The given expression is:

$\frac{a}{8} + \frac{5}{3}$

To perform this operation, we need to find a common denominator for the fractions.

Step 1: Find the Least Common Denominator (LCD)

The denominators are 8 and 3. The least common denominator is the least common multiple (LCM) of 8 and 3, which is 24.

Step 2: Convert Fractions

Now, express both fractions with a denominator of 24: $\frac{a}{8} = \frac{3a}{24} \quad \text{(since } 8 \times 3 = 24\text{)}$ $\frac{5}{3} = \frac{40}{24} \quad \text{(since } 3 \times 8 = 24\text{)}$

Step 3: Add the Fractions

Now, we can add the fractions: $\frac{3a}{24} + \frac{40}{24} = \frac{3a + 40}{24}$

Final Answer:

The result is: $\frac{3a + 40}{24}$

This is the simplified form of the given expression.

Would you like more details or have any further questions?

Related Questions:

1. How do you find the least common multiple (LCM) of two numbers?
2. What is the general method for adding fractions with different denominators?
3. Can this expression be factored further if specific values for $a$ are provided?
4. How do you simplify fractions once they are added?
5. What happens if $a$ is a specific number, such as 8?

Tip:

When adding fractions with different denominators, always start by finding the least common denominator to make the addition easier.