when a cross tile is placed on a number plane the centre number is the average of al the numbers covered. Explain why
Isn't it because the numbers around are similar as in they are not far apart. I don't actually know why. I have this question in my maths challenge as well.
well than we should work it out ourselves!
To understand why the center number of a cross tile placed on a number plane is the average of all the numbers covered, let's break it down step by step.
Step 1: Define the concept
First, we need to establish what a cross tile is. In this context, a cross tile refers to a pattern consisting of five numbers arranged in the shape of a cross, specifically on a number plane.
Step 2: Locate the center number of the cross tile
Next, we identify the center number of the cross tile. The center number is the one that is directly in the middle of the cross, surrounded by the other four numbers.
Step 3: Understand the cross tile arrangement
In a cross tile, each arm of the cross is assigned a set of numbers. The center number is shared by all four arms, while each arm has its unique set of numbers.
Step 4: Analyze the number arrangement
Since the center number is connected to all four arms, the numbers surrounding it are equally distributed in the arms. This means that each arm contains numbers that contribute to the final average of the center number.
Step 5: Calculate the average
To find the average, we sum up all the numbers in the arms and then divide the total by the number of arms. Since each arm has the same number of numbers, this simplifies the calculation. By dividing the total sum by four (the number of arms), we obtain the average.
Step 6: Understand the result
The center number represents the average because it is connected to all four arms. Therefore, the pattern of the cross tile ensures that the center number is influenced by all the surrounding numbers in equal proportions.
In conclusion, the center number of a cross tile on a number plane is the average of all the numbers covered because each arm contributes an equal number of values to the calculation. The arrangement of the cross tile ensures a fair distribution, resulting in the center number being the average of the surrounding numbers.