Math Is Fun Forum

Cammock

Member

Registered: 2009-11-10

Posts: 6

Apples and oranges

I have a repeating simplification problem that I cannot understand involving addition or subtraction of different exponents, that is, I cannot simplify the answer any further although I know that the answer can be completely simplified. Can anyone help?

I.E.:

(3518357487π + 2668642945/π) / (256191079 + 194318661/π2)

This is as far as I can simplify the problem; however, I know the answer can be completely simplified.

I.E.:

206π/15

The simplification is a 100 millionth out although this is not a problem.

Does anyone understand?

Last edited by Cammock (2009-12-01 10:25:54)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Apples and oranges

Hi;

(3518357487π + 2668642945/π) / (256191079 + 194318661/π2)

Is this what your expression looks like?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Cammock

Member

Registered: 2009-11-10

Posts: 6

Re: Apples and oranges

Yes, thanks, that is the expression, I have tried several times to simplfy such problems, however, the result is always the same, it seems to be apples and oranges, or different exponents, however, I know that the problem does completely simplify.

Here is smaller example:

(π/17) – (1/7) = (7π–17)/119

You can see how such problems build up with apples and oranges, that is, addition or subtraction from pi, or addition or subtraction of different exponents.

Does anyone understand?

Last edited by Cammock (2009-12-01 10:32:27)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Apples and oranges

Hi Cammock;

Why are you convinced that the larger problem completely simplifies?

(π/17) – (1/7) = (7π–17)/119

That is correct, but that doesn't mean the larger one simplifies.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Cammock

Member

Registered: 2009-11-10

Posts: 6

Re: Apples and oranges

Certiain variables are known before the problem which allow us to acertain the complete simplication after the problem, i.e.: after I have done the big expression, however, although I know that the answer can be a complete simplifaction of apples and oranges, it is kind of impossible to claim it as my answer.

I just found it intersting and wondered if anyone knew how to further simplify addition or subtraction of apples and oranges.

Another example of apples and oranges:

(2π/3) – (61/19) = (38π – 183)/57

In this small demonstration you can see how apples and oranges do not simplfiy, although in more complicated examples complete simplifcations can be ascertained after the problem, and given certain variables first.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Apples and oranges

Hi Cammock;

There are alternative ways to write your expression such as:

or

but I wouldn't exactly call them a simplification. What I am saying is that it doesn't look like there is a very simple, small simplification for that particular problem.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Cammock

Member

Registered: 2009-11-10

Posts: 6

Re: Apples and oranges

That is brilliant, your expressions should give me insight into how I am working out my expressions, and they could be neater, this also helps me understand that apples and oranges basically cannot be simplified. I am working on a solution that involves rounding and ascertaining the complete simplification, but it I can't really claim it.

Thank you

Graham Cammock

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Apples and oranges

Hi Cammoc;

That is brilliant, your expressions should give me insight into how I am working out my expressions,

Yes it is brilliant but it is not mine. I guess you can thank the late Jerry Keipfer of WRI.

I am working on a solution that involves rounding and ascertaining the complete simplification,

Sounds like you are talking about an approximation. That provides more leeway to getting a simpler solution.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.