To make the statement \( \frac{4}{3} \cdot ____ < \frac{4}{3} \) true, we need to find a number that, when multiplied by \( \frac{4}{3} \), results in a value less than \( \frac{4}{3} \).
We can denote the blank as \( x \): \[ \frac{4}{3} \cdot x < \frac{4}{3} \]
To isolate \( x \), we can divide both sides by \( \frac{4}{3} \) (noting that \( \frac{4}{3} \) is positive, so the inequality direction remains the same): \[ x < 1 \]
Among the options provided ( \( \frac{1}{5}, \frac{4}{3}, 1 \)), the numbers less than \( 1 \) are:
- \( \frac{1}{5} < 1 \)
- \( \frac{4}{3} \) is not less than \( 1 \).
- \( 1 \) is not less than \( 1 \).
Therefore, the choice that makes the statement true is:
\[ \frac{1}{5} \]
So the statement completes as: \[ \frac{4}{3} \cdot \frac{1}{5} < \frac{4}{3} \]
This is true.