Question

Consider this set of fractions.

2
3
, −2
3
, 1, −1, 1
3
, −1
3

Explain the order and placement of these numbers on the number line.

Answer 1

To order and place the given fractions and whole numbers on a number line, we need to convert them into a consistent representation and understand their values:

1. **Convert the numbers to a common format**:
- \( \frac{2}{3} \): This is approximately 0.67.
- \( -\frac{2}{3} \): This is approximately -0.67.
- \( 1 \): This is just 1.
- \( -1 \): This is just -1.
- \( \frac{1}{3} \): This is approximately 0.33.
- \( -\frac{1}{3} \): This is approximately -0.33.

2. **Order the numbers from least to greatest**:
- Start from the left (the most negative) to the right (the most positive):
- \( -1 \): This is the leftmost point.
- \( -\frac{2}{3} \): This is greater than -1 and approximately -0.67.
- \( -\frac{1}{3} \): This is greater than \( -\frac{2}{3} \) and approximately -0.33.
- \( \frac{1}{3} \): This is greater than \( -\frac{1}{3} \) and approximately 0.33.
- \( \frac{2}{3} \): This is greater than \( \frac{1}{3} \) and approximately 0.67.
- \( 1 \): This is the rightmost point.

3. **Number Line Representation**:
Placing these values on a number line would look like this:

```
-1 -2/3 -1/3 0 1/3 2/3 1
<---|-------|---------|--------|--------|-------|--------|--->
```

### Summary of the Order:
- From left to right, the order of the numbers is:
- \( -1 \)
- \( -\frac{2}{3} \)
- \( -\frac{1}{3} \)
- \( 0 \)
- \( \frac{1}{3} \)
- \( \frac{2}{3} \)
- \( 1 \)

This shows how each fraction and whole number fits on the number line in relation to each other, providing a clear visualization of their relative sizes.