To solve the equation:

\[
\frac{10}{a} = \frac{6}{9}
\]

### Step-by-Step Solution:

1. Start by simplifying the fraction on the right-hand side:

\[
\frac{6}{9} = \frac{2}{3}
\]

Now the equation becomes:

\[
\frac{10}{a} = \frac{2}{3}
\]

2. Cross-multiply to eliminate the fractions:

\[
10 \times 3 = a \times 2
\]

This simplifies to:

\[
30 = 2a
\]

3. Solve for \(a\) by dividing both sides of the equation by 2:

\[
a = \frac{30}{2} = 15
\]

### Final Answer:
\[
a = 15
\]

Would you like more details on any step or have questions?

Here are 5 related questions:
1. What if the equation was \( \frac{10}{a} = \frac{7}{9} \)?
2. How do you solve equations with variables in both denominators?
3. How would this equation change if there was an additional term like \( + 5 \) on both sides?
4. Can we solve \( \frac{b}{a} = \frac{6}{9} \) for \(b\) instead?
5. What happens when the fraction includes negative numbers?

**Tip**: Always simplify fractions before solving equations to make calculations easier.

This step-by-step guide explains how to solve the equation 10/a = 6/9 using cross-multiplication. Learn to simplify fractions and solve for variables, covering key algebraic concepts. Perfect for students in Grades 6-8.

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