Express `7/-3` as a rational number with denominator :
`12`

Answer

To express \( \frac{7}{-3} \) as a rational number with a denominator of \( 12 \), we can follow these steps:

### Step 1: Identify the required denominator
We need to convert the denominator from \( -3 \) to \( 12 \).

### Step 2: Determine the multiplication factor
To change \( -3 \) to \( 12 \), we need to find a number that we can multiply \( -3 \) by to get \( 12 \). We can calculate this as follows:
\[ -3 \times (-4) = 12 \]
So, we will multiply the denominator by \( -4 \).

### Step 3: Multiply the denominator and numerator
Since we are multiplying the denominator by \( -4 \), we must also multiply the numerator by \( -4 \) to keep the fraction equivalent:
\[ \frac{7}{-3} = \frac{7 \times (-4)}{-3 \times (-4)} \]

### Step 4: Perform the multiplication
Now, we calculate the new numerator and denominator:
- Numerator: \( 7 \times (-4) = -28 \)
- Denominator: \( -3 \times (-4) = 12 \)

Putting it all together, we have:
\[ \frac{7}{-3} = \frac{-28}{12} \]

### Step 5: Final answer
Thus, \( \frac{7}{-3} \) expressed as a rational number with a denominator of \( 12 \) is:
\[ \frac{-28}{12} \]

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