The difference between products on a number Essay Example

The difference between products on a number Essay Im going to investigate the difference between products on a number grid first Im going to draw a box round four numbers then I will find the product of top left, bottom right numbers, and then Im going to do the same with the top right, bottom right numbers in the box. Ill will then calculate the difference between these products. Not only I am going to investigate squares, but also rectangles, Ill use algebra to try and find a formula or a general rule that will give me this difference for any size shape. Im going to draw a box round four numbers then I will find the product of top left, bottom right numbers, and then Im going to do the same with the top right, bottom right numbers. 12 13 We will write a custom essay sample on The difference between products on a number specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on The difference between products on a number specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on The difference between products on a number specifically for you FOR ONLY $16.38 $13.9/page Hire Writer 22 23 The difference between 286 and 276 is 10 because 286 276 = 10 13 x 22 = 286 12 x 23 = 276 49 50 59 60 The difference between 2950 and 2940 is 10 because 2950 2940 = 10 50 x 59 = 2950 49 x 60 = 2940 5 6 15 16 The difference between 90 and 80 is 10 because 90 80 = 10 6 x 15 = 90 5 x 16 = 80 I predicted that the difference for all 22 spares will be 10, Ill do another 2 by 2 grid to confirm that my prediction is correct. 82 83 92 93 The difference between 7636 and 7626 is 10 because 7636 7626 = 10 83 x 92 = 7636 82 x 93 = 7626 This shows that my prediction is correct, that all 2 by 2 will equal to 10. 3 by 3 Im going to draw a box round nine numbers then I will find the product of top left, bottom right numbers, and then Im going to do the same with the top right, bottom right numbers. 1 2 3 11 12 13 21 22 23 The difference between 63 and 23 is 40 because 63 23 = 40. 3 x 21 = 63 1 x 23 = 23 6 7 8 16 17 18 26 27 28 The difference between 208 and 168 is 40 because 208 168 = 40. 8 x 26 = 208 6 x 28 = 168 25 26 27 35 36 37 45 46 47 The difference between 1215 and 1175 is 40 because 1215 1175 = 40 27 x 45 = 1215 25 x 47 = 1175 I predicted that the difference for all 3 by 3 spares will be 40, Ill do another 3 by 3 grid to confirm that my prediction is correct. 16 17 18 26 27 28 36 37 38 The difference between 648 and 608 is 40 because 648 608 = 40 18 x 36 = 648 16 x 38 = 608 This shows that my prediction is correct, that all 3 by 3 will equal to 30. 4 by 4 Im going to draw a box round sixteen numbers then i will find the product of top left, bottom right numbers, and then Im going to do the same with the top right, bottom right numbers. 14 15 16 17 24 25 26 27 34 35 36 37 44 45 46 47 The difference between 748 and 658 is 90 because 748 659 = 90. 17 x 44 = 748 14 x 47 = 658 24 25 26 27 34 35 36 37 44 45 46 47 54 55 56 57 The difference between 1458 and 1368 is 90 because 1458 1368 = 90. 27 x 54 = 1458 24 x 57 = 1368 55 56 57 58 65 66 67 68 75 76 77 78 85 86 87 88 The difference between 4930 and 4840 is 90 because 4930 4840 = 90. 58 x 85 = 4930 55 x 88 = 4840 I predicted that the difference for all 4 by 4 spares will be 90, Ill do another 4 by 4 grid to confirm that my prediction is correct. 51 52 53 54 61 62 63 64 71 72 73 74 81 82 83 84 The difference between 4930 and 4940 is 90 because 4930 4940 = 90. 54 x 81 = 4374 51 x 84 = 4284 This shows that my prediction is correct, that all 4 by 4 will equal to 90. 5 by 5 Im going to draw a box round twenty five numbers then I will find the product of top left, bottom right numbers, and then Im going to do the same with the top right, bottom right numbers. 1 2 3 4 5 11 12 13 14 15 21 22 23 24 25 31 32 33 34 35 41 42 43 44 45 The difference between 205 and 45 is 160 because 205 45 = 160. 5 x 41 = 205 1 x 45 = 45 55 56 57 58 59 65 66 67 68 69 75 76 77 78 79 85 86 87 88 89 95 96 97 98 99 The difference between 5605 and 5445 is 160 because 5605 5445 = 160. 59 x 95 = 5605 55 x 99 = 5445 42 43 44 45 46 52 53 54 55 56 62 63 64 65 66 72 73 74 75 76 82 83 84 85 86 The difference between 3772 and 3612 is 160 because 3772 3612 = 160. 46 x 82 = 3772 42 x 86 = 3612 I predicted that the difference for all 5 by 5 spares will be 160, Ill do another 5 by 5 grid to confirm that my prediction is correct. 35 36 37 38 39 45 46 47 48 49 55 56 57 58 59 65 66 67 68 59 75 76 77 78 79 The difference between 2925 and 2765 is 160 because 2925 2765 = 160. 39 x 75 = 2925 35 x 79 = 2765 This shows that my prediction is correct, that all 5 by 5 will equal to 160. 6 by 6 Im going to draw a box round twenty five numbers then I will find the product of top left, bottom right numbers, and then Im going to do the same with the top right, bottom right numbers. 21 22 23 24 25 26 31 32 33 34 35 36 41 42 43 44 45 46 51 52 53 54 55 56 61 62 63 64 65 66 71 72 73 74 75 76 The difference between 1846 and 1596 is 250 because 1846 1596 = 250. 26 x 71 = 1846 21 x 76 = 1596 1 2 3 4 5 6 11 12 13 14 15 16 21 22 23 24 25 26 31 32 33 34 35 36 41 42 43 44 45 46 51 52 53 54 55 56 The difference between 306 and 56 is 250 because 306 56 = 250. 6 x 51 = 306 1 x 56 = 56 33 34 35 36 37 38 43 44 45 46 47 48 53 54 55 56 57 58 63 64 65 66 67 68 73 74 75 76 77 78 83 84 85 86 87 88 The difference between 3154 and 2904 is 250 because 3154 2904 = 250. 38 x 83 = 3154 33 x 88 = 2904 I predicted that the difference for all 6 by 6 spares will be 250, Ill do another 6 by 6 grid to confirm that my prediction is correct. 14 15 16 17 18 19 24 25 26 27 28 29 34 35 36 37 38 39 44 45 46 47 48 49 54 55 56 57 58 59 64 65 66 67 68 69 The difference between 1216 and 966 is 250 because 1216 966 = 250. 19 x 64 = 1216 14 x 69 = 966