To solve the expression:

\[
3 + \frac{2}{5} \div 3 - \frac{2}{5}
\]

### Step 1: Handle the division first
The division \(\frac{2}{5} \div 3\) is equivalent to multiplying \(\frac{2}{5}\) by the reciprocal of 3, which is \(\frac{1}{3}\):

\[
\frac{2}{5} \times \frac{1}{3} = \frac{2 \times 1}{5 \times 3} = \frac{2}{15}
\]

### Step 2: Substitute back into the original expression
Now, the expression becomes:

\[
3 + \frac{2}{15} - \frac{2}{5}
\]

### Step 3: Convert to a common denominator
To combine the fractions \(\frac{2}{15}\) and \(\frac{2}{5}\), we need a common denominator. The least common denominator of 15 and 5 is 15. So, convert \(\frac{2}{5}\) to a fraction with denominator 15:

\[
\frac{2}{5} = \frac{6}{15}
\]

Now the expression is:

\[
3 + \frac{2}{15} - \frac{6}{15}
\]

### Step 4: Combine the fractions
Now combine the fractions \(\frac{2}{15}\) and \(\frac{6}{15}\):

\[
\frac{2}{15} - \frac{6}{15} = \frac{-4}{15}
\]

### Step 5: Add the integer and fraction
Now the expression is:

\[
3 + \frac{-4}{15} = \frac{45}{15} - \frac{4}{15} = \frac{41}{15}
\]

### Final Answer:
\[
\frac{41}{15}
\]

Would you like any further details or clarifications?

Here are some related questions for you:
1. What is the value of \(\frac{2}{5} \div 4 - \frac{1}{3}\)?
2. Can you simplify the expression \(4 + \frac{3}{4} - 2 \times \frac{1}{2}\)?
3. What is the least common denominator for \(\frac{3}{8}\) and \(\frac{5}{12}\)?
4. How do you solve \(2 + \frac{1}{2} \div 2 - \frac{1}{3}\)?
5. What happens when you divide one fraction by another?

**Tip:** When dividing fractions, always multiply by the reciprocal of the divisor.

Learn how to solve the arithmetic expression 3 + 2/5 ÷ 3 - 2/5 with a step-by-step breakdown. This solution covers the division of fractions, finding a common denominator, and the correct order of operations. Suitable for students in Grades 6-8.

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