https://file.aiquickdraw.com/mathbot/file/1727438688571v64zuys9.jpg

To solve the weighted average problem in the image:

### Given dataTo solve the weighted average problem in the image:

### Given 
- Numbers: \(-3\), \(-2\), \(6\)
- Corresponding weights:  
  \(w_{-3} = \frac{1}{3}, w_{-2} = \frac{1}{2}, w_6 = \frac{1}{6}\)

The formula for the weighted average is:

\[
\text{Weighted Average} = \frac{\sum (x_i \cdot w_i)}{\sum w_i}
\]

### Step 1: Calculate the weighted sum \(\sum (x_i \cdot w_i)\)
\[
\sum (x_i \cdot w_i) = (-3 \times \frac{1}{3}) + (-2 \times \frac{1}{2}) + (6 \times \frac{1}{6})
\]
\[
= -1 + (-1) + 1 = -1
\]

### Step 2: Calculate the sum of the weights \(\sum w_i\)
\[
\sum w_i = \frac{1}{3} + \frac{1}{2} + \frac{1}{6}
\]

Finding a common denominator (which is 6):
\[
\sum w_i = \frac{2}{6} + \frac{3}{6} + \frac{1}{6} = \frac{6}{6} = 1
\]

### Step 3: Compute the weighted average
\[
\text{Weighted Average} = \frac{-1}{1} = -1
\]

### Final Answer:
The weighted average is **\(-1\)**.

Would you like further clarification or more details?

Here are 5 related questions to consider:
1. How do you calculate the weighted average for more than three values?
2. What happens if the sum of the weights is not 1?
3. Can a weighted average be greater than any of the original numbers?
4. How would the result change if the weights were distributed differently?
5. In what scenarios is calculating a weighted average useful in real life?

**Tip**: Always ensure the sum of the weights equals 1 to simplify weighted average calculations.

What is the weighted average of the three numbers with the weights shown?

Learn how to calculate the weighted average of the numbers -3, -2, and 6 with weights 1/3, 1/2, and 1/6 respectively. This problem covers key arithmetic and algebraic concepts, suitable for students in Grades 8-10.

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