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To solve the equation \( \frac{v}{9} = \frac{4}{6} \), let's go step-by-step.

### Step 1: Simplify the right-hand side
First, simplify \( \frac{4}{6} \):
\[
\frac{4}{6} = \frac{2}{3}
\]
Now the equation is:
\[
\frac{v}{9} = \frac{2}{3}
\]

### Step 2: Solve for \( v \)
To eliminate the fraction on the left-hand side, multiply both sides of the equation by 9:
\[
v = 9 \times \frac{2}{3}
\]
Simplifying the right-hand side:
\[
v = 3 \times 2 = 6
\]

### Solution:
\[
v = 6
\]

Would you like further explanation on any part of this solution?

Here are five questions to deepen your understanding:
1. How would you solve if the right-hand side was not a fraction but a whole number?
2. Can you explain how multiplying both sides of an equation by the same number keeps it balanced?
3. What if the fraction was inverted, \( \frac{6}{4} \), how would the solution change?
4. How would you solve for \( v \) if the equation had a variable on both sides?
5. What if you had a decimal instead of a fraction on the right side?

**Tip:** Always simplify fractions before solving equations—it makes the process easier and reduces the chance of errors!

Learn how to solve the algebraic equation v/9 = 4/6 by simplifying fractions and using cross multiplication. This guide provides a clear step-by-step approach to solving proportions, suitable for middle school students.

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