Find he value of p such that `(-3)/(7) and (p)/(-28)` are equivalent rational numbers.

Answer

To find the value of \( p \) such that the rational numbers \( \frac{-3}{7} \) and \( \frac{p}{-28} \) are equivalent, we can follow these steps:

### Step 1: Write the given rational numbers
We have two rational numbers:
\[ \frac{-3}{7} \quad \text{and} \quad \frac{p}{-28} \]

### Step 2: Rewrite the second rational number
To make the comparison easier, we can rewrite \( \frac{p}{-28} \) by moving the negative sign from the denominator to the numerator:
\[ \frac{p}{-28} = \frac{-p}{28} \]

### Step 3: Set the two rational numbers equal
Since we want to find \( p \) such that the two rational numbers are equivalent, we can set them equal to each other:
\[ \frac{-3}{7} = \frac{-p}{28} \]

### Step 4: Cross-multiply
To eliminate the fractions, we can cross-multiply:
\[ -3 \times 28 = -p \times 7 \]
This simplifies to:
\[ -84 = -7p \]

### Step 5: Solve for \( p \)
Now, we can solve for \( p \) by dividing both sides by -7:
\[ p = \frac{84}{7} \]
Calculating the right side gives:
\[ p = 12 \]

### Final Answer
The value of \( p \) is:
\[ \boxed{12} \]

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