To simplify the expression \( \frac{8a}{b} + \frac{7b}{4} \), let's follow these steps:

### Step 1: Find the Least Common Denominator (LCD)
The denominators are \( b \) and \( 4 \). The least common denominator (LCD) of \( b \) and \( 4 \) is \( 4b \).

### Step 2: Rewrite Both Terms with the LCD
Now, express both terms with the denominator \( 4b \).

- For the first term \( \frac{8a}{b} \), multiply both numerator and denominator by 4:
  \[
  \frac{8a}{b} = \frac{8a \times 4}{b \times 4} = \frac{32a}{4b}
  \]
  
- For the second term \( \frac{7b}{4} \), multiply both numerator and denominator by \( b \):
  \[
  \frac{7b}{4} = \frac{7b \times b}{4 \times b} = \frac{7b^2}{4b}
  \]

### Step 3: Combine the Terms
Now that both terms have the same denominator, combine them:
\[
\frac{32a}{4b} + \frac{7b^2}{4b} = \frac{32a + 7b^2}{4b}
\]

### Final Answer:
\[
\frac{32a + 7b^2}{4b}
\]

Would you like further details or have any questions?

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Here are 5 related questions for practice:
1. Simplify \( \frac{5x}{3} + \frac{7y}{3} \).
2. Simplify \( \frac{4a}{b} + \frac{2a}{b} \).
3. What is the LCD of \( \frac{2}{5} + \frac{3}{7} \)?
4. Add \( \frac{6x}{y} + \frac{3y}{2} \).
5. Simplify \( \frac{12}{x} + \frac{8}{3x} \).

**Tip**: Always check the denominators first when adding fractions; finding the least common denominator is key to simplifying the expression.

Learn how to simplify the algebraic expression 8a/b + 7b/4 using the least common denominator (LCD) method. Follow step-by-step instructions to combine rational expressions. Suitable for students in Grades 7-9.

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