Lesson 2
Comparing Positive and Negative Numbers
Problem 1
Plot these points on a number line.
- -1.5
- the opposite of -2
- the opposite of 0.5
- -2
Solution
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Problem 2
Decide whether each inequality statement is true or false. Explain your reasoning.
- \(\text-5 > 2\)
- \(3 > \text-8\)
- \(\text-12 > \text-15\)
- \(\text-12.5 > \text-12\)
Solution
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Problem 3
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.
Solution
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Problem 4
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%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T150941Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=845807774420c94a743dc5d4773a286c049eea8af27039fb03f83f151adda5dc)
Solution
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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?
Solution
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(From Unit 4, Lesson 6.)Problem 6
Write the solution to each equation as a fraction and as a decimal.
-
\(2x = 3\)
-
\(5y = 3\)
-
\(0.3z = 0.009\)
Solution
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(From Unit 4, Lesson 5.)