does division mean the same regardless how you interpret either the "bar" or "original" symbol?

Question

9-3

_____  +  1       ASIDE FROM       9-3÷(1/3) + 1???

 

(1/3)

Answer 1

"÷" is the fundamental symbol for division.

 

"/" or   "____" are the algebraic symbols for division.

 

 

All of these symbols mean the same thing.  It is easier to use the latter when using algebra to prevent the work from being too messy and makes it easier to read.  Also, algebra includes fractional terms, such as 3/4.  We use the bar symbols (diagonal or horizontal) to indicate fractions.  A fraction can be interpreted as a whole being divided into several parts.

 

An example,

 

In the fraction 3/4, 3 is part of the whole 4.  You can also read this as 3 divide by 4.

Answer 2

The first version, written the way we would have put a problem on the BLACKBOARD (in olden days) yields 9+1 = 10.

 

But the second way, writing in a single line, as you did, is not equivalent, because the order of operations would be different. It would give 9 - 9 + 1.  Parenthesizing (9-3) would be required in order to be equivalent to the first way of presenting your problem.