Final answer:
To divide the mixed numbers 5 8/15 and 15 32/1, we first convert them to improper fractions 83/15 and 47/1, respectively. Then, we multiply 83/15 by the reciprocal of 47/1 to get 83/705, which is already in its simplest form as there are no common factors.
Step-by-step explanation:
When we divide mixed numbers, we should first convert them to improper fractions. The division of fractions involves multiplying the first fraction by the reciprocal (inverse) of the second fraction. To solve the given problem 5 8/15 ÷ 15 32/1, we first convert the mixed numbers to improper fractions: Convert 5 8/15 to an improper fraction: 5 + 8/15 = (5 × 15 + 8)/15 = (75 + 8)/15 = 83/15. Convert 15 32/1 to an improper fraction: 15 + 32/1 = (15 × 1 + 32)/1 = (15 + 32)/1 = 47/1. Now, divide 83/15 by 47/1 by multiplying 83/15 by the reciprocal of 47/1 which is 1/47: 83/15 × 1/47 = 83/(15 × 47) = 83/705.
We simplify the fraction by looking for any common factors. Since there are none between 83 and 705, the fraction is already in its simplest form. As 83 is less than 705, and there are no whole numbers present in the answer, the mixed number will only consist of the fractional part. Therefore, the answer is just the improper fraction converted back to a mixed number, which is still in its simplest form without any whole number component: The final answer is 83/705.