This question is a little hard for some people but look at what I think. The reason there is debate about the answer being 1 or 16 has to do with exactly what “beginning with the brackets/parentheses” means in the case of 8÷2(2+2).

If it means to take 2(2+2) and solve it entirely before moving to the 8÷ part of the equation, then we get to 8 ÷ 8 on our way to 1.

If it means to translate 2(2+2) into 2 x 4, then we end up with 8 ÷ 2 x 4, and order of operations tells us division and multiplication are equal, so work left to right. So we end up with 4 x 4 on our way to 16.

And here is where the first interesting part of the question comes: order of operations do not actively tell us what mathematical grammar we are required to use when writing a problem.

People figure they can just write it any old way, using the symbols they were taught in elementary school, and the order of operations will prevail.

What we see, then, is that mathematical grammar in the creation of the problem matters. And just because we throw a bunch of numbers and symbols together, doesn’t mean it is grammatically correct.

To know which is the actual right way to write the problem, we’d have to know the underlying meaning, the context of the numbers and symbols. Order of operations for these mathematical symbols only suggests how to evaluate these kinds of mathematical equations in the absence of context.

Try a word problem.

There are 8 coffees to be distributed to some drive through customers. The customers are arranged in two cars. In each car there are two customers in the front seat, and two customers in the back seat. If all 8 coffees are distributed equally, how many coffees will each customer get?

8 / 2(2+2) = 1

Or this word problem.

A coffee shop has to-go boxes to put coffees into, and each box holds exactly 4 coffees. Every morning the office next door orders 8 boxes of coffees. This morning, the office manager said to cut their order in half. How many individual coffees did they order today?

(8 ÷ 2)4 = 16 or better yet (8/2)4 = 16

In the case where a complex algebraic equation is being broken down to its simplest components, it is possible for something like 8÷2(2+2) to occur if the original equation includes the division symbol, but truly, division written as ÷ is always more confusing than when it is written as a fraction. For this reason, we don’t see the ÷ sign used in serious math.

8÷2(2+2) makes order of operations confusing. Replacing the division symbol with a division slash, thus: 8 / 2(2+2) makes it patently clear that the equation in the denominator must be simplified first, leaving us with 8/8 unambiguously equaling 1.

My takeaway is that the “division sign” ÷ we are taught in elementary school is bad math, and should simply disappear. It introduces grammatical inconsistencies into math problems. Using ÷ and x for division and multiplication are just a childish simplifications.

Teach kids 8/2 can be read “eight divided by two” and go ahead and teach division. Teach kids 2(2) can be read “two times two” or “two multiplied two times.” Once we remove ÷ and x from math, we automatically remove most of the order of operations confusions.

Try writing a confusing math equation without using ÷ or x. I don’t think you can.

TL;DR

The problem is not order of operations. The problem is the way math is written using ÷ for division and x for multiplication. These symbols are childish mathematical symbols used for grade school education. Serious math equations will never run into this confusion because division is written 8 / 2(2+2) and everyone will know that before dividing the denominator into 8, the denominator must be fully simplified. 8 / 2(2+2) = 8/2(4) = 8/8 = 1.

If the equation is meant to equal 16, it would then be written (8/2)(2+2) keeping out all elementary school division and multiplication symbols, retaining the exact numbers in the same order, and making it easy to know how to simplify the problem. The steps for that one would be (8/2)(2+2) = (4)(4) = 16.