The problem consists of three division problems involving fractions. We need to solve them step by step. The problems are: (6) $\frac{2}{7} \div \frac{5}{8}$ (8) $\frac{14}{15} \div \frac{7}{10}$ (10) $3\frac{1}{2} \div \frac{7}{9}$

1. Problem Description

The problem consists of three division problems involving fractions. We need to solve them step by step.

The problems are:

(6) $\frac{2}{7} \div \frac{5}{8}$

(8) $\frac{14}{15} \div \frac{7}{10}$

(10) $3\frac{1}{2} \div \frac{7}{9}$

2. Solution Steps

(6) $\frac{2}{7} \div \frac{5}{8}$

To divide fractions, we multiply by the reciprocal of the second fraction.

$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

$\frac{2}{7} \div \frac{5}{8} = \frac{2}{7} \times \frac{8}{5} = \frac{2 \times 8}{7 \times 5} = \frac{16}{35}$

(8) $\frac{14}{15} \div \frac{7}{10}$

$\frac{14}{15} \div \frac{7}{10} = \frac{14}{15} \times \frac{10}{7} = \frac{14 \times 10}{15 \times 7}$

We can simplify by cancelling common factors. $14 = 2 \times 7$ and $10 = 2 \times 5$ and $15 = 3 \times 5$

$\frac{14 \times 10}{15 \times 7} = \frac{2 \times 7 \times 2 \times 5}{3 \times 5 \times 7} = \frac{2 \times 2}{3} = \frac{4}{3}$

(10) $3\frac{1}{2} \div \frac{7}{9}$

First, convert the mixed number to an improper fraction.

$3\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}$

Then, divide by the fraction $\frac{7}{9}$.

$\frac{7}{2} \div \frac{7}{9} = \frac{7}{2} \times \frac{9}{7} = \frac{7 \times 9}{2 \times 7}$

We can simplify by cancelling the common factor

7. $\frac{7 \times 9}{2 \times 7} = \frac{9}{2}$

3. Final Answer

(6) $\frac{16}{35}$

(8) $\frac{4}{3}$

(10) $\frac{9}{2}$