Question

solve for m in the proportion.
\\(\frac{12}{27} = \frac{m}{45}\\)
\\(m = \square\\)

Explanation:

Step1: Cross - multiply the proportion

In a proportion \(\frac{a}{b}=\frac{c}{d}\), we cross - multiply to get \(a\times d = b\times c\). For the proportion \(\frac{12}{27}=\frac{m}{45}\), cross - multiplying gives us \(12\times45=27\times m\).
Calculating the left - hand side: \(12\times45 = 540\), so the equation becomes \(540 = 27m\).

Step2: Solve for \(m\)

To solve for \(m\), we divide both sides of the equation \(540 = 27m\) by 27. That is \(m=\frac{540}{27}\).
Simplifying \(\frac{540}{27}\), we can divide both the numerator and the denominator by 9: \(\frac{540\div9}{27\div9}=\frac{60}{3}=20\).

Answer:

\(m = 20\)