Final answer:
To divide fractions, convert the mixed numbers to improper fractions and multiply by the reciprocal.
Step-by-step explanation:
To divide fractions, we need to convert the mixed numbers into improper fractions. For the first division, 3 ¾ ÷ ⅘, we can convert 3 ¾ into the improper fraction 15/4. Then, we multiply 15/4 by the reciprocal of ⅘, which is 5/8. Multiplying the numerators (15 and 5) gives us 75, and multiplying the denominators (4 and 8) gives us 32. So, the answer is 75/32.
For the second division, 3 ¾ ÷ 5 ⅝, we convert 3 ¾ into the improper fraction 15/4 and 5 ⅝ into the improper fraction 45/8. Then, we divide 15/4 by 45/8 by multiplying 15/4 by the reciprocal of 45/8. This reciprocal is 8/45. Multiplying the numerators (15 and 8) gives us 120, and multiplying the denominators (4 and 45) gives us 180. So, the answer is 120/180, which can be simplified to 2/3.
For the third division, 6 ½ ÷ ¾, we convert 6 ½ into the improper fraction 13/2. Then, we multiply 13/2 by the reciprocal of ¾, which is 4/3. Multiplying the numerators (13 and 4) gives us 52, and multiplying the denominators (2 and 3) gives us 6. So, the answer is 52/6, which can be simplified to 26/3.