The product of two rational numbers is `-9`. If one of the numbers is `-12`, find the other.

Options

A. `(7)/(4) `
B. `(3)/(4) `
C. `(5)/(4) `
D. `(9)/(4) `

Answer

To find the other rational number when the product of two rational numbers is -9 and one of the numbers is -12, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Known Values:**
We know that the product of two rational numbers is -9, and one of the numbers is -12. Let's denote the unknown number as \( x \).

2. **Set Up the Equation:**
According to the problem, we can set up the equation:
\[ -12 \times x = -9 \]

3. **Isolate the Unknown Variable:**
To find \( x \), we need to isolate it. We can do this by dividing both sides of the equation by -12:
\[ x = \frac{-9}{-12} \]

4. **Simplify the Fraction:**
Since both the numerator and the denominator are negative, they will cancel each other out:
\[ x = \frac{9}{12} \]
Now, we can simplify \( \frac{9}{12} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
\[ x = \frac{9 \div 3}{12 \div 3} = \frac{3}{4} \]

5. **Conclusion:**
Therefore, the other rational number is:
\[ x = \frac{3}{4} \]

### Final Answer:
The other rational number is \( \frac{3}{4} \).

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