Final answer:
The answer to the multiplication of the two negative fractions -\(\frac{1}{2}\) and -\(\frac{9}{8}\) is \(\frac{9}{16}\), and it is already in its simplest form.
Step-by-step explanation:
The student is asking how to multiply two negative fractions and then reduce the answer fully. The specific fractions to be multiplied are -\(\frac{1}{2}\) and -\(\frac{9}{8}\). When multiplying fractions, we do not need a common denominator; we simply multiply the numerators together and the denominators together. Also, a negative times a negative is a positive.
The multiplication process is then: -\(\frac{1}{2}\) * -\(\frac{9}{8}\) = \frac{1*9}{2*8}. This results in \(\frac{9}{16}\), which is the product of the two negative fractions. The result is already in its simplest form, so no further reduction is necessary.
Understanding how units and exponents work when multiplying fractions is critical to simplifying the process and reducing errors. Remember that when units match in the numerator and denominator, they cancel each other out, leaving the desired units for the final answer. In this case, however, we are simply dealing with numbers without specific units.
Applying this understanding helps to demonstrate multiplication of fractions and their properties clearly.