Advanced Maths Help please

[It'sNotWorthComplaining!]

my 15 yr old son has some Math homework for the holdidays.
He's stuck on these, if any one is into advanced maths and could help it would be appreciated.

What he needs is the process of simplifying these . He not sure of how to go about it. if he knows the method then it'll make it easier.
Any one give an eg how to work it out please
https://www.aulro.com/afvb/images/imported/2010/04/1342.jpg

[p38arover]

.
2x + 3x
__ __
3 2



In this example, it's a matter of making the divisors the same so that the fractions can be added. The niumber which can be divided by 3 and 2 is 6, so make that the new divisor:

2x
__
3

=
4x
__
6

and
3x
__
2

=
9x
__
6

now you can add them:

(4x + 9x)
________
6
=
13x
__
6


Now try that with the remainder of the examples:


.


eg b.

4 3
_____ + ______
2
x +1 (x = 1 )


eg c .
2
5a 10a
_____ _____
2
12b Divided by 6b

[mike 90 RR]

Plenty of "Fraction calculators" + "Fractions explained" on the Net

Example ....

Dividing Fractions (http://www.helpwithfractions.com/dividing-fractions.html)

I have a fairly good Fractions calculator for explaining & checking the answers ... You want me to Email it to you??
It will show step by step how it achieved the final answer

Mike
:)

[josh aka sean]

Easiest way to get the denominator (bottom number) the same is to multiply them together ie if you have 2 and 3 as the bottom numbers multiply them to gether to get 6. THen all you need to do is multiply the top number by the opposite bottom number ie the one with a two for the bottom number number you will multiply by the 3 and the one with the 3 as the denominator you will multiply by the 2. Once you have done this you can simply add the two top numbers and just have the single bottom number.

hopefully that makes some sense

[p38arover]

Would like to help but not entirley sure what is being asked of him in the questions

Umm, simplify the equations.... :angel:

[Dmmos]

Seems relevant here - this site is amazing;

Wolfram|Alpha (http://www.wolframalpha.com/)

As an example, I've attached the link for the answer to the first question;

simplify (2x/3) + (3x/2) - Wolfram|Alpha (http://www.wolframalpha.com/input/?i=simplify+%282x%2F3%29+%2B+%283x%2F2%29)

It doesn't describe the method, although having the answer helps...

[josh aka sean]

Umm, simplify the equations.... :angel:
Yeah missed the original post and was reading a reply by accident :angel:

[It'sNotWorthComplaining!]

Hey it's Kris here.

So would the answer for 2a be:
(8xy)^3
--------
2xy

Just need confirmation I'm going in the right track.

[Dmmos]

I got 2x(y^2)

[It'sNotWorthComplaining!]

Would you be able to show this step-by-step so I can see where I went wrong? Greatly appreciated.

[josh aka sean]

Would you be able to show this step-by-step so I can see where I went wrong? Greatly appreciated.

In a multiplication you can cancel diagonally between the fractions

So the x^2 and the x cancel leaving just x on the top and just 1 on the bottom

The 2y cancels with the 4y^3 leaving 2y^2 on the top and just 1 on the bottom

then when you multiply the top by the top you get 2x(y^2) and simply 1 on the bottom

as it is just 1 you don't need to write it

x^2 4y^3
2y * x

x 4y^3
2y * 1

x 2y^2
1 * 1

2x(y^2)
1

2x(y^2)

don't need the brackets but there to make it clear only the y is squared

[Ferret]

Would you be able to show this step-by-step so I can see where I went wrong? Greatly appreciated.

There is a reasonably good web site for school maths here Dr Maths (http://mathforum.org/library/drmath/drmath.elem.html)

Look at the "Fraction" section, it will take you through a few examples and might be of some help to your son also.

[It'sNotWorthComplaining!]

In a multiplication you can cancel diagonally between the fractions

So the x^2 and the x cancel leaving just x on the top and just 1 on the bottom

The 2y cancels with the 4y^3 leaving 2y^2 on the top and just 1 on the bottom

then when you multiply the top by the top you get 2x(y^2) and simply 1 on the bottom

as it is just 1 you don't need to write it

x^2 4y^3
2y * x

x 4y^3
2y * 1

x 2y^2
1 * 1

2x(y^2)
1

2x(y^2)

don't need the brackets but there to make it clear only the y is squared

The whole cancelling out has really helped. Thankyou very much.

[incisor]

i am impressed as hell that you started a thread where you weren't actually complaining about something :eek:

but i have splinters in my fingers now.....:angel:

[mike 90 RR]

i am impressed :eek:


... It's OK man ... things will return to normal when he gets the results from the teacher ... :p


Mike
:D

[stevo68]

Bloody hell...back in my day...I had to work this kind of thing out myself. What aren't they teaching kids at school these days :confused:. At 30 when I went back to Uni to do a Commerce Degree.....I couldn't remember algebra as hadn't used it since I left school....3x + 2y= WTF :). As part of my degree I had to do Statistics and Business Mathematics... so I had to go and spend a semester doing a refresher course, before I could do them.

Regards

Stevo

[slug_burner]

The whole cancelling out has really helped. Thankyou very much.

The cancelling out business is just division e.g., 2/2 =1 as does x/x = 1

When you had the problems under the first group of exercises they were looking for the lowest common denominator and you cannot start your cancelling out (division) untill you have performed the addition.

I suspect that this is year 8 or 9 level maths

[awabbit6]

Now that you have the canceling sorted, lets move onto factorization ...

Many of the problems (particularly in Q2) require factorization at some stage. Here is a solution for Q1l as an example.

https://www.aulro.com/afvb/images/imported/2010/04/1248.jpg

In the second line, the denominator of the second fraction has been factorized to identify commonality with the denominator of the first fraction. The first fraction is then squared (top and bottom) to give the common denominator.

[EchiDna]

I remember being asked by a friend's daughter to help with solving a series of "single unknown" algebraic equations... took me about 10 minutes to work it out as I kept trying to figure out the step by step process because I'm more used to working with 2+ unknowns!

[It'sNotWorthComplaining!]

The cancelling out business is just division e.g., 2/2 =1 as does x/x = 1

When you had the problems under the first group of exercises they were looking for the lowest common denominator and you cannot start your cancelling out (division) untill you have performed the addition.

I suspect that this is year 8 or 9 level maths
Actually it's VCE level 1 general math. my son is has just started year 10 so this is 1 yr level ahead of his time. Often teachers don't explain things thoroughly for students to get a grip. Hence we ask our learned friends on AULRO for help

[Blknight.aus]

do you mean that thats year 11 math or thats year 10 math now...?

either way, no, you're joking... its year 8 at best surely...

[Forest]

its been a very long time

how do we get from x squared + 8x + 16 to (x + 4)(x + 4)

????

[It'sNotWorthComplaining!]

do you mean that thats year 11 math or thats year 10 math now...?

either way, no, you're joking... its year 8 at best surely...
Vic without calculator not QLD with calculator :wasntme:

[Blknight.aus]

Its easier to do it in reverse to how you asked it... when youve got that down reversing it isnt too hard. (providing that its done with simple squares and multiples)

(X+4)^2
becomes
(x+4)(x+4) (simple expansion of a square)

then you just multiply all of the contents of the first bracket with all of the contents of the second one part at a time sooo.. doing the X first gives

X*X + X*4

doing the 4 gives

4*X + 4*4

when massage those down to the easiest way of writing it and put it on one line you get

x^2 +4X +4X +16

which then becomes
x^2 +8x +16..

for INWC, when I was doing math at school that was WA year 8 math.

[digger]

Does this help?
YouTube- Ma & Pa Kettle Math

I watched it and it seems correct!?:)

digger

[It'sNotWorthComplaining!]

Does this help?
YouTube- Ma & Pa Kettle Math (http://www.youtube.com/watch?v=Bfq5kju627c)

I watched it and it seems correct!?:)

digger
NOW THAT WAS EVEN EASIER- THANKS;)

[WhiteD3]

Sign him up to Maths Online. It's free, very good and he can pick to the topic to do.

Maths Online - Free Maths Tuition For All Australian High School Students (http://www.mathsonline.com.au/)

[DiscoStew]

Now that you have the canceling sorted, lets move onto factorization ...

Many of the problems (particularly in Q2) require factorization at some stage. Here is a solution for Q1l as an example.

https://www.aulro.com/afvb/images/imported/2010/04/1248.jpg

In the second line, the denominator of the second fraction has been factorized to identify commonality with the denominator of the first fraction. The first fraction is then squared (top and bottom) to give the common denominator.

Sorry to be pedantic but there is an error going from line 2 to 3 in the left hand fraction. You do not simply square both of the top and the bottom, you have to multiply them by the same value. So if you multiply the bottom by (x+4) to get (x+4)^2 then you multiply the top to get 2(x+4).

Not that this detracts from your factorisation description but I would hate for Kris to think you can square both top and bottom.

[DiscoStew]

do you mean that thats year 11 math or thats year 10 math now...?

either way, no, you're joking... its year 8 at best surely...


Bloody hell...back in my day...I had to work this kind of thing out myself. What aren't they teaching kids at school these days :confused:. At 30 when I went back to Uni to do a Commerce Degree.....I couldn't remember algebra as hadn't used it since I left school....3x + 2y= WTF :). As part of my degree I had to do Statistics and Business Mathematics... so I had to go and spend a semester doing a refresher course, before I could do them.

Regards

Stevo

This story goes back nearly 20 years now but from what I can see nothing has changed, the trend has probably continued.

My father started work as a high school maths teacher and then later become a university lecturer of algebra and geometry. Starting sometime in the late 80's he and a colleague put on remedial classes, in their own time, just to bring their students to the level that they should have left school with. It was the only way they could get a decent number of them to pass. We were not talking about 1 or 2 students that needed tutoring, we are talking about putting on scheduled classes. Don't blame the students, they can only learn what they are taught.

You don't find many academics who would do that but then he considered himself to be a teacher not an academic. He also gave out his home phone number at the start of each semester. He is beautiful but weird.