\rfloor+b\left\{\frac{a}{b}\right\}$ that $b\left\lfloor\frac{a}{b}\right\rfloor=a$. Hence, $\frac{a}{b}=\left\lfloor\frac{a}{b}\right\rfloor$ is an integer. Obviously, $b$ is not necessary an integer even if $a$ is an integer.