A rational number -2/3_______.

Options

A. lies to the left side of 0 on the number line.
B. lies to the right side of 0 on the number line.
C. lies between -2 and 3.
D. lies between 2 and -3.

Answer

To solve the question about the rational number -2/3 and where it lies on the number line, we can follow these steps:

### Step-by-Step Solution:

1. **Draw a Number Line**: Start by drawing a horizontal line. Mark the center point as 0. On the left side of 0, mark negative numbers (-1, -2, etc.), and on the right side, mark positive numbers (1, 2, etc.).

2. **Identify the Position of -2/3**: Since -2/3 is a negative rational number, it will be located to the left of 0 on the number line. To find its exact position, we need to understand that -2/3 is between -1 and 0.

3. **Estimate the Position**: Since -2/3 is closer to 0 than to -1, we can visualize it as being slightly less than -0.67 (which is -2/3 in decimal form). Therefore, it will be positioned between 0 and -1.

4. **Determine the Statements**: Now, we evaluate the statements given in the question:
- **Lies to the left side of 0**: This is true since -2/3 is negative.
- **Lies to the right side of 0**: This is false since -2/3 is negative.
- **Lies between -2 and 3**: This is true because -2 is less than -2/3 and 3 is greater than -2/3.
- **Lies between 2 and -3**: This is also true because -3 is less than -2/3 and 2 is greater than -2/3.

5. **Conclusion**: The correct statements regarding the position of -2/3 on the number line are:
- It lies to the left side of 0.
- It lies between -2 and 3.
- It lies between 2 and -3.

### Final Answer:
- The statements that are correct are:
- Lies to the left side of 0.
- Lies between -2 and 3.
- Lies between 2 and -3.