Question

2 \\(\frac{3}{12} = \frac{x}{68}\\)

Explanation:

Step1: Cross - multiply the proportion

To solve the proportion \(\frac{3}{12}=\frac{x}{68}\), 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 \(12\times x=3\times68\).

Step2: Simplify the right - hand side

Calculate \(3\times68 = 204\). So the equation becomes \(12x = 204\).

Step3: Solve for \(x\)

Divide both sides of the equation \(12x = 204\) by 12. \(x=\frac{204}{12}\). Simplify \(\frac{204}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 12? Wait, no. The GCD of 204 and 12: \(204\div12 = 17\) with a remainder? Wait, \(12\times17 = 204\)? Wait, \(12\times17=204\)? \(12\times10 = 120\), \(12\times7 = 84\), \(120 + 84=204\). So \(\frac{204}{12}=17\).

Answer:

\(x = 17\)