To solve the equation \(\frac{w}{3} + \frac{2}{5} = \frac{1}{15}\), we need to isolate the variable \(w\).

### Step 1: Subtract \(\frac{2}{5}\) from both sides of the equation
\[
\frac{w}{3} = \frac{1}{15} - \frac{2}{5}
\]

### Step 2: Find a common denominator to subtract the fractions on the right side
The least common denominator (LCD) between 15 and 5 is 15.

\[
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
\]

So, the equation becomes:
\[
\frac{w}{3} = \frac{1}{15} - \frac{6}{15} = \frac{1 - 6}{15} = \frac{-5}{15}
\]

### Step 3: Simplify the fraction
\[
\frac{-5}{15} = -\frac{1}{3}
\]

So the equation is now:
\[
\frac{w}{3} = -\frac{1}{3}
\]

### Step 4: Multiply both sides by 3 to solve for \(w\)
\[
w = -\frac{1}{3} \times 3 = -1
\]

### Final Answer:
\[
w = -1
\]

Would you like more details or have any questions?

Here are five related questions:
1. How do you solve equations with multiple fractions?
2. What is the least common denominator, and how do you find it?
3. How do you add or subtract fractions with different denominators?
4. How do you simplify complex fractions?
5. What are common mistakes when working with fractions in equations?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation \(\frac{w}{3} + \frac{2}{5} = \frac{1}{15}\) with a detailed step-by-step solution. This problem involves adding and subtracting fractions and isolating variables in equations. Suitable for students in Grades 6-8.

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