Viral Maths Problems

Each year we are treated to another viral math problem. Can you solve (insert bad equation here)? The answer is rarely given, and the equation is poorly structured. So, lets unpack one such problem and explain why I believe they are so badly formed.

Example

The last one I saw online was the challenge:

Can you solve?

8 ÷ 2(2+2)

My first observation is the unusual use of ÷ (mathematicians prefer '/') and bad bracketing. Let us clean up the expression to clear up some ambiguity:

8 ÷ 2 × (2+2)

This makes it much easier to the next step of applying BODMAS.

The order of operations here are:

1. Solve the Brackets, then
2. From left to right apply division's and multiplications
3. From left to right apply addition's and subtraction's

Here: division and multiplication have equal precedence as do addition and subtraction.

Applying these operations gives:

8 ÷ 2(2+2) = 8 ÷ 2 × (2 + 2)
                 =  8 ÷ 2 × 4
                 =  4 × 4

                 =  16

So, why is this a badly formed question? A goal of mathematics is to accurately and unambiguously provide solutions to problems. The real challenge is to answer the right problem. If the purpose of the problem was to provide a correct answer and not lead to argument on interpretation then the question could have been asked in a number of different ways:

Question What is (8 ÷ 2) × (2 + 2) ?

Answer (8 ÷ 2) × (2 + 2) = (4) × (4) = 4 × 4 = 16

Or, you could ask:

Question What is 8 ÷ (2 × (2 + 2)) ?

Answer 

8 ÷ (2 × (2 + 2)) = 8 ÷ (2 × 4) = 8 ÷ 8 = 1

Another variant of this question could be:

Question Explain the order of operations for 8 ÷ 2 × (2 + 2)  ?

Answer

Apply BODMAS and evaluate from left to right:

1. First evaluate the terms inside the brackets: 8 ÷ 2 × (2 + 2) = 8 ÷ 2 × 4
2. Then evaluation from left to right: 8 ÷ 2 × 4 = 4 × 4
3. Giving the final operation: 4 × 4 = 16

So, the problem could be much clearer about it's intent.

What was the point of the original challenge?

I feel that the problem as stated in so many online forums is more click-bait to generate an argument than as a pedagogical exercise.