Question

1. (31) \\(\frac{5}{12} = \frac{1.25}{k}\\)

Explanation:

Step1: Cross - multiply the proportion

In a proportion \(\frac{a}{b}=\frac{c}{d}\), we can cross - multiply to get \(a\times d = b\times c\). For the equation \(\frac{5}{12}=\frac{1.25}{k}\), cross - multiplying gives us \(5\times k=12\times1.25\).

Step2: Calculate the right - hand side

First, calculate \(12\times1.25\). We know that \(1.25=\frac{5}{4}\), so \(12\times\frac{5}{4}=15\). So the equation becomes \(5k = 15\).

Step3: Solve for \(k\)

To solve for \(k\), divide both sides of the equation \(5k = 15\) by 5. That is \(k=\frac{15}{5}=3\).

Answer:

\(k = 3\)