# On Your Mark, Get Set, Multiply — Quanta Magazine

Did you get caught up in the latest viral math problem, 8÷2(2+2)?

The problem here is simply how we interpret the division symbol. Does ÷ mean divide by the one number right after it or by everything after it? This isn’t much of a concern for most mathematicians, as they don’t use this symbol very often. Ask them to solve this problem and they’ll probably just make the whole thing into a multiplication problem: Once you choose to write it as either $8 \times \frac{1}{2} \times (2 + 2)$ or $8 \times \frac{1}{2(2+2)}$,

the ambiguity is gone and the answer is clear. As a multiplication question, this isn’t particularly interesting.

But one multiplication question mathematicians do find interesting may surprise you: What is the best way to multiply?

And what is the best way to multiply? The answer may surprise you! Find out by reading my latest column for Quanta Magazine, freely available here.

### 1 Comment #### Dashiell · October 23, 2019 at 5:08 pm

I’m late and a bit confused, the answer should be 16 as it is in the first equation 8x(1/2)x(2+2)=8x(1/2)x4=4×4=16 but in the second equation you wrote the answer is 1: 8x(1/(1/2)x(2+2))=8x(1/(1/2)x4)=8x(1/8)=8/8=1. It would seem to me that the ambiguity is not gone and the answer is not clear.

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