Let's solve the equation \( \frac{5}{4}p = \frac{4}{3} + \frac{5}{2} \).

### Step 1: Find a common denominator for the terms on the right side.
The denominators are 3 and 2. The least common denominator (LCD) is 6.

- Convert \( \frac{4}{3} \) to have a denominator of 6:  
  \[
  \frac{4}{3} = \frac{4 \times 2}{3 \times 2} = \frac{8}{6}
  \]
- Convert \( \frac{5}{2} \) to have a denominator of 6:  
  \[
  \frac{5}{2} = \frac{5 \times 3}{2 \times 3} = \frac{15}{6}
  \]

Now the equation becomes:
\[
\frac{5}{4}p = \frac{8}{6} + \frac{15}{6}
\]

### Step 2: Add the fractions on the right side.
\[
\frac{8}{6} + \frac{15}{6} = \frac{23}{6}
\]

Now the equation is:
\[
\frac{5}{4}p = \frac{23}{6}
\]

### Step 3: Solve for \( p \).
To isolate \( p \), multiply both sides of the equation by the reciprocal of \( \frac{5}{4} \), which is \( \frac{4}{5} \).

\[
p = \frac{23}{6} \times \frac{4}{5}
\]

### Step 4: Simplify.
Multiply the numerators and denominators:
\[
p = \frac{23 \times 4}{6 \times 5} = \frac{92}{30}
\]

Simplify the fraction by dividing both the numerator and denominator by 2:
\[
p = \frac{46}{15}
\]

### Final Answer:
\[
p = \frac{46}{15}
\]

Would you like further details on this solution?

Here are 5 related questions to expand your understanding:
1. How do you add or subtract fractions with different denominators?
2. What are common mistakes to avoid when multiplying fractions?
3. How do you simplify complex fractions in multi-step equations?
4. How can cross-multiplication be applied in fraction equations?
5. Can you solve a similar equation with more complex fractions?

**Tip:** Always check if fractions can be simplified before performing operations to reduce the complexity of the problem.

Learn how to solve the equation 5/4p = 4/3 + 5/2 through a step-by-step process. This problem covers important algebraic concepts such as adding fractions, finding a common denominator, and isolating the variable to find the solution. Suitable for students in Grades 8-10.

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