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The question on the screen asks how to determine the sum of all numbers in a 3x3 magic square. Based on the provided image, the magic square shown contains numbers arranged such that the sum of every row, column, and diagonal is the same.

In a 3x3 magic square, the sum of the numbers can be found using a simple method:

- **The magic constant (the sum of each row, column, and diagonal)** is given by the formula:

\[
M = \frac{n(n^2 + 1)}{2}
\]

Where \(n\) is the size of the square, which in this case is \(n = 3\).

So for a 3x3 magic square:

\[
M = \frac{3(3^2 + 1)}{2} = \frac{3(9 + 1)}{2} = \frac{30}{2} = 15
\]

The total sum of all numbers in the square is \( 3 \times 15 = 45 \).

Given the provided choices, let's analyze the options:

- **Option A: Multiply the center number by 9**. This would work because in a 3x3 magic square, the center number is always 5 (for squares with consecutive numbers 1 to 9), and \( 5 \times 9 = 45 \), which is the correct sum of the magic square.
- **Option B: Multiply the largest number by 5**. The largest number in the square is 9, and \( 9 \times 5 = 45 \), so this also works.
- **Option C: Multiply the bottom middle number by 6**. This would depend on the specific value of that number, but it generally doesn’t work for all cases.
- **Option D: Multiply the top left number by 10**. This is also unlikely to work universally for magic squares.

Therefore, the best answer here is **Option B**: "Multiply the largest number by 5."

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

Here are 5 related questions:
1. How is a magic square defined?
2. What is the general formula for the magic constant in an \(n \times n\) magic square?
3. What are the properties of a 3x3 magic square?
4. Why does multiplying the center number by 9 also work for finding the sum in a 3x3 magic square?
5. How can magic squares be extended to larger sizes?

**Tip:** In magic squares, the sum of any row, column, or diagonal always equals the magic constant.

Examine the 3 by 3 magic square. For a 3 by 3 magic square, how can you determine the sum of all the numbers in the square by using a key value in the magic square?

Learn how to find the sum of all numbers in a 3x3 magic square using key values. This problem explores magic squares, arithmetic patterns, and provides a detailed explanation of the magic constant formula. Suitable for students in Grades 7-9.

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