Lesson 3
Comparing Positive and Negative Numbers
Let’s compare numbers on the number line.
Problem 1
Decide whether each inequality statement is true or false. Explain your reasoning.
- \(\text-5 > 2\)
- \(3 > \text-8\)
- \(\text-12 > \text-15\)
- \(\text-12.5 > \text-12\)
Problem 2
Here is a true statement: \(\text-8.7 < \text-8.4\). Select all of the statements that are equivalent to \(\text-8.7 < \text-8.4\).
-8.7 is further to the right on the number line than -8.4.
-8.7 is further to the left on the number line than -8.4.
-8.7 is less than -8.4.
-8.7 is greater than -8.4.
-8.4 is less than -8.7.
-8.4 is greater than -8.7.
Problem 3
Plot each of the following numbers on the number line. Label each point with its numeric value. 0.4, -1.5, \(\text-1\frac{7}{10}\), \(\text{-}\frac{11}{10}\)
![A number line with 5 evenly spaced tick marks, labeled negative 2 through 2.](https://staging-cms-im.s3.amazonaws.com/cYhaEKnkJzR9cKCQhMEYhtFV?response-content-disposition=inline%3B%20filename%3D%226.7.A.PP.Image.01.png%22%3B%20filename%2A%3DUTF-8%27%276.7.A.PP.Image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T112248Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6d05e40368a8cc27d858089c0c477ddbc49faf682662852fcea83adc476de173)
Problem 4
The table shows five states and the lowest point in each state.
Put the states in order by their lowest elevation, from least to greatest.
state | lowest elevation (feet) |
---|---|
California | -282 |
Colorado | 3350 |
Louisiana | -8 |
New Mexico | 2842 |
Wyoming | 3099 |
Problem 5
Each lap around the track is 400 meters.
-
How many meters does someone run if they run:
2 laps?
5 laps?
\(x\) laps?
- If Noah ran 14 laps, how many meters did he run?
- If Noah ran 7,600 meters, how many laps did he run?
Problem 6
A stadium can seat 16,000 people at full capacity.
- If there are 13,920 people in the stadium, what percentage of the capacity is filled? Explain or show your reasoning.
- What percentage of the capacity is not filled?