Question

solve for w in the proportion.
\\(\frac{2}{w} = \frac{16}{24}\\)
\\(w = \square\\)

Explanation:

Step1: Cross - multiply the proportion

To solve for \( w \) in the proportion \(\frac{2}{w}=\frac{16}{24}\), we use the cross - multiplication property of proportions. If \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d = b\times c\). So, we have \(2\times24=16\times w\).
\(48 = 16w\)

Step2: Solve for \( w \)

Divide both sides of the equation \(48 = 16w\) by 16 to isolate \( w \).
\(w=\frac{48}{16}\)
Simplifying the right - hand side, we get \(w = 3\).

Answer:

\(3\)