To solve for \( q \) in the equation
\[ 90 \cdot (224 \cdot q) = (90 \cdot 224) \cdot 464, \]
we can apply the associative property of multiplication, which states that the way in which numbers are grouped in multiplication does not change the product.
First, we can simplify the right side of the equation:
\[ (90 \cdot 224) \cdot 464 = 90 \cdot (224 \cdot 464). \]
This means our equation can be rewritten as:
\[ 90 \cdot (224 \cdot q) = 90 \cdot (224 \cdot 464). \]
Next, we can divide both sides of the equation by \( 90 \) (assuming \( 90 \neq 0 \)):
\[ 224 \cdot q = 224 \cdot 464. \]
Now, we can divide both sides by \( 224 \) (assuming \( 224 \neq 0 \)):
\[ q = 464. \]
Thus, the value of \( q \) that makes the multiplication sentence true is
\[ \boxed{464}. \]
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