Question

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

Short answer

Numbers plotted on a number line: -1/2 positioned on the left side and 1/3 on the right. Two inequalities: \( -\frac{1}{2} < \frac{1}{3} \) and \( \frac{1}{3} > -\frac{1}{2} \).

Step-by-step solution

Plotting numbers

Concentration is required to plot two numbers, -1/2 and 1/3 on a number line. The given numbers are fractions and one of these is a negative number. Therefore, it is crucial to position these accurately. A number line usually starts from 0 in the middle, where numbers to the right are positive and to the left are negative. In this scenario, -1/2 will be plotted on the left side of the zero while 1/3 will be positioned on the right.

Writing the inequalities

The purpose of the inequalities is to compare two numbers. So, this comparison can be \( -\frac{1}{2} < \frac{1}{3} \) which reads as negative half is less than one third. On the flip side, this can also be written as \( \frac{1}{3} > -\frac{1}{2} \), implying one third is greater than negative half. This is an important consideration as the position of each number on the number line relies on its value.