We need to solve two division problems involving fractions: Problem 7: $\frac{8}{3} \div \frac{4}{5}$ Problem 9: $12 \div \frac{8}{11}$

1. Problem Description

We need to solve two division problems involving fractions:

Problem 7: $\frac{8}{3} \div \frac{4}{5}$

Problem 9: $12 \div \frac{8}{11}$

2. Solution Steps

Problem 7:

To divide by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{4}{5}$ is $\frac{5}{4}$.

So, $\frac{8}{3} \div \frac{4}{5} = \frac{8}{3} \times \frac{5}{4}$.

$\frac{8}{3} \times \frac{5}{4} = \frac{8 \times 5}{3 \times 4} = \frac{40}{12}$.

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is

4. $\frac{40}{12} = \frac{40 \div 4}{12 \div 4} = \frac{10}{3}$.

Problem 9:

We need to solve $12 \div \frac{8}{11}$.

To divide by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{8}{11}$ is $\frac{11}{8}$.

So, $12 \div \frac{8}{11} = 12 \times \frac{11}{8}$.

We can rewrite 12 as $\frac{12}{1}$.

Then, $12 \times \frac{11}{8} = \frac{12}{1} \times \frac{11}{8} = \frac{12 \times 11}{1 \times 8} = \frac{132}{8}$.

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is

4. $\frac{132}{8} = \frac{132 \div 4}{8 \div 4} = \frac{33}{2}$.

3. Final Answer

The answer to Problem 7 is $\frac{10}{3}$.

The answer to Problem 9 is $\frac{33}{2}$.