We are given the equation:

\[
\frac{2}{8} = \frac{5}{p + 10}
\]

### Step 1: Simplify \(\frac{2}{8}\)
\[
\frac{2}{8} = \frac{1}{4}
\]

Now the equation becomes:
\[
\frac{1}{4} = \frac{5}{p + 10}
\]

### Step 2: Cross-multiply to eliminate the fractions
\[
1 \cdot (p + 10) = 4 \cdot 5
\]
\[
p + 10 = 20
\]

### Step 3: Solve for \(p\)
Subtract 10 from both sides:
\[
p = 20 - 10
\]
\[
p = 10
\]

Thus, the solution is:
\[
p = 10
\]

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What happens if you change the numerator in the original equation to 3?
2. How would the solution change if you added 2 to both sides of the equation?
3. Can you solve a similar equation: \(\frac{4}{6} = \frac{7}{x + 3}\)?
4. How can you check if \(p = 10\) is the correct solution?
5. How does cross-multiplication help in solving proportions?

**Tip**: Always simplify fractions as early as possible to make equations easier to solve.

Learn how to solve the proportion equation 2/8 = 5/(p + 10) with step-by-step instructions. This problem focuses on simplifying fractions and using cross-multiplication to find the solution for p. Suitable for students in Grades 6-8.

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