Technically, I do not think that it will matter whether you do it left to right than right to left. Here's an example: 5*9*4.

5*9 is 45, 45*4 is 180.

9*4 is 36, 36*5 is 180.

I can't think of a situation when left to right may be different than right to left, but there could be one.

Tulle Roubie & SP

**SP - while what you used is a good example as to how it doesn't always have to be left-to-right, it is a bit invalid as it only included multiplication.

Technically, you are both right and wrong. Basing on the subject, this seems to be late elementary/early middle school math. (this is based off my own learning, no offense intended). It may not seem like it now, but when you reach math containing more numbers, it's super important.

For example, if we take 2+8/4x2 (2 plus 8 divided by 4 times 2) 

1. 2 + 8 / 4 x 2 | we start left-to-right multiplication/division, so solve 8/4
2. 2 + 2 x 2 | plug in our answer, (2) continue down the line with 2x2
3. 2 + 4  | Plug in the answer again, (4) go back to the beginning and add 2
4. 6 | finish off with the correct answer, 6.

or else if you don't follow PEMDAS...

1. 2 + 8 / 4 x 2 | starting on the far right, multiply 4x2
2. 2 + 8 / 6 | plug in the answer, (6) then use it to divide 8
3. 2 + 1.334 | you are left with an infinite number, (1.333 repeated or 1 1/3) add 2
4. 3.334 | end up with this mess of a number, 3.333 repeated or 3 1/3

So yes, multiplication and division can be swapped back and forth between each other, as defined by PEMDAS. However, this does not mean you can go from right to left; what it actually means is that when read correctly, if division comes before multiplication, you may flip the M and D in PEMDAS. A Good way to remember is to imagine PEMDAS as though it was written like PE(MD)(AS) as it separates the 3 main parts out.

Sorry this is long, but its important to explain it properly.

Wishing you goodluck! - AP~L