Express `78/(-117)` as a rational number with numerator (i) -6 (ii) 2

Answer

To express \( \frac{78}{-117} \) as a rational number with the specified numerators (-6 and 2), we can follow these steps:

### Step 1: Simplify the Original Fraction
First, we simplify \( \frac{78}{-117} \).

\[ \frac{78}{-117} = \frac{78 \div 39}{-117 \div 39} = \frac{2}{-3} \]

### Step 2: Express with Numerator -6
To express \( \frac{2}{-3} \) with a numerator of -6, we can multiply both the numerator and the denominator by -3:

\[ \frac{2}{-3} = \frac{2 \times -3}{-3 \times -3} = \frac{-6}{9} \]

### Step 3: Express with Numerator 2
Now, to express \( \frac{2}{-3} \) with a numerator of 2, we can simply keep the fraction as it is:

\[ \frac{2}{-3} \]

### Summary of Results
1. With numerator -6: \( \frac{-6}{9} \)
2. With numerator 2: \( \frac{2}{-3} \)

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