Solving the proportion 3/9 = x/27

To solve the given problem, we need to find the value of \( x \) in the equation:

\[
\frac{3}{9} = \frac{x}{27}
\]

Step 1: Simplify the left-hand side

The fraction on the left-hand side, \(\frac{3}{9}\), can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3:

\[
\frac{3}{9} = \frac{3 \div 3}{9 \div 3} = \frac{1}{3}
\]

So, the equation becomes:

\[
\frac{1}{3} = \frac{x}{27}
\]

Step 2: Cross-multiply to solve for \( x \)

To eliminate the fractions, we cross-multiply. This means we multiply the numerator of the left-hand side by the denominator of the right-hand side, and the numerator of the right-hand side by the denominator of the left-hand side:

\[
1 \cdot 27 = 3 \cdot x
\]

This simplifies to:

\[
27 = 3x
\]

Step 3: Solve for \( x \)

To isolate \( x \), divide both sides of the equation by 3:

\[
x = \frac{27}{3}
\]

\[
x = 9
\]

Final Answer:

\[
\boxed{9}
\]

Explanation:

1. We simplified the fraction \(\frac{3}{9}\) to \(\frac{1}{3}\) to make the equation easier to work with.
2. Cross-multiplication is a standard technique for solving equations involving proportions. It helps us eliminate the fractions and solve for the unknown variable.
3. After cross-multiplying, we solved the resulting linear equation \(27 = 3x\) by dividing both sides by 3.

Thus, the value of \( x \) is \(\boxed{9}\).