Answer
$-\displaystyle \frac{5}{2} < -\frac{5}{3},$ fill the box with $ < .$
Work Step by Step
On the real number line, the real numbers increase from left to right.
The lesser of two real numbers is the one farther to the left on a number line.
The greater of two real numbers is the one farther to the right on a number line.
The symbols $> $ and $< $ are called inequality symbols. These symbols always point to the lesser of the two real numbers when the inequality is true.
---
Writing both numbers with a common denominator,
$-\displaystyle \frac{5}{2}=-\frac{5\times 3}{2\times 3}=-\frac{15}{6},\qquad-\frac{5}{3}=-\frac{5\times 2}{3\times 2}=-\frac{10}{6}$
$-15 $ is farther (to the left) from zero than $-10$ is, so
$-\displaystyle \frac{15}{6} < -\frac{10}{6},$
$-\displaystyle \frac{5}{2} < -\frac{5}{3},$ fill the box with $ < .$
