# Does juxtaposition always show multiplication?

1. Jan 24, 2005

### C0nfused

Hi everybody,
I just want to make something clear: does juxtaposition always show multiplication? For example 2ab(c+d)e(pi)=2*a*b*(c+d)*e*(pi) ? Generally it applies to any multiplication as long as there are no confusions,despite the number of factors?(obviously 23 is not 2*3!) ?
And one more thing: when we write
a+b
---- we mean (a+b):(c-d) ? In other worlds the fraction bar shows that
c-d
everything that is above it, after it's calculated ,is divided with the final value of the expression under it, right? Is this always called a fraction?For example when a is irrational is it called a fraction? In any case every rule applied to fractions applies to this kind of "fraction" too? They are general rules of division?(example a a*c
- = ----
b b*c )
Thanks

2. Jan 24, 2005

### arildno

Hi, C0nfused:
These are very important questions, because an unambiguous notation is absolutely essential in mathematics!

So:
Juxtaposition rule:
You are right, but there are a couple of important exceptions:
1) 23 should ALWAYS be read as "twenty-three", never "2 times 3".
In general, juxtaposed digits are to be read in the "usual" manner we learn in school.
The following is a really bad notation:
2*a*3=2a3; the right hand side is plain awful; either keep the explicit left hand side, or rewrite it as 6a.

2) Functions:
If you have a function f of x, it is common to write the value as f(x).
This does NOT mean f*x!!

Parenthesis rule:
Parentheses is one of the most important notational tools to get an unambiguous notation. Hence, study parenthesis conventions thouroughly!

Fractions:
If you haven't access to a good formatting program, you should ALWAYS enclose complicated denominators and numerators in brackets.
For example:
(a+3b+45)/(d-14e+f) is unambiguous, whereas a+3b+45/d-14e+f not only invites confusion, but is plain wrong.
The only explicit fraction in the last expression is 45/d, which is something completely different..

And yes, we may call an expression a/b a fraction even if either a or b (or both) is irrational.

Welcome to PF, by the way!

Last edited: Jan 24, 2005
3. Jan 26, 2005

### C0nfused

Thank you arildno for your really helpful and accurate answer