Final answer:
To solve (3\(\frac{2}{3}\)) \div (7\(\frac{1}{2}\)), first convert to improper fractions and multiply by the reciprocal of the divisor. The result is 22/45 in its simplest form as there are no common factors between numerator and denominator and no whole units.
Step-by-step explanation:
The question involves performing a division operation between two mixed numbers. To find the result of (3\(\frac{2}{3}\)) \div (7\(\frac{1}{2}\)), we will first convert the mixed numbers into improper fractions. For 3\(\frac{2}{3}\), we have 3 \times 3 + 2 which equals 11/3. For 7\(\frac{1}{2}\), we have 7 \times 2 + 1 which equals 15/2. Division of fractions requires multiplying by the reciprocal of the divisor, so we multiply 11/3 by the reciprocal of 15/2 which is 2/15.
Now we multiply the numerators together and the denominators together: (11 \times 2) / (3 \times 15), which simplifies to 22/45. Since there are no common factors between the numerator and the denominator, this fraction cannot be reduced further. However, it is not in mixed number form. As 22 is less than 45, this fraction is already in its simplest form and there are 0 whole units, so the mixed number is simply 0 plus the fraction, which is 22/45.