Multiplication (powers) of fractions

[bimochan]

I am having difficulty putting this question...i can't explain exactly what i mean

Can anyone tell me in detail (history, number theory and all) about multiplication of fractions?

I know that 5^2 means taking 5, 5 times and adding them.
But what does 0.5^70 mean?

I need indepth answer! Any link would be appreciated as well.

thanking u in advance :-)

 

[Zurtex]

It's really quite simple:

\frac{a}{b} \frac{c}{d} = \frac{ac}{bd}

Therefore:

\left( \frac{x}{y} \right)^z = \frac{x^z}{y^z}

So taking your problem of 0.5^70, is the same as:

\left(\frac{1}{2}\right)^{70} = \frac{1^{70}}{2^{70}}

Which is:

\frac{1}{1180591620717411303424}

 

[bimochan]

Zurtex, 5^10 = 5+5+5+5+5+5+5+5+5+5
Similarly, what is 0.5^10? I want an answer in terms of addition (or subtraction maybe)

 

[matt grime]

Well, why? And why can't you interpret what Zurtex wrote that way on top and bottom of the fraction if you *really* must. Incidentally, what is 1^10 in your version of thinking, since your idea of 5^10 is a factor of N off where N is a *really* big number.

 

[bimochan]

grime, zurtex, I get your point. But isn't there a deeper insight into division, multiplication,...? Maybe a brief history lesson will help.

 

[bimochan]

oooppsss,
5^10= (((((((((5*5)*5)*5)...)
5*5=5+5+5+5+5

likewise what is 0.5^10?
I don't want it in terms of division! Is it possible to express it in terms of addition only?

 

[Gokul43201]

No, it's not (and it's not necessary), because the number that you multiply with is the number of times you add. But this "number of times" is something that you should be able to count, so it must be a whole number.

 

[chronon]

likewise what is 0.5^10?
I don't want it in terms of division! Is it possible to express it in terms of addition only?

0.5*X= The number which when multiplied by 2 gives X = The number which when added to itself gives X

Therefore

0.5^10=The number which when added to itself gives the number which when added to itself gives the number which when added to itself gives the number which when added to itself gives the number which when added to itself gives the number which when added to itself gives the number which when added to itself gives the number which when added to itself gives the number which when added to itself gives the number which when added to itself gives one.

Well you asked for it.

 

[bimochan]

Gokul, if this "number of times" isn't a whole number as is the case here what should be done?

chronon, i'll reply to u later!

 

[nnnnnnnn]

Zurtex, 5^10 = 5+5+5+5+5+5+5+5+5+5
Similarly, what is 0.5^10? I want an answer in terms of addition (or subtraction maybe)

umm... isn't that 5*10?

If you come up with a method that works to get 5^10 by adding then use that method on the numerator and the denominator of the fraction, then put the fraction back together. (3/4)^2 = (3/4) three forths times... it doesn't make much sense without multiplying or splitting it up.

 

[Gokul43201]

Gokul, if this "number of times" isn't a whole number as is the case here what should be done?

You should embrace fractions !

 

[Zurtex]

The problem is I don't think there is much of an in-depth answer, it's just a simple extension of fraction multiplication which is very elementary.

 

[bimochan]

I heard that Vector not only simplified writing formula but also led to other stuffs that wasn't obvious before. Was it the case with multiplication too? It came to rescue addition and led to other things??

Is there any proof in mathematics which shows that (x) can be expressed in terms of (+) for positive integers only and not for fractions?

 

[Zurtex]

I heard that Vector not only simplified writing formula but also led to other stuffs that wasn't obvious before. Was it the case with multiplication too? It came to rescue addition and led to other things??

Is there any proof in mathematics which shows that (x) can be expressed in terms of (+) for positive integers only and not for fractions?

It's a conceptual jump really. Take for example:

3a = a + a + a

For any real value of a, similarly:

a^3 = a*a*a

However, how would you deinfe 2.5*a? Well it's fairly simply:

2.5*a = (2 + 0.5)a = 2a + 0.5a = a + a + 0.5*a

Similarly:

a^{2.5} = a^{(2 + 0.5)} = a^2 * a^{0.5} = a*a*a^{0.5}

But how does that help us at all? Although the 1st two where a nice way to think about what multiplication and raising to a certain power means, the latter 2 just confuse the situation and you need to just stick to rules for multiplication and raising to powers.

 

[bimochan]

well, ok This much will be enough for now!

zurtex, can you tell me something about inventing new operators (and about fitting it into the already vast mathematics. or will it blend in magically?)?

What branches of mathematics should I study for these sort of stuffs?

 

[Integral]

bimochan,

It would be a very good idea to get a handle on the existing ones before you start trying dream up new ones.

How would you know if they were new or different?

 

[bimochan]

I agree with you Integral. But I don't care if it's new or old. I just want to enjoy mathematics . What I wanted to understand was the development of completely new ideas in mathematics?

 

[Zurtex]

I agree with you Integral. But I don't care if it's new or old. I just want to enjoy mathematics . What I wanted to understand was the development of completely new ideas in mathematics?

I've not heard of the development of a completely new area of mathematics in a very very long times. Even quite revolutionary area of mathematics like probability or calculus that have only really come to light in the last few hundred years are still very much based on the mathematics that was already existing. A lot of mathematics is just building on old mathematics so you need to have good foundation of a lot of mathematics before you can start to understand new stuff.

I suggest you stick around on this forum, help people when you can and try and soak in as much maths that is beyond the level you are being taught. I've certainly built up my maths way beyond my peers by doing this.

 

[bimochan]

Thanks for the tip zurtex. I think i'll follow it

Hey I think you've heard this one before but here it is anyway...

Descartes went to a bar. The bartender asked him if he wanted some beer to which Rene answered,
Rene - I don't think.. (and he disappeared)

P.S. I love this cute devil! And why can't I create a signature? Do I need to reach a minimum posting count for that??

 

[geraldmcgarvey]

Think in terms of multiplication.

"Zurtex, 5^10 = 5+5+5+5+5+5+5+5+5+5
Similarly, what is 0.5^10? I want an answer in terms of addition (or subtraction maybe)"

5^10 is not 5+5+5+5+5+5+5+5+5+5 (which is 5*10), 5^10 is 5*5*5*5*5*5*5*5*5*5
similarly, .5 is .5*.5*.5*.5*.5*.5*.5*.5*.5*.5
which is the same as
1 / 2^10 or 1 / 2*2*2*2*2*2*2*2*2*2