Number grid.

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Maths coursework number grid

In this project, I am going to investigate a number grid. Using a set of instructions, that, have been given to me. The instructions are to find the product of various numbers. Before I start I will like to explain exactly why I have colour coded my work. If you look at my project you will find that there are certain numbers in colour the reason for this is, that it makes it easier to understand what is being multiplied and what is being subtracted.

The numbers that were initially given to me were 12, 13, 22, 23 presented in a number grid marked by a two by two box.

I was told to find the product of top left, (12) and the bottom right number (23). We then had to do the same to the top right (13) and bottom left (22). Once I we had worked out both products I had to calculate the difference.

I am now going to give two examples to show you what I had to do.

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Example One

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12 13 DIFFERENCE

x 23 x 22 286

= 276 = 286 - 276

= 10

I would like to show one more example of this to see if the difference will always be 10.

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24

25

14 15 Difference

x 25 x 24 360

350 360 - 350

10

I am now going to use algebra to try and prove that the difference will always be

Ten and that the examples shown above are not just coincidences.

X

X+1

X+10

X+11

Remember that this box is exactly the same as the first but the numbers have been put in to algebraic expressions.

Using my original set of instructions, I am going to work out the algebraic two by two box.

X(11+X) (X+1)(X+10)

=X2+11X =X2+11+1

DIFFERENCE

I am now going to subtract the answers I got from the algebra and see if the difference is 10.

X2+11+1

-X2+11X

=10

I have just used algebra and proved the difference will always be ten.

The algebra was labelled using the terms X, X+1, X+10 And X+11. the point of this was, when we look at the original box that was used in example one, the first number is twelve to replace this, the first number in the algebraic two by two box is going to be X. the second number is 11, which is one unit bigger than twelve therefore the second term which was used for algebra is X+1. In example one the number below the twelve (X) is 22 which is 10 units bigger than twelve therefore the term we used for this, is X+10. Finally the number below 13 (X+1) is 23 which is 11 units bigger than 12 (X) Therefore the term I used for this is X+11.
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Using my original set of instructions, I am going to work out the algebraic three by three box.

Note that the numbers not being used are not coloured nor are they under lined

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48

49

57

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68

69

Difference

47 49 3283

x 69 x 67 - 3243

3243 3283 40

Like I did before I am now going to use algebra to see if the difference is always

Forty, in a three by three ...

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