The Partitions of 12.

Rahul Dey        9P        Version 1.2

Year 9

Maths Coursework

Form: 9P

Contents

3. Coursework Version History

4. Question 1

5-9. Question 2

10. Question 3

Coursework Project History

Version 1.0 – Added all of the needed information into the coursework.

Version 1.1 – Neatened up layout of partitions, and elaborated briefly on some ideas

Version 1.2 – Put all of the partitions into tables to save space, and to neaten it up.

Question 1

The Partitions of 12:

Using the following systematic process, the number 12 can be partitioned into the following pairs:

(NOTE: I HAVE ALSO PUT THE PRODUCT COLUMN HERE TO SHOW THE PRODUCTS OF THE TWO PARTITIONING INTEGERS WHEN MULTIPLIED)

Due to the fact that there are infinite partitions of the number 12 (and indeed any other number), I have only broken them down into halves, to show that it works with fractional numbers.

The answer to question 1 is 6x6. This is because 6x6 gives the highest product when multiplies together.

Notes:

I notice that there are some interesting facts regarding the answer.

1. 6 is no ordinary number, it is actually half of 12. When you multiply something by ½, you are actually also dividing it by 2. This is interesting because we are trying to find pairs and pairs mean two of something.
2. 6 must multiply by itself to produce the highest product. This is also another name for squaring. Since squaring a number involves the power of 2, it also interesting.

However, to prove any similarities in other partitioning, I will have to actually test more.

Question 2

The second question involves me choosing numbers of my own. I have chosen three numbers. They are: 5, 20 and 35.

I have chosen 5 because it is a small odd number (whereas 12 was a small even number).

I have chosen 20 because it is quite a large even number.

I have chosen 35 because it is quite a large odd number.

I have chosen these numbers to see if there are any similarities to different situations.

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