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.

  1. \(\text-5 > 2\)
  2. \(3 > \text-8\)
  3. \(\text-12 > \text-15\)
  4. \(\text-12.5 > \text-12\)

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 \(\text-8.7 < \text-8.4\).

A:

-8.7 is further to the right on the number line than -8.4.

B:

-8.7 is further to the left on the number line than -8.4.

C:

-8.7 is less than -8.4.

D:

-8.7 is greater than -8.4.

E:

-8.4 is less than -8.7.

F:

-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.

  

Solution

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Problem 5

Each lap around the track is 400 meters.

  1. How many meters does someone run if they run:

    2 laps?

    5 laps?

    \(x\) laps?

  2. If Noah ran 14 laps, how many meters did he run?
  3. 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.

  1. \(2x = 3\)

  2. \(5y = 3\)

  3. \(0.3z = 0.009\)

Solution

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(From Unit 4, Lesson 5.)