Visual representation of rational numbers on a number line, illustrating how fractions are placed between integers.

It looks like you've provided a detailed explanation about how to represent rational numbers on a number line, but there seems to be a mistake in the example given. Let's go through the problem carefully and correct it.

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Objective:

Represent the rational number $-\frac{2}{5}$ on the number line.

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Step-by-step Explanation:

#### 1. Understand the Sign of the Number
The rational number is $-\frac{2}{5}$. Since it's negative, it will lie to the left of 0 on the number line.

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#### 2. Determine the Interval
We know that:
- $-\frac{2}{5}$ is between $-1$ and $0$, because:
- $-\frac{2}{5} = -0.4$, which is greater than $-1$ and less than $0$.

So, we focus on the interval from $-1$ to $0$.

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#### 3. Divide the Interval into Equal Parts
To represent $-\frac{2}{5}$, we divide the space between $-1$ and $0$ into 5 equal parts, since the denominator is 5.

Each part represents:
$$
\frac{1}{5} \text{ unit}
$$

So, starting from $-1$, moving right:
- $-1 + \frac{1}{5} = -\frac{4}{5}$
- $-1 + \frac{2}{5} = -\frac{3}{5}$
- $-1 + \frac{3}{5} = -\frac{2}{5}$ ← This is our target!
- $-1 + \frac{4}{5} = -\frac{1}{5}$
- $-1 + \frac{5}{5} = 0$

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#### 4. Marking $-\frac{2}{5}$
So, $-\frac{2}{5}$ lies 2 units to the right of $-1$, or equivalently, 2 fifths of the way from $-1$ to $0$.

Thus, we mark it at the third tick (counting from $-1$) toward $0$.

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✔ Corrected Number Line Representation:

```
<---|-----|-----|-----|-----|-----|----->
-1 -4/5 -3/5 -2/5 -1/5 0
↑
-2/5
```

But in your image, it says:

> "Marking $-\frac{2}{5}$ at 2 units to the left of 0..."

This is incorrect.

- 2 units to the left of 0 is $-2$, not $-\frac{2}{5}$.
- That would be a major error.

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✘ Mistake in Your Image:

You wrote:
> "Marking $-\frac{2}{5}$ at 2 units to the left of 0"

But:
- $-\frac{2}{5} = -0.4$, which is only 0.4 units to the left of 0.
- 2 units to the left of 0 is $-2$, which is much farther.

So the final diagram showing $-\frac{2}{5}$ at $-2$ is wrong.

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✔ Correct Diagram Should Look Like This:

```
<---|-----|-----|-----|-----|-----|----->
-1 -4/5 -3/5 -2/5 -1/5 0
↑
-2/5
```

And the point should be placed between -1 and 0, closer to 0 than to -1.

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🔍 Summary:

- Rational numbers like $-\frac{2}{5}$ are represented by dividing the interval between two integers into equal parts based on the denominator.
- For $-\frac{2}{5}$, divide the segment from $-1$ to $0$ into 5 equal parts.
- Count 2 parts from $-1$ toward $0$ → this gives $-\frac{2}{5}$.
- It is not 2 units to the left of 0 — that’s $-2$.

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✔ Final Answer:

To represent $-\frac{2}{5}$ on the number line:
1. Locate the interval between $-1$ and $0$.
2. Divide it into 5 equal parts.
3. The second division from $-1$ (or third from $0$) marks $-\frac{2}{5}$.

✔ So, the correct position is 0.4 units to the left of 0, or 2/5 of the way from -1 to 0.

Let me know if you'd like a visual sketch or help with other rational numbers!