Final answer:
To reduce the problem 5 2/3 divided by 3 1/9 to the lowest terms, convert the mixed numbers to improper fractions, divide the fractions, and simplify the final fraction.
Step-by-step explanation:
To reduce the problem 5 2/3 divided by 3 1/9 to the lowest terms, we can convert the mixed numbers to improper fractions and then divide.
First, convert 5 2/3 to the improper fraction 17/3.
Next, convert 3 1/9 to the improper fraction 28/9.
Now, divide 17/3 by 28/9. To divide fractions, multiply the first fraction by the reciprocal of the second fraction. So, (17/3) * (9/28) = 153/84. Finally, simplify the final fraction by dividing both numerator and denominator by their greatest common divisor. The simplified fraction is 51/28.