Question

1. solve: \\(\frac{10}{6} = \frac{21}{d}\\)

Explanation:

Step1: Cross - multiply the proportion

To solve the proportion \(\frac{10}{6}=\frac{21}{d}\), 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 \(10\times d=6\times21\).

Step2: Simplify the right - hand side

Calculate \(6\times21 = 126\). So the equation becomes \(10d = 126\).

Step3: Solve for \(d\)

Divide both sides of the equation \(10d = 126\) by 10. \(d=\frac{126}{10}\), and simplifying the fraction \(\frac{126}{10}\) gives \(d = 12.6\) or \(d=\frac{63}{5}\).

Answer:

\(d = \frac{63}{5}\) (or \(d = 12.6\))