[SeaHawkFan]

Did you ignore this part: “parentheses outrank division”?

Go throught the purplemath example and use the same principles and you will see the correct answer is 2.

[grateful]

No, I didn't ignore it. I did the parentheses first.

48÷2(9+3)
48÷2(12) = (Parentheses equation solved.)

Now, using order of operations, since there is both division and multiplication and both are of equal precedence, we go left to right.

24(12) = 24*12 = 288

You are arguing there are brackets in the original equation, which there are not.

[CharacterCounts]

I went to the TI site and got this:

Does implied multiplication and explicit multiplication have the same precedence on TI graphing calculators?

Implied multiplication has a higher priority than explicit multiplication to allow users to enter expressions, in the same manner as they would be written. For example, the TI-80, TI-81, TI-82, and TI-85 evaluate 1/2X as 1/(2*X), while other products may evaluate the same expression as 1/2*X from left to right. Without this feature, it would be necessary to group 2X in parentheses, something that is typically not done when writing the expression on paper.

This order of precedence was changed for the TI-83 family, TI-84 Plus family, TI-89 family, TI-92 Plus, Voyage™ 200 and the TI-Nspire™ Handheld in TI-84 Plus Mode. Implied and explicit multiplication is given the same priority.

[spunkets]

"Did you ignore this part: “parentheses outrank division”?"

Parenthesis have no effect external to their boundary. In the woman's example "2(2)" all hte parenthesis do after the contents have been reduced to "2" is to distinguish 2(2) from 22. The example reduces to: 16*(1/2)*2+1=17. That's not 5 as the both of you contend, but you may continue to do so with your own special arbitrary, adhoc rules that are inconsistent with the standard rules of arithmetic, such as multiplicative commutivity and the concept of multiplicative inverse.