Find: `(7)/(12)div(14)/((-15))`

Answer

To solve the expression \(\frac{7}{12} \div \frac{14}{-15}\), we will follow these steps:

### Step 1: Rewrite the Division as Multiplication
The first step in dividing fractions is to rewrite the division as multiplication by the reciprocal. This means we will change the division into multiplication and flip the second fraction.

\[ \frac{7}{12} \div \frac{14}{-15} = \frac{7}{12} \times \frac{-15}{14} \]

### Step 2: Multiply the Numerators and Denominators
Now we will multiply the numerators together and the denominators together.

\[ \text{Numerator: } 7 \times -15 = -105 \]
\[ \text{Denominator: } 12 \times 14 = 168 \]

So we have:

\[ \frac{7}{12} \times \frac{-15}{14} = \frac{-105}{168} \]

### Step 3: Simplify the Fraction
Next, we need to simplify the fraction \(\frac{-105}{168}\). We can find the greatest common divisor (GCD) of 105 and 168.

The GCD of 105 and 168 is 21. Now we divide both the numerator and the denominator by 21:

\[ \frac{-105 \div 21}{168 \div 21} = \frac{-5}{8} \]

### Final Answer
Thus, the final simplified answer is:

\[ \frac{-5}{8} \]

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