Simplify the rational number and represent them on the number line.
`(-4)/(9) - (1)/(9)`

Answer

To simplify the rational number \((-4)/(9) - (1)/(9)\) and represent it on the number line, follow these steps:

### Step 1: Identify the expression
We start with the expression:
\[ -\frac{4}{9} - \frac{1}{9} \]

### Step 2: Check the denominators
Both fractions have the same denominator, which is \(9\). This allows us to combine the fractions directly.

### Step 3: Combine the numerators
Since the denominators are the same, we can combine the numerators:
\[ -\frac{4}{9} - \frac{1}{9} = \frac{-4 - 1}{9} \]

### Step 4: Simplify the numerator
Now, simplify the numerator:
\[ -4 - 1 = -5 \]
So, we have:
\[ \frac{-5}{9} \]

### Step 5: Final result
The simplified expression is:
\[ -\frac{5}{9} \]

### Step 6: Represent on the number line
To represent \(-\frac{5}{9}\) on the number line, we first draw a horizontal line and mark the center as \(0\).

### Step 7: Mark the negative values
Since \(-\frac{5}{9}\) is negative, we will mark it to the left of \(0\). We need to divide the section between \(0\) and \(-1\) into \(9\) equal parts (since the denominator is \(9\)).

### Step 8: Label the points
The points will be labeled as follows:
- \(-\frac{1}{9}\)
- \(-\frac{2}{9}\)
- \(-\frac{3}{9}\)
- \(-\frac{4}{9}\)
- \(-\frac{5}{9}\)
- \(-\frac{6}{9}\)
- \(-\frac{7}{9}\)
- \(-\frac{8}{9}\)
- \(-1\)

### Step 9: Plot \(-\frac{5}{9}\)
Locate \(-\frac{5}{9}\) on the number line and mark it clearly.

### Final Representation
The final representation of \(-\frac{5}{9}\) on the number line is shown, and we have successfully simplified the rational number and plotted it.

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