# Multiplication (powers) of fractions

1. Nov 17, 2004

### bimochan

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

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?

Last edited: Nov 17, 2004
2. Nov 17, 2004

### 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:

$$\frac{1}{1180591620717411303424}$$

3. Nov 17, 2004

### bimochan

:grumpy: 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)

4. Nov 17, 2004

### 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.

5. Nov 17, 2004

### bimochan

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

6. Nov 17, 2004

### 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?

7. Nov 17, 2004

### Gokul43201

Staff Emeritus
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.

8. Nov 18, 2004

### chronon

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.

9. Nov 18, 2004

### 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!

10. Nov 18, 2004

### nnnnnnnn

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.

11. Nov 18, 2004

### Gokul43201

Staff Emeritus
You should embrace fractions !

12. Nov 18, 2004

### 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.

13. Nov 18, 2004

### bimochan

I heard that Vector not only simplified writing forumla 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?

14. Nov 19, 2004

### Zurtex

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.

15. Nov 20, 2004

### 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?)? :tongue2:

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

Last edited: Nov 20, 2004
16. Nov 21, 2004

### Integral

Staff Emeritus
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?

17. Nov 21, 2004

### 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?

18. Nov 22, 2004

### Zurtex

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.

19. Nov 22, 2004

### 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??

Last edited: Nov 22, 2004
20. Nov 28, 2004

### 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