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The image shows the following mathematical problem:

\[
\frac{5}{6} a = \frac{4}{9} b, \text{ sehingga nilai } \frac{a}{b} \text{ adalah ...}
\]

We are asked to find the value of \(\frac{a}{b}\).

### Steps to solve:

1. Start with the given equation:
   \[
   \frac{5}{6} a = \frac{4}{9} b
   \]
   
2. To find \(\frac{a}{b}\), we can divide both sides of the equation by \(b\):
   \[
   \frac{\frac{5}{6} a}{b} = \frac{\frac{4}{9} b}{b}
   \]
   
3. Simplify the right side:
   \[
   \frac{5}{6} \cdot \frac{a}{b} = \frac{4}{9}
   \]
   
4. Now, solve for \(\frac{a}{b}\) by multiplying both sides of the equation by \(\frac{6}{5}\):
   \[
   \frac{a}{b} = \frac{4}{9} \cdot \frac{6}{5}
   \]
   
5. Multiply the fractions:
   \[
   \frac{a}{b} = \frac{4 \times 6}{9 \times 5} = \frac{24}{45}
   \]

6. Simplify the fraction \(\frac{24}{45}\) by dividing both the numerator and denominator by 3:
   \[
   \frac{a}{b} = \frac{8}{15}
   \]

So, the value of \(\frac{a}{b}\) is \(\frac{8}{15}\).

---

Do you want further details or have any questions?

Here are 5 related questions you might find helpful:
1. What if the equation had different coefficients, like \(\frac{3}{4}a = \frac{7}{10}b\)?
2. How do you simplify complex fractions involving variables?
3. How can you solve equations with three or more fractions involved?
4. What are the techniques to check if your fraction simplifications are correct?
5. How does this method apply to more advanced algebra problems?

**Tip:** Always simplify your fractions step-by-step to avoid errors in large numbers or complex algebraic expressions.

Jika \( \frac{5}{6} a = \frac{4}{9} b \), sehingga nilai \( \frac{a}{b} \) adalah ...

This page provides a step-by-step solution to the algebraic proportion problem \( \frac{5}{6} a = \frac{4}{9} b \), focusing on simplifying fractions and solving for \( \frac{a}{b} \). Suitable for students in Grades 7-9.

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