#### Answer

The statement is true.

#### Work Step by Step

$15\displaystyle \cdot(3\div b)=15\cdot(3\cdot\frac{1}{b})=\qquad $( definition of division)
$=(15\displaystyle \cdot 3)\cdot\frac{1}{b}\qquad $(associative property of multiplication)
$=45\displaystyle \cdot\frac{1}{b}\qquad $(simplify $15\cdot 3$)
$=45\div b\qquad $( definition of division)
The statement is true.