Choose from the following to make the statement true: 1/5

Question

, 4/3
, 1.

4/3⋅_____<4/3

(1 point)

Answer 1

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 product that is less than \( \frac{4}{3} \).

Testing the given options:

1. If we choose \( \frac{1}{5} \): \[ \frac{4}{3} \cdot \frac{1}{5} = \frac{4}{15} \] This is less than \( \frac{4}{3} \), so this works.

2. If we choose \( \frac{4}{3} \): \[ \frac{4}{3} \cdot \frac{4}{3} = \frac{16}{9} \] This is greater than \( \frac{4}{3} \), so this does not work.

3. If we choose \( 1 \): \[ \frac{4}{3} \cdot 1 = \frac{4}{3} \] This is not less than \( \frac{4}{3} \), so this does not work.

Thus, the only option that makes the statement true is:

\(\frac{1}{5}\).

So, the correct answer is \( \frac{1}{5} \).