Simplify the rational number and represent them on the number line.
`(-7)/(9) xx (3)/(2)`

Answer

To simplify the rational number \((-7)/(9) \times (3)/(2)\) and represent it on the number line, follow these steps:

### Step 1: Multiply the Rational Numbers
We start with the expression:
\[ \frac{-7}{9} \times \frac{3}{2} \]

### Step 2: Multiply the Numerators and Denominators
Multiply the numerators together and the denominators together:
\[ \text{Numerator: } -7 \times 3 = -21 \]
\[ \text{Denominator: } 9 \times 2 = 18 \]
So, we have:
\[ \frac{-21}{18} \]

### Step 3: Simplify the Fraction
Now, we need to simplify \(\frac{-21}{18}\). We can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3:
\[ \frac{-21 \div 3}{18 \div 3} = \frac{-7}{6} \]

### Step 4: Final Result
The simplified form of the rational number is:
\[ \frac{-7}{6} \]

### Step 5: Represent on the Number Line
To represent \(\frac{-7}{6}\) on the number line, we first note that \(-7/6\) is a negative number.

1. **Identify the Position**: Since \(-7/6\) is less than \(-1\) (because \(-6/6 = -1\)), we can find its position between \(-1\) and \(-2\).
2. **Convert to Mixed Number**: \(-7/6\) can be expressed as \(-1 \frac{1}{6}\).
3. **Mark on the Number Line**: On the number line, we locate \(-1\) and then move one-sixth of the way towards \(-2\).

### Final Representation
The point \(-7/6\) is plotted between \(-1\) and \(-2\) on the number line.

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