Final answer:
To simplify 8/-3 divided by -4/9, you multiply 8/-3 by the reciprocal of -4/9, which is 9/-4, resulting in 72/12. Simplifying this fraction gives us the final answer of 6.
Step-by-step explanation:
To simplify the fraction 8/-3 divided by -4/9, we can multiply by the reciprocal of the second fraction. Multiplication and division are interconnected operations; to divide by a number or fraction, we multiply by its reciprocal. In this case, we flip the fraction -4/9 to its reciprocal, which is 9/-4. So, the operation turns into 8/-3 multiplied by 9/-4.
Now, we follow the step of multiply the top numbers and divide by the bottom numbers in the fractions. Multiplying the numerators (8 and 9) gives us 72, and multiplying the denominators (-3 and -4) gives us 12. So, the resulting fraction is 72/12. Finally, we simplify the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 12. Thus, 72 divided by 12 equals 6. Therefore, the simplified result of the division 8/-3 divided by -4/9 is 6.