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A simple question but I know two conflicting rules on this:

  • Multiplication is stronger that dividing: $8:4\times2=8:8=1$

  • Dividing is the same as multiplication with the inverse: $8:4\times2=8\times4^{-1}\times2=4$

Which rule should rule?

Sorry if it is a duplicate.

drhab
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  • This is essentially the same question as the one that flooded the internet some couple of years ago. I'm sure that we can find at least one copy that wasn't deleted from the site. – Asaf Karagila Dec 13 '14 at 08:59
  • Here's one which itself is a duplicate. – Asaf Karagila Dec 13 '14 at 09:01
  • @AsafKaragila This is not about parentheses though. – peterwhy Dec 13 '14 at 09:03
  • @AsafKaragila Thanks. In my teaching to students on what you can call high-schools uptil now I always avoided this. This to spare myself embarassment. I simply didn't know. – drhab Dec 13 '14 at 09:03
  • @peterwhy: All those threads are essentially about precedence of operations, and there are several acceptable interpretation. And since mathematicians don't really deal with these sort of issues, mathematicians usually don't care very much about that. – Asaf Karagila Dec 13 '14 at 09:09

1 Answers1

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Your first example is wrong. Multiplication has the same precedence as division. So whatever comes first, is evaluated¹.

In you example you have $$8 / 4 \times 2 = (8 / 4) \times 2 = 2 \times 2 = 4$$

Multiplication and division have higher precedence than, for example, addition or subtraction. Note that addition and subtraction have again the same precedence.

1: Note that this does not account for parentheses, but they have higher precedence than arithmetic operators, so by the time you have to evaluate multiplication and division there should not be any parentheses lying around.

rubik
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  • Thank you, and I will be glad to believe you. Do you also have some underground for your statement? Someone must have told you. – drhab Dec 13 '14 at 09:11
  • There are many references. You can find some here: http://en.wikipedia.org/wiki/Order_of_operations – rubik Dec 13 '14 at 09:12
  • I know enough now and will delete my question. I will look for a good answer of you on another question in order to upvote. Cheers. – drhab Dec 13 '14 at 09:14
  • Ahah whatever... I'm just happy I could be of help. – rubik Dec 13 '14 at 09:22