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Advanced Math/Parentheses in multiplication - theory based

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Expert: - 7/22/2009


Question
I'm asking a theory oriented question as opposed to an actual math problem.

What is the basis for allowing 5x to mean 5 times x?

Is it some sort of shorthand for 5(x) or is it that any two numbers that you want to multiply together can be put next to each other such as 5,6 and the parenthesis serves as a separation device for the multiplcation as opposed to the operator itself?

Thanks for your time.

Answer
Yes, it is shorhand that is accepted to everyone who knows any math.
Allowing 5x to be 5*x avoids using the multiplication sign.
To get even more on this subject, read the rest of this note.

As a person gets higher in math, there would be far too many places that would need a multiplication sign.

Another useful symbol is ².  For example, 3² = 3*3 = 9.

Using both of these principals, 2*2*3*3*5*5*7*11*11 could be rewritten as 2·2·3·3·5·5·7·11·11 as 2²3²5²7*11².  It is also 4*9*25*7*121, which can be multiplied out to 847*900 = 762,300.

Note that when a*a occurs, the '*' is written, otherwise it looks like there is a variable referred to as aa.  It is usually written a². When they have a*b, however, it is usually written ab.

Now where 5 is being multiplied by 6, it is usually written 5*6 or by hand could be 5·6.  If it were 56, it would be read as
"fifty six".

However, if 5 is being multiplied by A, it is written 5A.
When that is read, it is read as "5 times A".

When written by hand, sometimes you see 5*6, sometimes 5x6, sometimes 5·6, and sometimes 5(6).  All of them are 30.

Also, when writing by hand it is easier to do 5(6), but on the computer it is easier to d 5*6.  This is because by hand there are only two strokes of the hand to make '(' and '), whereas there are three strokes of the hand to make '*'.  On the computer, however, there is one key pressed to do a '*' and two keys pressed to do '(' and ')'.  What is better yet is just to write '·' by hand, for that is just a dot, which is realy fast.

Sometimes variables, as mentioned above with aa, can be written as a string of characters.  For example, we might call a variable 'rd' and say it is 100.  There might be another variable called 'nk' with the value 9.  Note that when they are multiplied together,
you might see (rd)(nk), rd(nk), (rd)nk or rd*nk.  In any form, the value is 900.  It is all a matter of choice.

The main place to drop them is when there are a string of varialbles,
like 52*a*b*c, which is written as 52abc in a document in which it is known that a, b, and c are all different variables.

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