A magic square is a square of numbers with each row, column, and diagonal of the square adding up to the same sum, called the magic sum. Arrange the numbers,

-1,0,1,2,3,4,5,6,and 7 into a magic square. How does the average of these numbers compare with the magic sum?
--Please can you help me i need to show my work also but i don't understand what to do...thanks!!

To create a magic square with the given set of numbers (-1, 0, 1, 2, 3, 4, 5, 6, and 7), we need to follow a specific process. Let's go step by step:

Step 1: Determine the size of the magic square.
The given set of numbers consists of nine elements, which means we need to construct a 3x3 magic square.

Step 2: Find the magic sum.
Since all rows, columns, and diagonals should have the same sum, we can find the magic sum by adding all the numbers in the set and then dividing the total by the number of rows. In this case, the magic sum would be ( -1 + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 ) / 3 = 27 / 3 = 9.

Step 3: Order the numbers.
To create a magic square, the numbers should be arranged in a specific order. A common approach is to start with the middle cell of the first row and then move diagonally upwards and to the right.

6 1 8
7 5 3
2 9 4

Step 4: Check the magic sum.
Now we need to verify whether this arrangement indeed forms a magic square. Add up each row, column, and diagonal to check if they all equal the magic sum of 9.

Row 1: 6 + 1 + 8 = 15
Row 2: 7 + 5 + 3 = 15
Row 3: 2 + 9 + 4 = 15
Column 1: 6 + 7 + 2 = 15
Column 2: 1 + 5 + 9 = 15
Column 3: 8 + 3 + 4 = 15
Diagonal 1: 6 + 5 + 4 = 15
Diagonal 2: 8 + 5 + 2 = 15

As all the sums are equal to the magic sum of 15, this arrangement forms a magic square.

Now, let's calculate the average of these numbers (-1, 0, 1, 2, 3, 4, 5, 6, and 7). We will add up all the numbers and then divide the total by the number of elements in the set.

Average = ( -1 + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 ) / 9
= 27 / 9
= 3

Therefore, the average of these numbers (-1, 0, 1, 2, 3, 4, 5, 6, and 7) is 3. The average is different from the magic sum of 9.

To arrange the numbers -1, 0, 1, 2, 3, 4, 5, 6, and 7 into a magic square, we need to follow the steps below:

Step 1: Find the magic sum
Since a magic square requires each row, column, and diagonal to add up to the same number, we need to calculate the magic sum.

The total sum of the numbers is:

-1 + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 = 27

Since a magic square is a 3x3 square, it has 3 rows, 3 columns, and 2 diagonals. Therefore, each row, column, and diagonal must add up to:

27 / 3 = 9

So, the magic sum is 9.

Step 2: Arrange the numbers into the magic square
To create the magic square, we will place the numbers in a 3x3 grid. We start by placing the numbers in ascending order from left to right, starting from the top-left corner.

Here's how to arrange the numbers:

7 2 1
0 5 -1
3 4 6

Step 3: Calculate the average of the numbers
To find the average of the numbers, we sum up all the numbers and divide by the total count. In this case, we have 9 numbers.

-1 + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 = 27

27 / 9 = 3

Therefore, the average of the numbers -1, 0, 1, 2, 3, 4, 5, 6, and 7 is 3.

Step 4: Comparing the average with the magic sum
The magic sum we calculated earlier was 9, while the average of the numbers is 3.

The average of the numbers is less than the magic sum.