FOR ADMT-TOY DESIGN

For Maths WALL WISHER

Algebra Puzzle Solution(:

3x4 grid

3x3 grid

My Solution:(3 x 3)

• Let a represent apple.
• Let b represent present box.
• Let c represent gear.
• 3a= 54
• a= 54/3
• Therefore, a = 18
• Since 2a + c = 42
• 2(18) + c = 42
• 36 + c = 42
• c = 42 - 36
• Therefore, c = 6.
• Since 2c + b = 17
• 2(6) + b = 17
• 12 + b = 17
• b = 17 - 12
• Therefore, b = 5

In conclusion, each apple represents 18, each present box represents 5 and each gear represents 6.

My Solution: (3 x 4)

• Let a represent ice cream
• Let b represent drum
• Let c represent toy car
• 3a + b = 74
• 2a + b = 57
• (3a + b) - (2a + b)= 74 - 57
• a = 17
• b= 57 - 2(17)
• b= 57 - 34
• b= 23
• 2a + c = 44
• 2(17) + c = 44
• 34 + c = 44
• c= 44- 34
• c= 10

In conclusion, each ice cream represents 17, each drum represents 23 and each toy car represents 10.

Prime Factorisation

Textbook p9 #25:

The Prime factorisation of a number is 2^4 X 3^5 X 7^2 X 11.

Write down 3 factors of the number that are greater than 100.

(Hint: 16 X 11 = 176, which is a factor.)

How I work out my answer:

First, I know that 2,3,7 and 11 are factors of the number but they are smaller than 100.

As to find out 3 factors of the number that are greater than 100, I simply just take 7^2 X 11 and 3^5 X 11. Like this, I will get 539 and 2673.

Because of the example given is the answer of 2^4 X 11, I feel that i should not write the same. Therefore I simply just take 3^4 X 11 and got 891 as another answer.

Lastly, I calculated 2^4 X 3^5 X 7^2 X 11 and the answer is 2095632.

I then use the answer to divide the factors to ascertain my answer.

So, my answer is: 539, 891 & 2673.

Textbook p9 #26:

The Prime factorisation of two numbers are 2 X 3^2 X 7^3 X 13 and3 X 7^2 X 13^3 X 17 .

Write down 3 common factors of the numbers.

From these two numbers, I can see some similar prime factors in them.

So, I simply see what are the similar prime factors and they are the common factors of this two numbers.

They are: 1(a common factor is every number above 0),3 & 7.

JJ(:

Mathematics HW(:

A mathematician proposed that "Every even number greater than 2 can be expressed as a sum of two prime numbers." Do you agree? Why?

Yes, I agree.

Even numbers have several ways to be the sum of two prime numbers. For example, the number 22 can be shown as '11+11', '3+19', or '5+17'. By looking at these examples, it appears that the higher the even number, the more pair of prime numbers there are that add up to it.

There is an assumption that says that every even number can be expressed as the sum of two prime numbers at least in one way. This assumption is known as Goldbach's conjecture, after Christian Goldbach, a Prussian mathematician who propounded it. It remains to be one of the most ancient problems that is yet not completely solved in the field of mathematics. The conjecture basically states that every even integer that is greater than the number 2 can be expressed as the sum of two primes.

Adapted from: http://www.blurtit.com/q710414.html

I understand that even numbers apart from 2 can be expressed as the sum of two prime numbers as 2 is the only prime number that is an even number.

JJ(:

Communication(:

Why is communication important?

It is important as in the social field it is regarded as a very essential thing to keep in touch with other people(such as relatives and old friends). Communication would also allow people to express their feelings.

What is/are your favourite form/s of communication? Why?

My favourite form of communicating is by talking on the telephone. I find it very convenient to talk to one another as you do not need to wait for the other person to reply. Besides that, it would also allow three people or more to talk in a conference, making to it much easier.

How do you decide which form of communication to use in a situation?

It depends on what kind of situation. For most situations, I would use my handphone as it operates very fast and is very convenient.

What difficulties do you face in communicating with others?

I do not really face much problems in communicating with others except sometimes I do not catch what others have said.

JJ(:

12 January: Numbers as a Language

These are the numerals! ^^

After researching on the internet about different kinds of numeral systems and looking through the developement of the systems, I have decided to choose the Mayan Numeral System to represent 2010. I chose this because Mayan Numerals makes a good connection between Math and Social Studies. Besides that, adding and subtracting numbers by using this system is also very easy.
Although, multiplication and division may be a little hard, it would just require a bit more effort. We should do our best in everything. A little obstacle is easy to break. So in this year 2010 at SST, I would just put in more effort in my work (:

JJ(: