To solve the equation \(\frac{4}{12} = \frac{w}{9}\), we can use cross-multiplication.

The equation is:
\[
\frac{4}{12} = \frac{w}{9}
\]

By cross-multiplying, we get:
\[
4 \times 9 = 12 \times w
\]

Simplifying:
\[
36 = 12w
\]

Now, divide both sides by 12 to solve for \(w\):
\[
w = \frac{36}{12} = 3
\]

Thus, \(w = 3\).

Would you like any additional details or explanations?

Here are 5 related questions:
1. What is cross-multiplication, and when is it useful?
2. Can you simplify the fraction \(\frac{4}{12}\) first?
3. How would the solution change if the equation were \(\frac{4}{12} = \frac{w}{10}\)?
4. What happens if \(w\) is negative in a proportion equation like this?
5. How can proportions be applied in real-world scenarios, like scaling recipes?

**Tip:** Simplifying fractions at the start can often make solving proportion problems quicker and easier.

Learn how to solve the proportion equation 4/12 = w/9 using cross-multiplication. This solution walks through the key steps, including simplifying fractions and applying the proportionality theorem. Suitable for students in Grades 5-7.

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