Simple Algebra Division question

1. Jan 22, 2008

DeepGround

Hello,

I am not grasping how to deal with multiple divisions properly.

If I have a/1 divided by b/1 divided by c/1

How do I know if the compressed form is ac/b or a/bc?

2. Jan 22, 2008

JukkaVayrynen

It's simple: you don't.

3. Jan 22, 2008

coverband

a/bc

4. Jan 22, 2008

dodo

What poster #2 is saying, is that (a/b)/c is not equal to a/(b/c). So talking about a/b/c, without properly using parenthesis to tell which of the two cases is meant, is simply ambiguous.

5. Jan 22, 2008

mathwonk

i would have chosen a/(bc) as what was meant, but i see the problem.

6. Jan 22, 2008

DeepGround

Is it ever possible to be working on a problem and end up with a\b\c?

7. Jan 23, 2008

dodo

a/b/c are just written-down symbols that stand for an idea on your mind; if you work on a problem and get that result, in your mind you'll know what you mean (if you're not insane). Now, other people won't understand you unless you use parenthesis, or write something more graphical like $$\frac {a/b}{c}$$ or $$\frac {a}{b/c}$$.

8. Jan 23, 2008

coverband

I think what this problem is lacking is parentheses! ( )

9. Jan 23, 2008

HallsofIvy

Staff Emeritus
Is a/1= a, b/1= b, c/1= c? If so why write it that way?

What does "\" mean here?

10. Jan 23, 2008

DeepGround

To specify that all variables are already a fraction. Some math texts show a/b/1 is a/b and a/1/b is ab/1

I meant / by "\"

11. Jan 23, 2008

HallsofIvy

Staff Emeritus
a/b/1 can be interpreted as (a/b)/1= a/b or a/(b/1)= a/b so that's not a problem. a/1/b could be interpreted as (a/1)/b= a/b or a/(1/b)= ab. That's a problem.

It really doesn't matter whether a or b are "already" fractions.

12. Jan 23, 2008

DeepGround

Oh wow, I just figured out where I went wrong, now I see how it does not matter where the main division is located because the if all denominators are 1 then it doesnt matter if you multiply the 1 by the numberator or the denominator.

13. Jan 24, 2008

Diffy

I thought the general rule for an ambiguous case was to work from left to right and which would be ((a/1)/(b/1))/(c/1) = a/bc.