>>16676363
It's neither the old way nor common core. It's just a different order of operations. Most of the used order of operations put multiplication and division in the same precedence, but some of them will put multiplication before division. It's further confused because they don't explicitly specify the multiplication sign between the 5 and the parenthesis. Regardless of order of operations, you get 20 / 5 * (2 * 2) = 20 / 5 * 4. If multiplication has precedence, the 5 * 4 is done first, giving 20 / 20 =1. Otherwise it's 20 / 5 * 4 = 4 * 4 = 16.
The woman in the picture is misrepresenting it, because the "old way" uses PEMDAS in a way that groups MD and AS as the same precedence, and so would also give 16.
>>16676374
>Order of operations gives us 20/20
There are many rules for order of operations that vary based on fields of mathematics and programming, particularly in fields where there are multiple kinds of multiplication (like linear algebra). In common arithmetic (and up through algebra and calculus, consequently), multiplication and division are at the same precedence, so it should be 16.
The important thing to remember is that Order of Operations is not a rule of math. It's a rule for interpreting a written equation in a way that groups things that are commonly intended to be grouped to reduce the number of parentheses required to be explicit. Without order of operations or with one that is badly-constructed, you have to use a lot of grouping symbols to express the correct intent.
Sage for off-topic post.
Common core doesn't change order of operations, though. It's a bait image.