To solve the expression $3 \frac{3}{5} + \frac{1}{4} - \frac{2}{5}$, let's break it down step by step.

Step 1: Convert the mixed number to an improper fraction.

$3 \frac{3}{5} = \frac{18}{5}$

Step 2: Add and subtract the fractions.

Now the expression becomes: $\frac{18}{5} + \frac{1}{4} - \frac{2}{5}$ To perform the addition and subtraction, we need a common denominator. The least common denominator (LCD) of 5 and 4 is 20.

• Convert $\frac{18}{5}$ to have a denominator of 20: $\frac{18}{5} = \frac{72}{20}$
• Convert $\frac{1}{4}$ to have a denominator of 20: $\frac{1}{4} = \frac{5}{20}$
• Convert $\frac{2}{5}$ to have a denominator of 20: $\frac{2}{5} = \frac{8}{20}$

Step 3: Perform the addition and subtraction.

$\frac{72}{20} + \frac{5}{20} - \frac{8}{20} = \frac{72 + 5 - 8}{20} = \frac{69}{20}$

Step 4: Simplify the result.

$\frac{69}{20} = 3 \frac{9}{20}$

Thus, the final result is $3 \frac{9}{20}$.

Would you like further details on any step, or do you have any questions?

Here are some related questions:

1. How do you convert a mixed number to an improper fraction?
2. What is the least common denominator (LCD) and how is it used?
3. How do you add and subtract fractions with different denominators?
4. What are the steps for simplifying improper fractions?
5. Can you explain how to estimate fractions mentally?

Tip: When adding or subtracting fractions, finding the least common denominator is essential for simplifying the process!