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To divide fractions, you need to multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of 2/9 is 9/2, so the division problem becomes:
-1/6 * 9/2
Next, multiply the numerators together and the denominators together:
-1 * 9 = -9
6 * 2 = 12
So, the answer is -9/12.
To simplify the fraction, divide both the numerator and denominator by their greatest common divisor, which is 3:
-9/12 ÷ 3 = -9/4
Therefore, the simplified answer is -9/4.
The correct option is:
C) -9/4