Math Is Fun Forum

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

question...

This may seem like a wierd question, but here I go : If I have  8/3 . 8/5 = 64/15 why can't I reduce my two 8's at the beginning ? I can reduce my fractions diagonaly or I can reduce the number above the fraction sign and the other one below it. But why can't I do it in a straight line ? Would it be to hard to explain and I have to take it like it is ? Thank you (I like to understand how things works ^^)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: question...

Hi Al-Allo;

Reduce the eights by what?

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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.

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: question...

By 8 on the two sides, isn't it possible ?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: question...

Hi;

You mean do this?

---

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.

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: question...

Yes, here's an example where I could reduce  : 4/2 . 1/8  (The 4 and the 8 divided by 4) but in the previous one, it wouldn't be possible. WHy ?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: question...

One way of looking at it is

You end up with a 4 on the top and on the bottom. You can cancel them.

When you do the other one.

There is nothing to cancel.

---

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.

therussequilibrium

Member

Registered: 2012-12-21

Posts: 36

Re: question...

The way I look at it is like this, much like when you are working in algebra, if you do something to one side of an equation you have to do it to the other side of an equation for it to still be equal.

Well, like that, if we are working only on one side of an equation, if we do something to that side of the equation we have to do the opposite or inverse of that action for that side of the equation to still hold true. Simple example: if our equation was 5+5=10

If we decided to subtract 3 from the first side we'd get 5+5-3=10, well that's not true , but as long as we did the opposite of that our equation would still be true. 5+5-3+3=10, now it's true again.

Same goes for with the fractions, in essence when looking at

All we are doing is dividing that entire side of the equation, and at the same time multiplying the entire side of the equation by 4. Like this:

and at the same time

With what you are trying to do, you are dividing the same side of the equation by 8, twice. Going back to my simple example, 5+5=10,     your action would look something like this, 5+5-3-3=10. And that just can't work, if you do something to a side, you have to do the opposite to keep the equation equal.

So, what you did would look like this:

And that equation is definitely not the same as

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: question...

hi Al-Allo

This goes right back to the idea of cancelling (reducing ?) and why it works.

My diagram shows a rectangle split into 12 parts with 3 shaded.

Then I've split the same rectangle into just 4 parts with one shaded.

so

The twelve parts have been collected together into groups of 3 to show that 3 parts in 12 is the same as 1 part in 4

All cancelling relies on this.

If there's a factor of the top that is also a factor of the bottom, you may cancel it.  But cancelling a factor of the top with another factor of the top would change the value of the fractions completely.

this is ok:

because the eights are one on the top and one on the bottom.

http://www.mathsisfun.com/equivalent_fractions.html

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: question...

Thank you, I finaly understood ! It makes sense lol  (Im wondering how come I didn't know that....)