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

Answer

To solve the problem step by step, we will follow the mathematical reasoning provided in the video transcript.

### Step-by-Step Solution:

1. **Understand the Problem**: We know that the product of two rational numbers is -9, and one of the numbers is -12. We need to find the other number.

2. **Set Up the Equation**: Let the other number be represented as \( x \). According to the problem, we can write the equation as:
\[ -12 \times x = -9 \]

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

4. **Simplify the Fraction**: When we divide two negative numbers, the result is positive. Therefore:
\[ x = \frac{9}{12} \]
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**: The other rational number is \( \frac{3}{4} \).

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

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