I have stopped my table because the answers of the product are now starting to be repeat it self
My Maxi Product is (4,4) =16. Both numbers of the product are even. I got this by dividing the main number by 2 and then multiplying it by itself again to get maxi product.
I have stopped my table because the answers of the product are now starting to be repeated.
My Maxi Product is (8, 8) which equals to 64. I got this by doing the partitions of the number and then with the partition I multiplied it to the power of 2.
Now i am going to do this with an odd number to see the different results.
Now i have stopped my table because the answers of the product keep coming the same now.
My Maxi Product is (6.5, 6.5) which equals to 42.25.
My Table
Below i have put my data onto a table so it easier for me to see and easier to find the rule.
My Rule:
To find the maxi product you have to take the original number and divide it by 2 that will give you a partition. When you get the partitions you have to multiply both numbers together from this you will get the maxi-product. For instance if i have 16, then i will divide it by 2 then square the number I get by dividing 16 and this is how I will get my answer.
Below is another example i am going to show you.
Now i have stopped my table because the answers of the product keep coming the same now.
My Maxi Product is (5, 5) which equals to 64.
Rule in Words:
Maxi Product equals the number selected divided by two and then the answer squared.
Rule in Algebra: Key: M= Maxi Product N= Number
M=
Predict my rule and proving it:
To show that my rule was correct I will do it on a new number. By doing this I can check if my formula is correct. I will also draw a table to find my maxi product in an easier way.
Firstly i will do this with my algebric rule and i predict that the maximum product is 7. Then after i will use the number 7 into my formula m=
M=(7/2) M=(3.5) M=3.5x3.5 M=12.25
M=(3.5)
i have done this with my algebric rule and I can now predict that the maximum product for the number 7 is 12.25 with the partition (3.5,3.5).
Below is a table proving my rule
My table proves that my algebraic rule m= is correct. It shows that my maximum product was 12.25. My partition for this was (3.5,3.5)
Triplets
I have stopped my table because the answers of the product have started to repeat itself. My maxi product is (4, 4, 4) which equals to 64.I got this by dividing 12 by 3 and then with the answer I multiplied it to the power of 3.
I have stopped my table because the answers of the product have started to repeat itself.My maxi product is (3, 3, 3,) which equals to 27 .I got this by dividing 21 by 3 and then with the answer I multiplied it to the power of 3.
I have stopped my table because the answers of the product have started to repeat itself.My maxi product is (6, 6, 6) which equals to 216 .I got this by dividing 15 by 3 and then with the answer I multiplied it to the power of 3.
Below is a table to show you my results and to conclude my investigation.
Rule in words:
The main number is divided by 3 which will give you 3 partitions .Then you have to multiply the 3 numbers from the partition then you will get your maxi product. For example if I do 21 3x7=21 then I multiply the 3 partitions which are (7,7,7) which equal to 343 so 343 will be my maximum product.
Rule in Algebra: Key: M=Maxi product N=Number
M=(N/3)³
RULE FOR MY RECORDINGS:
Predicting the rule for quadruple.
I predict that in quadruples you have to divide the main number by 4. This will give you a partition. Then multiply it to the power of 4. This will give you the maxi product.
Rule in Algebra: Key: M=Maxi product N=Number
M=
Rule for 5 partition
I predict that in 5 partitions you have to divide the main number by 5. This will give you a partition. Then multiply it to the power of 5. This will give you the maxi product.
Rule in Algebra: Key: M=Maxi product N=Number
M=
Rule for 6 partition
I predict that in 6 partitions you have to divide the main number by 6. This will give you a partition. Then multiply it to the power of 6. This will give you the maxi product.
Rule in Algebra: Key: M=Maxi product N=Number
M=
Overall rule and my conclusion.
I conclude this investigation/coursework.The number you divide by is always then powered by the same number.So the over all rule for this investigation is (x/n)