Final answer:
To find the quotient of (2/9) divided by (-(3/27)), simplify the divisor to -1/9, then multiply by its reciprocal to get -2 as the simplified answer.
Step-by-step explanation:
The question requires finding the quotient and simplifying the expression (2/9) ÷ (-(3/27)).
First, we simplify the divisor (-(3/27)) by dividing both the numerator and the denominator by their greatest common factor, which is 3. This simplifies to -1/9.
Next, we divide the original fraction, (2/9), by our simplified divisor (-1/9). Division of fractions involves multiplying by the reciprocal. Thus, we multiply by -9, since the reciprocal of -1/9 is -9/1.
The multiplication gives us (2/9) × (-9/1) which equals to -2. There are no common terms that can be eliminated, so this is the simplified answer.
Finally, we check the answer to see if it is reasonable. Considering that the original expression involved dividing a positive number by a negative number, the answer being negative is indeed reasonable.