Express `7/-3` as a rational number with denominator :
`-15`

Answer

To express \( \frac{7}{-3} \) as a rational number with a denominator of \(-15\), follow these steps:

### Step 1: Identify the original fraction
We start with the fraction:
\[ \frac{7}{-3} \]

### Step 2: Determine the factor needed to change the denominator
We need to change the denominator from \(-3\) to \(-15\). To do this, we can find a factor that, when multiplied by \(-3\), gives us \(-15\).

Calculating:
\[ -3 \times 5 = -15 \]
So, we need to multiply the denominator by \(5\).

### Step 3: Multiply the denominator and the numerator by the same factor
To keep the value of the fraction the same, we multiply both the numerator and the denominator by \(5\):
\[ \frac{7}{-3} \times \frac{5}{5} \]

### Step 4: Perform the multiplication
Now we multiply:
\[ \text{Numerator: } 7 \times 5 = 35 \]
\[ \text{Denominator: } -3 \times 5 = -15 \]

### Step 5: Write the new fraction
Putting it all together, we have:
\[ \frac{35}{-15} \]

### Step 6: Simplify the fraction if necessary
The fraction \( \frac{35}{-15} \) can also be written as:
\[ -\frac{35}{15} \]
This is a valid rational number with a denominator of \(-15\).

### Final Answer:
Thus, \( \frac{7}{-3} \) expressed as a rational number with a denominator of \(-15\) is:
\[ \frac{35}{-15} \text{ or } -\frac{35}{15} \]

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