Express `frac(-36)(24)` as a rational number with numerator
(i) -9,
(ii) -6.

Answer

To express \(\frac{-36}{24}\) as a rational number with different specified numerators, we will follow these steps:

### Step 1: Express \(\frac{-36}{24}\) with numerator -9
1. Start with the fraction \(\frac{-36}{24}\).
2. We want to change the numerator from -36 to -9. To do this, we need to determine what we can multiply -9 by to get -36.
- Since \(-36 \div -9 = 4\), we will multiply both the numerator and the denominator by 4.
3. Therefore, we write:
\[ \frac{-36}{24} = \frac{-36 \div 4}{24 \div 4} = \frac{-9}{6} \]

### Step 2: Express \(\frac{-36}{24}\) with numerator -6
1. Start again with the fraction \(\frac{-36}{24}\).
2. We want to change the numerator from -36 to -6. To do this, we need to determine what we can multiply -6 by to get -36.
- Since \(-36 \div -6 = 6\), we will multiply both the numerator and the denominator by 6.
3. Therefore, we write:
\[ \frac{-36}{24} = \frac{-36 \div 6}{24 \div 6} = \frac{-6}{4} \]

### Summary of Results
- With numerator -9: \(\frac{-36}{24} = \frac{-9}{6}\)
- With numerator -6: \(\frac{-36}{24} = \frac{-6}{4}\)