Question

solve the proportion.
\\(\frac{6}{18} = \frac{k}{6}\\)
\\(k = ?\\)

Explanation:

Step1: Cross - multiply the proportion

To solve the proportion \(\frac{6}{18}=\frac{k}{6}\), we use the cross - multiplication property of proportions. If \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d = b\times c\). So, \(6\times6=18\times k\).

Step2: Simplify the equation

First, calculate the left - hand side: \(6\times6 = 36\). So the equation becomes \(36 = 18k\). Then, divide both sides of the equation by 18 to solve for \(k\). \(\frac{36}{18}=\frac{18k}{18}\).

Step3: Calculate the value of k

Simplify \(\frac{36}{18}\) to get 2, and \(\frac{18k}{18}\) simplifies to \(k\). So \(k = 2\).

Answer:

\(k = 2\)