Question

Graph the numbers on a number line. Then write two inequalities that compare the two numbers. $$ -\frac{1}{2} \text { and } \frac{3}{2} $$

Short answer

The plotted numbers on the number line can be compared with two inequalities: \( -\frac{1}{2} < \frac{3}{2} \) and \( \frac{3}{2} > -\frac{1}{2} \).

Step-by-step solution

Create a Number Line

First, draw a horizontal line and mark it with equal intervals. Dedicate the center point to the number 0 and then determine which points correspond to the numbers \( -\frac{1}{2} \) and \( \frac{3}{2} \). The number \( -\frac{1}{2} \) is situated to the left of 0, and the number \( \frac{3}{2} \) is situated to the right.

Plot the Numbers on the Number Line

Mark the point corresponding to \( -\frac{1}{2} \) on the number line, then do the same for \( \frac{3}{2} \).

Write Two Inequalities Comparing the Numbers

Now we can compare the two numbers. The number \( -\frac{1}{2} \) is smaller than \( \frac{3}{2} \), so we write the inequality \( -\frac{1}{2} < \frac{3}{2} \). Conversely, the number \( \frac{3}{2} \) is greater than \( -\frac{1}{2} \), therefore we can also write the inequality \( \frac{3}{2} > -\frac{1}{2} \).