8 ÷ 2 (2 + 2) ≠ 8 ÷ 2 ×(2 + 2)

Destroying the Internet Meme with Math

You’ve probably seen this image on Facebook, X or Instagram.

The answer is 1, and now I’m going to use math to prove it.

Most everyone remembers their basic math such as 1 + 1, 2 x 2, 3 ÷ 3. Basic math uses infix operators to define the operations performed on numbers. In basic math, infix operators are not optional. Because of this, 8 ÷ 2 (2 + 2) is not a valid basic math expression. This is because the notation used in the term 2(2 + 2) is missing the multiplication operator, instead it uses an implied multiplication notation that is not valid in basic math but is valid in Algebra.

In Algebra we use implied multiplication to express magnitude of a variable. Since the meme is tricking the reader by asking the user to solve an Algebra problem, people who understand Algebra will follow the Algebraic order of operations and receive an answer of 1. The troll who posted the meme will then jump on this person claiming the answer is 16. To rationalize this, they will point to 5th grade Basic Math order of operations, which has no concept of implicit multiplication. But of course, they didn’t post a Basic Math problem, they posted an Algebra problem.

Let’s use Algebra to prove that implicit multiplication and infix multiplication are different. If they are…