Question

solve for q in the proportion.\\(\frac{q}{9} = \frac{4}{3}\\)\\(q = \square\\)

Explanation:

Step1: Cross - multiply the proportion

To solve for \( q \) in the proportion \(\frac{q}{9}=\frac{4}{3}\), we use the cross - multiplication property of proportions. If \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d = b\times c\). Here, \(a = q\), \(b = 9\), \(c = 4\), and \(d = 3\). So we get \(q\times3=9\times4\).

Step2: Simplify the right - hand side

Calculate \(9\times4\), which is equal to 36. So the equation becomes \(3q = 36\).

Step3: Solve for \( q \)

Divide both sides of the equation \(3q = 36\) by 3. \(\frac{3q}{3}=\frac{36}{3}\), which simplifies to \(q = 12\).

Answer:

\(q = 12\)