The expression you provided, $\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}$, can be evaluated by finding a common denominator or adding each fraction individually. Here’s how it works:

Step-by-Step Solution

1. Identify the fractions: $\frac{1}{3}$, $\frac{1}{4}$, $\frac{1}{5}$, and $\frac{1}{6}$.

2. Find a common denominator: The least common multiple of 3, 4, 5, and 6 is 60.

3. Convert each fraction to have a denominator of 60:

   • $\frac{1}{3} = \frac{20}{60}$
   • $\frac{1}{4} = \frac{15}{60}$
   • $\frac{1}{5} = \frac{12}{60}$
   • $\frac{1}{6} = \frac{10}{60}$

4. Add the fractions: $\frac{20}{60} + \frac{15}{60} + \frac{12}{60} + \frac{10}{60} = \frac{57}{60}$

5. Simplify the result: $\frac{57}{60}$ simplifies to $\frac{19}{20}$.

Final Answer

$\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} = \frac{19}{20}$

Would you like additional details on any of these steps?

Here are 5 related questions:

1. How do you find the least common multiple of a set of numbers?
2. How can you add fractions with different denominators?
3. What other methods can you use to approximate the sum of fractions?
4. How do you simplify fractions after summing them?
5. What are other ways to calculate the sum of a series with fractional terms?

Tip: Always check for a common denominator to make addition of fractions simpler and avoid mistakes.