Question

solve for p.
\\(\frac{19}{9} = \frac{p}{15}\\)

p = \boxed{\quad} (type an integer or a simplified fraction.)

Explanation:

Step1: Cross - multiply the equation

To solve for \( p \) in the equation \(\frac{19}{9}=\frac{p}{15}\), we use cross - multiplication. Cross - multiplication means that if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d = b\times c\).
Applying this to our equation, we get \(19\times15=9\times p\).

Step2: Calculate the left - hand side

First, calculate \(19\times15\). \(19\times15=(20 - 1)\times15=20\times15-1\times15 = 300 - 15=285\). So our equation becomes \(285 = 9p\).

Step3: Solve for \( p \)

To solve for \( p \), we divide both sides of the equation \(285 = 9p\) by 9. So \(p=\frac{285}{9}\).
Then we simplify the fraction \(\frac{285}{9}\). We can divide both the numerator and the denominator by 3. \(\frac{285\div3}{9\div3}=\frac{95}{3}\).

Answer:

\(\frac{95}{3}\)