We can solve the expression step by step.

Given: 

\[
\frac{8}{10} : 2 \frac{6}{9}
\]

### Step 1: Convert mixed fractions into improper fractions
The term \( 2 \frac{6}{9} \) can be written as:

\[
2 \frac{6}{9} = 2 + \frac{6}{9} = \frac{18}{9} + \frac{6}{9} = \frac{24}{9}
\]

Thus, the expression becomes:

\[
\frac{8}{10} : \frac{24}{9}
\]

### Step 2: Apply the division rule for fractions
Dividing by a fraction is the same as multiplying by its reciprocal. So,

\[
\frac{8}{10} \times \frac{9}{24}
\]

### Step 3: Multiply the fractions
Multiply the numerators and denominators:

\[
\frac{8 \times 9}{10 \times 24} = \frac{72}{240}
\]

### Step 4: Simplify the fraction
Now simplify \( \frac{72}{240} \). Both the numerator and denominator can be divided by their greatest common divisor (GCD), which is 24:

\[
\frac{72 \div 24}{240 \div 24} = \frac{3}{10}
\]

Thus, the final result is:

\[
\boxed{\frac{3}{10}}
\]

Would you like a more detailed explanation, or do you have any questions?

Here are some related questions for further practice:

1. Simplify \( \frac{12}{18} \times \frac{15}{24} \).
2. Convert \( 3 \frac{4}{5} \) into an improper fraction.
3. Find the value of \( \frac{5}{8} : \frac{7}{12} \).
4. Simplify \( \frac{10}{14} + \frac{12}{21} \).
5. Multiply \( 2 \frac{5}{6} \times 3 \frac{1}{2} \).

**Tip:** When dividing fractions, always remember to multiply by the reciprocal of the divisor!

Explore how to divide fractions and mixed numbers step-by-step. This solution covers converting mixed numbers to improper fractions and applying the division rule for fractions. Learn how to simplify the result with practical examples. Suitable for Grades 5-7.

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