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I came to this questions because someone posted on Twitter: How much is 8÷2(2+2)

There seems to be some controversy about the order in which the calculations are to be performed. What is the official answer? Is there such a thing as the official answer?

John Stoneman
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    The first step is alway to not use the symbol $÷$ to avoid precisely such ambiguity. – Servaes Aug 02 '19 at 19:17
  • Welcome to MSE! About your question: It is very similar to this question, which has been asked many times on MSE. – Maximilian Janisch Aug 02 '19 at 19:18
  • If this were written as $\frac{8}{2}\times (2+2)$ or as $\frac{8}{2\times (2+2)}$ there would be no ambiguity. As you grow and learn about when certain notations are ambiguous, you learn to avoid them, such as using $\sin^{-1}$ to represent the functional inverse of sine. – JMoravitz Aug 02 '19 at 19:25
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    As an aside, do be more careful with what tags you use. "Multiplicative order" has nothing to do with the question you asked and is a group theory concept, something studied during an undergraduate math major. This is a question on basic arithmetic and order of operations, totally unrelated. – JMoravitz Aug 02 '19 at 19:27
  • In my experience at Math Help Forum and Math Help Boards, people who asked this kind of question were very often trolls. Servaes has the right answer. Expressions like these should never be written, and questions like these should not be asked. – Adrian Keister Aug 02 '19 at 19:27
  • @Servaes Why do you think that the choice of symbol matters? – Bill Dubuque Aug 02 '19 at 19:29
  • @JMoravitz, I tried the tag order-of-operations, but that didn't exist. – John Stoneman Aug 02 '19 at 19:56
  • Order-of-operations is a notation thing, so I added the "notation" tag. – Tanner Swett Aug 02 '19 at 21:22
  • @Servaes, which symbol should I use? Or should I not divide at all? – John Stoneman Aug 02 '19 at 21:55
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    Using a fraction bar instead would be a good idea: you can write either $\frac82 (2+2)$ or $\frac{8}{2(2+2)}$. – Tanner Swett Aug 02 '19 at 22:04

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