Let's solve the given problem step by step.

The expression is:

$\frac{8}{9} + \frac{1}{3} \times \frac{5}{6}$

Step 1: Perform Multiplication First

Using the order of operations (PEMDAS/BODMAS), we first solve the multiplication:

$\frac{1}{3} \times \frac{5}{6} = \frac{1 \times 5}{3 \times 6} = \frac{5}{18}$

Step 2: Add the Fractions

Now, we add:

$\frac{8}{9} + \frac{5}{18}$

Find a common denominator for 9 and 18. The least common denominator (LCD) is 18.

Convert $\frac{8}{9}$ to have denominator 18:

$\frac{8}{9} = \frac{16}{18}$

Now add:

$\frac{16}{18} + \frac{5}{18} = \frac{21}{18}$

Step 3: Simplify the Fraction

$\frac{21}{18}$ can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 3:

$\frac{21 \div 3}{18 \div 3} = \frac{7}{6}$

Final Answer:

$\frac{7}{6}$

Let me know if you need further clarification!

Here are five related questions to deepen your understanding:

1. How do you find the least common denominator (LCD) of two fractions?
2. What is the order of operations when working with fractions?
3. How do you simplify improper fractions to mixed numbers?
4. How can you multiply and divide fractions easily?
5. Why is it important to express answers in the simplest form?

Tip: Always perform multiplication before addition when following the order of operations!