The equation you provided is:

\[
\frac{10}{y} = \frac{2}{9}
\]

To solve for \( y \), follow these steps:

### Step 1: Cross-multiply
You can cross-multiply to eliminate the fractions:

\[
10 \times 9 = 2 \times y
\]

This simplifies to:

\[
90 = 2y
\]

### Step 2: Solve for \( y \)
Now, divide both sides of the equation by 2 to isolate \( y \):

\[
y = \frac{90}{2} = 45
\]

### Final Answer:
\[
y = 45
\]

Would you like a further explanation or to verify this result? Here are some additional related questions:

1. How would you solve for \( y \) if the equation was \( \frac{10}{y} = \frac{3}{8} \)?
2. What happens if the equation had a negative fraction (e.g., \( \frac{10}{y} = \frac{-2}{9} \))?
3. How do you check if your solution is correct by substituting \( y = 45 \) back into the equation?
4. How can this technique be applied to more complex fractional equations?
5. Can you set up and solve a similar proportion where \( y \) is in the numerator, e.g., \( \frac{y}{10} = \frac{2}{5} \)?

**Tip:** Cross-multiplying is a powerful tool for solving equations with fractions. Just be careful to keep terms balanced on both sides.

Learn how to solve the proportion 10/y = 2/9 using cross-multiplication. This step-by-step solution is ideal for students in Grades 6-8, covering key algebraic concepts such as proportions and cross-multiplication.

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