# 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

### 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. $$\text-12.5 > \text-12$$

### 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.

### Problem 4

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

### 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

(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. $$0.3z = 0.009$$