The 3 x 3 Grid Puzzle(Algebra)

Let a represents apple
Let c represents car
Let p represents pen

3a = 6
a = 6 ÷ 3
a = 2

Therefore, a = 2

a + 2c = 4
3a = 6
2a - 2c = 6 - 4
2a - 2c = 2
a - c = 2 ÷ 2
a - c = 1

Since a is 2, we substitute a with 2 and it will look something like this:

2 - c = 1
2 - 1 = 1

Therefore, c = 1

a + 2p = 34

Since a is 2, we substitute a with 2 again and it will look something like this:

2 + 2p = 34
2p = 34 - 2
2p = 32
p = 32 ÷ 2
p = 16

Therefore, p = 16

Prime Factorisation

Textbook Page 9 #25

The prime factorisation of a number is 24 x 35 x 72 x 11. Write down 3 factors of the number that are greater than 100.

24x35x72x11=(2x2x2x2) x (3x3x3x3x3) x (7x7) x 11

=16 x 243 x 49 x 11

=2 095 632

2 095 632=1 x 2 095 632

=2 x 1 047 816

=3 x 698 544... ...(so on and so forth)

How do we get 3 factors of 2 095 632? We cannot possibly be dividing until we get our answer. We should take the factors from the index notation and multiply them to get our answer.

We can take 243 x 7(49/7=7), and we get 1701. (Check: 2 095 632/1701=1232[correct]) We also know that 1232, which is larger than 100, is also a factor of 2 095 632. Then, we take 1232/2 to get 616. We first assume it is a factor and we then check it. Can 2 095 632 be divided 616? Yes, and we will get 3402, another factor of 2 095 632.

So, the answer is 1701, 1232 and 616.

Textbook Page 9 #26

The prime factorisation of two numbers are 2 x 32 x 73 x 13 and 3 x 72 x 133 x 17. Write down 3 common factors of each numbers.

First, we find out WHAT exactly are the numbers?

2 x 32 x 73 x 13= 2 x 9 x 343 x 13

= 80 262

3 x 72 x 133 x 17= 3 x 49 x 2197 x 17

= 5 490 303

What do 5 490 303 and 80 262 have in common? Well, they will surely have common factors. Obviously, they will have 1 as their common factor. Then, we try to work out the answer like this:

5 490 303= 1 x 5 490 303

= 3 x 1 830 101

= 7 x 784 329

= 13 x 422 331

= 17 x 322 959

80 262= 1 x 80 262

= 2 x 40 131

= 3 x 26754

= 6 x 13 377

= 7 x 11 466

So, the answer is 1, 3 and 7.

Mathematics Textbook Page 8 #24

A mathematics proposed that “Every even number greater 2 can be expressed as a sum of two prime numbers.” I agree with his proposal. We can view some examples like: 4=2+2, 6=3+3, 8=5+3, 10=5+5, 12=7+5, 14=7+7, 16=13+3(you cannot use 14+2 as the number '14' is a composite number)... ...56=53+3. The reason is because all even numbers after 2 are composite numbers. Composites numbers can easily be created by the addition of prime numbers.

12 January: Numbers as a Language

In the early civilizations, people invented calendars to meet basic needs. As a result, number systems are from different cultures invented different number systems. If I have the choice, I will pick Roman numbers to represent the year 2010. This is due to the fact that they are very common yet interesting. I also think using Roman numbers is interesting as numbers are represented in letters.(For example: I[one], V[five], X[ten], L[fifty], C[one hundred], D[five hundred], M[one thousand]) The main reason I want 2010 to be represented by Roman letters is because the year is going to be challenging. Furthermore, Roman numbers is "difficult and tricky".

SST English Task

Why is communication important?

Communication is important as it allows us to express our thoughts, opinions and feelings. It also allows us to convey messages from one person to another. If communication is absent, everyone will be living in their own world.

What is/are your favourite form/s of communication? Why?
I like to communicate via the telephone and Internet. These forms of communication are much more convenient compared to meeting people face to face. However, we have to meet each other once in a while as we may be too dependant on technology. Furthermore, we can save our own time too if we use these ways to communicate.


 How do you decide which form of communication to use in a situation?
If it is something like an emergency, I will prefer using my handphone to dial for help as it saves time. If I have a lot of time to spare, perhaps I will chat with my friend on the Internet or most of the time, meet up to play soccer.

What difficulties do you face in communicating with others?
So far, I do not face any challenges in communicating with others. The only main challenge in communication is the time limit. Since I am occupied with homework every time, I can only chat with my friends for a short while before proceeding to my assignments on my MacBook Pro.