MU123 Discovering mathematics

TMA02

M3040733

TMA02

Question 1.

(a)

(i) 1560 is a composite number, that is, a number greater than 1 that is not a prime

number. Looking at the number 1560 it can be written as a product of 6 factors

(2x2x2x5x3x13). I started by dividing 1560 by 8 then continued until I had prime

numbers at the end of the tree.

It follows from fig1 that 1560= 2x2x2x5x3x13... in a simplified form I could write the

2x2x2 as 2

3

... ergo... 1560= 2

3

x5x13

I started with 8x195...but I could have used anything that ended up with whole

numbers. I checked my answer by trying 3x520 and got the same prime factors.

(ii)

RICHARD FORD 11 STARLING RD TEWKESBURY GL20 7TD

richdebtomdom@googlemail.com

01684276415

1

MU123 Discovering mathematics

TMA02

M3040733

Firstly I give myself a strong reminder that this is an addition/subtraction problem that

follows BIDMAS...

So, my first step was to add the

.

If the dominators were the same I could just add them...but they are not so I need a

common denominator, in this case I chose 12. I write the denominator 12 and then

multiply the numerator by how many times the original denominator goes into it... We

now have:

I now simplify the answer and get:

So, to recap:

Returning now to the subtraction... I have:

Again I cannot simply subtract because the denominators are different-I chose 42 as the

lowest common, applied the appropriate multiplication factor to the numerators and

simplified the answer:

RICHARD FORD 11 STARLING RD TEWKESBURY GL20 7TD

richdebtomdom@googlemail.com

01684276415

2

MU123 Discovering mathematics

TMA02

M3040733

I am not sure I have this right as it seems a little counter intuitive to have a minus

fraction!

(iii)

To simplify the surd

First, I combine the two numbers together-making the product of the surds to be two

numbers:

Now factor out a common denominator (I chose 3)...

=

Now I can split up the radical â€“the reverse of how I combined them:

The...

TMA02

M3040733

TMA02

Question 1.

(a)

(i) 1560 is a composite number, that is, a number greater than 1 that is not a prime

number. Looking at the number 1560 it can be written as a product of 6 factors

(2x2x2x5x3x13). I started by dividing 1560 by 8 then continued until I had prime

numbers at the end of the tree.

It follows from fig1 that 1560= 2x2x2x5x3x13... in a simplified form I could write the

2x2x2 as 2

3

... ergo... 1560= 2

3

x5x13

I started with 8x195...but I could have used anything that ended up with whole

numbers. I checked my answer by trying 3x520 and got the same prime factors.

(ii)

RICHARD FORD 11 STARLING RD TEWKESBURY GL20 7TD

richdebtomdom@googlemail.com

01684276415

1

MU123 Discovering mathematics

TMA02

M3040733

Firstly I give myself a strong reminder that this is an addition/subtraction problem that

follows BIDMAS...

So, my first step was to add the

.

If the dominators were the same I could just add them...but they are not so I need a

common denominator, in this case I chose 12. I write the denominator 12 and then

multiply the numerator by how many times the original denominator goes into it... We

now have:

I now simplify the answer and get:

So, to recap:

Returning now to the subtraction... I have:

Again I cannot simply subtract because the denominators are different-I chose 42 as the

lowest common, applied the appropriate multiplication factor to the numerators and

simplified the answer:

RICHARD FORD 11 STARLING RD TEWKESBURY GL20 7TD

richdebtomdom@googlemail.com

01684276415

2

MU123 Discovering mathematics

TMA02

M3040733

I am not sure I have this right as it seems a little counter intuitive to have a minus

fraction!

(iii)

To simplify the surd

First, I combine the two numbers together-making the product of the surds to be two

numbers:

Now factor out a common denominator (I chose 3)...

=

Now I can split up the radical â€“the reverse of how I combined them:

The...