Investigating The Answer When The Products Of Opposite Corners on Number Grids Are Subtracted
Introduction
The purpose of this investigation is to explore the answer when the products of opposite corners on number grids are subtracted and to discover a formula, which will give the answer in all cases. I hope to learn some aspects of mathematics that I previously did not know.
The product is when two numbers are multiplied together.
There is one main rule: the product of the top left number and the bottom right number must be subtracted from the product of the top right and bottom left numbers. It cannot be done the other way around.
I plan to achieve my aim by attempting a series of different
…show more content…
(15 x 19) – (13 x 21) 285 – 273 = 12 Answer = 12 (The same) 13
14
15
16
17
18
19
20
21
The formula will not be the same for these. There will be a different formula for each kind. So the easiest way is to substitute the numbers in the grid for 1,2,3,4 and so on. Then you can use the formula for that type of grid to work out the answer. However this will only be easy for smaller number grids.
Sequences
Now I have tried grids with number sequences. First where the numbers increase by 2.
Text Box: (4 x 6) – (2 x 8) 24 – 16 = 8 Answer = 8 The answer is four times that of the previous 2 x 2 grids I have done. 2 x 2 Grid
2
4
6
8
I have checked this by doing another 2 x 2 grid but with different numbers.
Text Box: (5 x 7) – (3 x 9) 35 – 27 = 8 Answer = 8 (The same) 2 x 2 Grid
3
5
7
9
I have now done a 3 x 3 grid just to check this rule.
Text Box: (6 x 14) – (2 x 18) 84 – 36 = 48 Answer = 48 The answer to the previous 3 x 3 grid was 12 and 4 x 12 =
…show more content…
In a 2 x 2 grid with consecutive numbers the answer is 2.
The formula however will not be exactly the same. Instead of having D it will be replaced by W, because it is a square grid.
It will be:
W (W²) + W - W² - W²
= W³ + W - 2W²
= 2³ + 2 - 2 x 2²
= 8 + 2 - 8
= 2 : Which is correct.
I have checked this with a 4 x 4 grid. The answer should be 36.
W³ + W - 2W²
= 4³ + 4 - 2 x 4²
= 64 + 4 - 32
= 68 - 32
= 36: Which is correct
Therefore this formula does work.
Even though the formulas I got before I simplified them look different, when simplified they are the same:
N (1 + N² - N) - N²(1 + N - N)
= N³ - 2N² + N
W (W²) + W - W² - W²
= W³ - 2W² + W
Decimals
Now I have decided to investigate decimals in number grids.
Text Box: (0.2 x 0.3) – (0.1 x 0.4) 0.06 – 0.04 = 0.02 Answer = 0.02 0.1
0.2
0.3
Text Box: Table 2. Humerus length and height of female student in the classText Box: Table 1. Humerus length and height of male student in the class
The last activity that we did was taking ten Q tips and made three attached squares and her assignment was to make a 4th enclosed box without adding an additional items. Once I told her to start she immediately started moving the Q tips around trying to create another box. After trying for a few minutes she then say there is no way to add another box.
A Couple of Squares is a company specializing in producing and selling gourmet cookies to retail stores. Recently, A Couple of Squares has been brainstorming the idea of starting an e-commerce website so they can sell there gourmet cookies directly to consumers instead of selling to retailers. There are many considerations that need to be evaluated when deciding to launch an e-commerce website. First, the risks of launching an e-commerce site and the steps to mitigate the risks must be evaluated. Along with the risks of launching an e-commerce site, the benefits of launching an e-commerce site also need to be taken into account. In order to seek profitability a break even analysis must be performed. Once profitability is feasible, A Couple
entered one at a time and their volume was computed in order to add to
numbers 1 to 9 and 0, and the words yes and no. A smaller board, shaped like a
asked to divide the same square into two parts half the original size. By asking the boy a
Display the Unifix cubes on the table; first, explain to the child what we call a subtraction. Next, write down for the child the
By using combinations from the above – But this approach has to be made with caution, because confusion can appear in the message.
difference of product is going to be same as the size of a grid (in
on the entire left side of the triangle (column 3) to represent n things going into groups of 0. There is only one way to do this, so every cell with a blank box can be said to have one item in it. I am using a box because it does not have a specific “value” but it is more of a holding place for new elements. In cell (B, 4), I placed an “a” because this represe...
The human brain loves to make its job easier, especially when handling large amounts of information and numbers. There was a student that wanted to test his mental abilities, he selected the number nine hundred ninety nine and multiplied it by itself ten times and came up with the correct thirty digit number. How does someone keep track of so many numbers and multiplications without overwhelming his or her brain? The answer is that the brain has the ability to automatically perform calculations to make its job easier, in the case of the student he was able to do this because he had practiced for several years in order to perfect this ability.
Using a square, both the length & the width are equal. I am using a
This problem has parentheses, exponents, and multiplication. The first set of brackets is a symbol of product. It indicates that the second set is multiplication. Grouping symbols are handled first.
The ratio for length to width of rectangles is 1.61803398874989484820. The numeric value is called “phi”.
We cannot have a negative width, so the negative answer is not considered. Therefore, the