Investigating the Maxi Product of Numbers
Introduction ------------
In this investigation, I am going investigate the Maxi Product of numbers. I am going to find the Maxi Product for selected numbers and then work out a general rule after individual rules are worked out for each step. I am going to find the Maxi Product for double numbers, I will find two numbers which added together equal the number selected and when multiplied will equal the highest number possible that can be retrieved from two numbers multiplied together. I am also going to find the Maxi Product for triple numbers, I will find three numbers which added together equal the number selected and when multiplied will equal
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I will try now in fractional numbers if I can get a number higher than 49.
(7 1/10, 6 9/10)= 14 à 7 1/10+6 9/10 à 7 1/10x6 9/10 =48.99
(7 4/15, 6 11/15)= 14 à 7 4/15+6 11/15 à 7 4/15x6 11/15=48.929 (3dp)
(7 1/15, 6 14/15)= 14 à 7 1/15+6 14/15 à 7 1/15x6 14/15=48.996 (3dp)
I have found that 7 and 7 are the two numbers which added together make 14 and when multiplied together make 49 which is the highest possible answer which is retrieved when two numbers added together equal 14 are multiplied.
15
(1,14)= 15 à 1+14 à 1x14=14
(2,13)= 15 à 2+13 à 2x13=26
(3,12)= 15 à 3+12 à 3x12=36
(4,11)= 15 à 4+11 à 4x11=44
(5,10)= 15 à 5+10 à 5x10=50
(6,9)= 15 à 6+9 à 6x9 =54
(7,8)= 15 à 7+8 à 7x8 =56
I have found that 56 is the highest number so far that can be retrieved from 7 and 8 when the number is 15, in whole numbers. I will now try in decimal numbers if I can get a number higher than 56.
(7.1,7.9)= 15 à 7.1+7.9 à 7.1x7.9=56.09
(7.2,7.8)= 15 à 7.2+7.8 à 7.2x7.8=56.16
(7.3,7.7)= 15 à 7.3+7.7 à 7.3x7.7=56.21
(7.4,7.6)= 15 à 7.4+7.6 à
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16
(1,14,1)= 16 à 1+14+1 à 1x14x1=14
(2,13,1)= 16 à 2+13+1 à 2x13x1=26
(2,12,2)= 16 à 2+12+2 à 2x12x2=48
(3,11,2)= 16 à 3+11+2 à 3x11x2=66
(3,10,3)= 16 à 3+10+3 à 3x10x3=90
(4,9,3)= 16 à 4+9+3 à 4x9x3 =108
(4,8,4)= 16 à 4+8+4 à 4x8x4 =128
(5,7,4)= 16 à 5+7+4 à 5x7x4 =140
(5,6,5)= 16 à 5+6+5 à 5+6+5 =150
I am now going to use decimal numbers as I have found the highest possible result in whole numbers. I will see in decimal numbers if I can retieve a higher result than 150 when three numbers are multiplied together.
(5.01,5.90,5.09)= 16 à5.01+5.90+5.09 à 5.01x5.90x5.09=150.45531
(5.25,5.30,5.45)= 16 à5.25+5.30+5.45 à 5.25x5.30x5.45=151.64625
I will now move on to fractional numbers as there can be no other decimal number that can give a result higher than 151.64625 using three numbers. I will see in fractional numbers if I can get a number higher than 151.64625 from three fractional numbers.
(5 1/20,5 7/20,5 12/20)= 16 à 5 1/20+5 7/20+5 12/20 à 5 1/20x5 7/20x5 12/20=
151.298
(5 1/50,5 20/50,5 29/50)= 16 à 5 1/50+5 20/50+5 29/50 à 5 1/50x5 20/50x5 29/50=
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