Express `7/-3` as a rational number with denominator :
`18 `

Answer

To express the rational number \( \frac{7}{-3} \) with a denominator of \( 18 \), we can follow these steps:

### Step 1: Identify the current rational number
We start with the rational number:
\[ \frac{7}{-3} \]

### Step 2: Determine the factor needed to change the denominator
We want to change the denominator from \(-3\) to \(18\). To do this, we need to find a factor that we can multiply \(-3\) by to get \(18\).

Calculating:
\[ -3 \times (-6) = 18 \]
So, we need to multiply by \(-6\).

### Step 3: Multiply both the numerator and denominator by the same factor
To keep the value of the fraction unchanged, we multiply both the numerator and the denominator by \(-6\):
\[ \frac{7}{-3} \times \frac{-6}{-6} = \frac{7 \times -6}{-3 \times -6} \]

### Step 4: Perform the multiplication
Now, we perform the multiplication:
\[ \frac{7 \times -6}{-3 \times -6} = \frac{-42}{18} \]

### Step 5: Write the final answer
Thus, the expression \( \frac{7}{-3} \) expressed as a rational number with a denominator of \( 18 \) is:
\[ \frac{-42}{18} \]

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