Final answer:
To solve 8/9 + (-5/6) divided by 1/6, convert the division to multiplication by using the reciprocal of 1/6. Then multiply and subsequently add fractions to get the final answer of -37/9.
Step-by-step explanation:
When attempting to solve the expression 8/9 + (-5/6) ÷ 1/6, we first recognize that division by a fraction is the same as multiplying by its reciprocal. Therefore, ÷ 1/6 becomes × 6/1.
Applying this to our original expression, we get 8/9 + (-5/6) × 6/1.
Multiplication is straightforward: -5/6 × 6 equals -5.
Now we just have to add 8/9 to -5.
Since -5 is equivalent to -45/9 when expressed with a common denominator of 9, the expression now looks like 8/9 - 45/9.
Subtracting these gives us -37/9 as the final answer which cannot be simplified further.