The problem consists of two parts. The first part requires filling in the blanks regarding the concepts of fraction division. The second part requires identifying which of the provided fraction division calculations are correct. The third part requires solving fraction division problems.

1. Problem Description

The problem consists of two parts. The first part requires filling in the blanks regarding the concepts of fraction division. The second part requires identifying which of the provided fraction division calculations are correct. The third part requires solving fraction division problems.

2. Solution Steps

Part 1:

(1) In fraction division, we multiply by the reciprocal of the divisor. So the blanks should be filled with "numerator" and "denominator".

(2) Mixed multiplication and division problems can be calculated by converting integers and decimals to fractions and then converting division to multiplication.

(3) When dividing by a number less than 1, the quotient is larger than the dividend.

Part 2:

(A) $\frac{5}{3} \div \frac{5}{6} = \frac{5}{3} \times \frac{6}{5} = \frac{5 \times 6}{3 \times 5} = \frac{30}{15} = 2$. The solution given is $\frac{1}{2}$, which is incorrect.

(I) $12 \div \frac{3}{10} = \frac{12}{1} \times \frac{10}{3} = \frac{120}{3} = 40$. The solution given is 40, which is correct.

(U) $\frac{1}{4} \div 0.1 = \frac{1}{4} \div \frac{1}{10} = \frac{1}{4} \times \frac{10}{1} = \frac{10}{4} = \frac{5}{2} = 2.5$. The solution given is $\frac{5}{2}$, which is correct.

(E) $\frac{4}{7} \div 4 = \frac{4}{7} \times \frac{1}{4} = \frac{4}{28} = \frac{1}{7}$. The solution given is $\frac{16}{7}$, which is incorrect.

Part 3:

(1) $\frac{3}{8} \div \frac{2}{5} = \frac{3}{8} \times \frac{5}{2} = \frac{3 \times 5}{8 \times 2} = \frac{15}{16}$

(2) $\frac{14}{15} \div 3 = \frac{14}{15} \times \frac{1}{3} = \frac{14 \times 1}{15 \times 3} = \frac{14}{45}$

(3) $20 \div \frac{4}{5} = \frac{20}{1} \times \frac{5}{4} = \frac{20 \times 5}{1 \times 4} = \frac{100}{4} = 25$

(4) $9 \div 0.6 \times 1\frac{1}{3} = 9 \div \frac{6}{10} \times \frac{4}{3} = 9 \times \frac{10}{6} \times \frac{4}{3} = \frac{9 \times 10 \times 4}{6 \times 3} = \frac{360}{18} = 20$

(5) $16 \times 9 \div 30 = \frac{16}{1} \times \frac{9}{1} \div \frac{30}{1} = \frac{16 \times 9}{30} = \frac{144}{30} = \frac{72}{15} = \frac{24}{5}$

3. Final Answer

Part 1:

(1) numerator, denominator

(2) multiplication

(3) larger

Part 2:

(I), (U)

Part 3:

(1) $\frac{15}{16}$

(2) $\frac{14}{45}$

(3) $25$

(4) $20$

(5) $\frac{24}{5}$