Question

solve \\(\frac{10}{y} = \frac{2}{9}\\). the solution is \\(y = \square\\).

Explanation:

Step1: Cross - multiply the equation

Given the equation \(\frac{10}{y}=\frac{2}{9}\), cross - multiplying (which is based on the property that if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d = b\times c\)) gives us \(10\times9=2\times y\).

Step2: Simplify the equation

Simplify the left - hand side and the right - hand side of the equation. The left - hand side \(10\times9 = 90\), and the right - hand side is \(2y\). So our equation becomes \(90 = 2y\).

Step3: Solve for y

To solve for \(y\), we divide both sides of the equation \(90 = 2y\) by 2. \(\frac{90}{2}=\frac{2y}{2}\), which simplifies to \(y = 45\).

Answer:

\(45\)