Lesson 3

Comparing Positive and Negative Numbers

Problem 1

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 2

Here is a true statement: $$\text-8.7 < \text-8.4$$. Select all of the statements that are equivalent to $$\text-8.7 < \text-8.4$$.

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 3

Plot each of the following numbers on the number line. Label each point with its numeric value. 0.4, -1.5, $$\text-1\frac{7}{10}$$, $$\text{-}\frac{11}{10}$$

Solution

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(From Unit 7, Lesson 2.)

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
Louisiana -8
New Mexico 2842
Wyoming 3099

Solution

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(From Unit 7, Lesson 4.)

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 6, Lesson 6.)

Problem 6

A stadium can seat 16,000 people at full capacity.

1. If there are 13,920 people in the stadium, what percentage of the capacity is filled? Explain or show your reasoning.
2. What percentage of the capacity is not filled?

Solution

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(From Unit 3, Lesson 16.)