Question

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