To solve the equation \( \frac{4}{3} \div 4 = x \cdot \frac{1}{3} \), we can rearrange and simplify it.
First, let's simplify the left side:
\[ \frac{4}{3} \div 4 = \frac{4}{3} \times \frac{1}{4} = \frac{4 \times 1}{3 \times 4} = \frac{1}{3} \]
Now the original equation becomes:
\[ \frac{1}{3} = x \cdot \frac{1}{3} \]
To find \( x \), we can multiply both sides by \( 3 \):
\[ 1 = x \]
So the answer to the equation is:
\[ x = 1 \]
Thus, \( \frac{4}{3} \div 4 = 1 \cdot \frac{1}{3} \).