To solve the expression \( 1 \frac{2}{15} + \left( -3 \frac{1}{2} \right) \), we need to follow these steps:

### Step 1: Convert the mixed numbers into improper fractions.
- For \( 1 \frac{2}{15} \):
  \[
  1 \frac{2}{15} = \frac{15}{15} + \frac{2}{15} = \frac{17}{15}
  \]

- For \( -3 \frac{1}{2} \):
  \[
  -3 \frac{1}{2} = -\left( \frac{6}{2} + \frac{1}{2} \right) = -\frac{7}{2}
  \]

### Step 2: Find a common denominator to add the fractions.
The least common denominator (LCD) of 15 and 2 is 30.

- Convert \( \frac{17}{15} \) to a denominator of 30:
  \[
  \frac{17}{15} = \frac{17 \times 2}{15 \times 2} = \frac{34}{30}
  \]
- Convert \( -\frac{7}{2} \) to a denominator of 30:
  \[
  -\frac{7}{2} = \frac{-7 \times 15}{2 \times 15} = \frac{-105}{30}
  \]

### Step 3: Add the fractions.
\[
\frac{34}{30} + \frac{-105}{30} = \frac{34 - 105}{30} = \frac{-71}{30}
\]

### Step 4: Convert back to a mixed number (if needed).
\[
\frac{-71}{30} = -2 \frac{11}{30}
\]

### Final Answer:
\[
1 \frac{2}{15} + \left( -3 \frac{1}{2} \right) = -2 \frac{11}{30}
\]

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to expand your knowledge:
1. How do you subtract mixed numbers?
2. What are the steps to simplify improper fractions?
3. How do you convert improper fractions to mixed numbers?
4. Why is finding a common denominator necessary in fraction addition?
5. Can you solve \( 5 \frac{3}{4} + (-2 \frac{2}{5}) \)?

**Tip**: When dealing with mixed numbers, converting them into improper fractions first often simplifies the process of addition or subtraction.

Learn how to solve the expression 1 2/15 + (-3 1/2) by converting mixed numbers into improper fractions, finding a common denominator, and adding fractions. Suitable for students in Grades 5-7, this detailed explanation covers essential concepts like improper fractions and fraction addition.

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