Question

example:
\\(\frac{6}{8} = \frac{15}{y}\\)
\\(6 \times y = 8 \times 15\\)
\\(6y = 120\\)
\\(\div 6\\) \\(\div 6\\)
\\(y = 20\\)
show all work.
\\(\frac{3}{12} = \frac{x}{68}\\)
\\(\frac{81}{18} = \frac{x}{14}\\)

Explanation:

Step1: Cross - multiply the proportion

Given the proportion \(\frac{81}{18}=\frac{x}{14}\), by the cross - multiplication property of proportions (if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d = b\times c\)), we get \(81\times14=18\times x\).

Step2: Calculate the left - hand side

Calculate \(81\times14\): \(81\times14=(80 + 1)\times14=80\times14+1\times14 = 1120+14=1134\). So the equation becomes \(1134 = 18x\).

Step3: Solve for \(x\)

Divide both sides of the equation \(1134 = 18x\) by 18. \(x=\frac{1134}{18}\). Simplify \(\frac{1134}{18}\): divide numerator and denominator by 18, \(1134\div18 = 63\).

Answer:

\(x = 63\)