Number pairs Added together multiplied together Product
I will also go further into my investigation by using 0.7,0.8 and 0.9.
Number pairs Added together multiplied together Product
I have noticed in my tables that the maxi product of 12 is 6 and 6 which when multiplied together make 36.
Patterns
In my second table I have noticed that each time the maxi product increases the difference between the maxi product and the next maxi product decreases by 2 each time.
Maxi product of table 2
5.75
> 10
15.75 > 2
> 8
23.75 > 2
> 6
29.75 > 2
> 4
33.75 > 2
> 2
35.75
The list of 2 is called the second difference. The list starting at 10 is the 1st difference. When finding a rule using algebra, if a number has a second difference it means there will be a number that has a squared with it in the rule.
My next task will be choosing my own No and investigating to find the maxi product.
4
Number pairs Added together multiplied together Product
The maxi product for 4 is 4 with the multiples being 2 x 2.
7
Number pairs Added together multiplied together Product
Looking at the table I need to multiply 3.5 by 3.5 to make 12.25 making that the maximum product for 7.
12
Number pairs Added together multiplied together Product
I have noticed in my tables that the maxi product of 12 is 6 and 6 which when multiplied together make 36.
The partition is 6 and 6.
28
Number pairs Added together multiplied together Product
I have noticed that the maxi product for 28 is 196. The partition is 14 and 14.
35
Number pairs Added together multiplied together Product
The maxi product for 35 is 306.25. The partition is 17.5
I noticed that to get the maxi product for a double I must divide the No by 2 then square it.
I have found a rule and now I will try it out.
(N – 2)²
I will now test my rule for the maxi product of 79.
79 – 2 = 39.5 x 39.5 = 1560
My rule is correct.
My third task is to split the numbers into triples
Number pairs Added together multiplied together Product
The maximum product for 7 is 12.7. The partitions are 2.3,2.3,2.3.
Number pairs Added together multiplied together Product
The partitions for 12 are 4,4,4. Multiply these together to make the maximum product for 12, which is 64.
Number pairs Added together multiplied together Product
The maxi product for 28 when split into 3, is 813. The partitions are 9.3, 9.3, and 9.3.
Number pairs Added together multiplied together Product
The partitions for 35 are 11.6, 11.6 and 11.6 multiplied together. The maxi product is 1587.96.
I have noticed that to get the maxi product for a triple No I must divide the No by 3 then cube it. Here is my formula.
(N/3)³
I will now test my rule.
80/3 = 26.67
26.67³ = 18962.96
My rule is correct after testing it on a calculator.
