Question

1. (\frac{3}{12} = \frac{-24}{m})

Explanation:

Step1: Cross - multiply the proportion

To solve the proportion \(\frac{3}{12}=\frac{- 24}{m}\), we use the cross - multiplication property of proportions. If \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\). Here, \(a = 3\), \(b = 12\), \(c=-24\) and \(d = m\). So we get \(3\times m=12\times(-24)\).

Step2: Simplify the right - hand side

Calculate \(12\times(-24)\). \(12\times(-24)=-288\). So the equation becomes \(3m=-288\).

Step3: Solve for \(m\)

Divide both sides of the equation \(3m=-288\) by 3. \(\frac{3m}{3}=\frac{-288}{3}\), which simplifies to \(m = - 96\).

Answer:

\(m=-96\)