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How to perform the following division?

74628/25/12?

which division is to be performed first?First or second and why?

miracle173
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Anwesa Roy
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  • the usual rule is 'left to right' so 74628 gets divided by 25, then that answer is divided by 12 - this does matter, because division is not commutative. The reason 'why' we have a convention is because we need one to prevent ambiguity. – Cato Oct 31 '16 at 12:57
  • The better way to prevent ambiguity is setting parantheses, in particular , if misunderstandings can occur. If you use fractions instead of the "/"-sign, you can easily make clear what is meant without needing parantheses. – Peter Oct 31 '16 at 13:00
  • Not sure, whether "left to right" is the normal convention. $a\uparrow b\uparrow c$ is normally considered to be $a\uparrow (b\uparrow c)$. This might be different for divisions. – Peter Oct 31 '16 at 13:05
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    With division, yes @Peter, the convention IS to proceed left to right. Indeed, multiplication and division are at the same level of precedence, so when one or both occur, we proceed from left to right, e.g. $(a/b\cdot c) = (a/b) \cdot c = \frac ab \cdot c.$ – amWhy Oct 31 '16 at 13:14

3 Answers3

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In the absence of grouping symbols, one normally performs multiplication and division in order from left to right. So this would mean $(74628/25)/12$.

If $74628/(25/12)$ were intended, the grouping symbols would be necessary.

MPW
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Division is not commutative so the order does matter. Math is read from left to right, so written like that, the correct order would be (74628/25)/12.

rosaqq
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Order of operations dictates that you go from left to right and that you treat $\times$ and $/$ as equally important. So $74628/25/12 = (74628/25)/(12)$.

I find it helps to replace each $``/ n"$ with $``\times \dfrac 1n"$.

So $74628/25/12 = 74628 \times \dfrac{1}{25} \times \dfrac{1}{12}$

As amWhy has pointed out, I don't mean for you to do things like

$74628/25/12 = 74628/(25/12) = 74628 \times \dfrac{1}{25/12}$.

That is wrong. You must proceed from left to right as shown in my example.

Steven Alexis Gregory
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  • So translating division in terms of multiplication does not eliminate the need to follow the order of operations (for multiplication/division), which dictates evaluation from left to right. – amWhy Oct 31 '16 at 16:41
  • @amWhy - If you see $a/b/c$, then order of operations dictates you must first compute $a/b$ and then compute $(a/b)/c$. I'm trying to suggest that, if you write $a/b/c$ as $a \times \frac 1b \times \frac 1c$, then you can compute the product in whatever order you want. For example $1690/5/13 = 1690 \times \frac{1}{5} \times \frac{1}{13} = 130 \times \frac{1}{5} = 26$ – Steven Alexis Gregory Nov 01 '16 at 04:23
  • @amWhy - Thank you for your comments. I appreciate knowing why I got a down vote. However, comments like "Well, since you do not seem inclined to improve your answer, my comments will remain here unless, until you do so. " have nothing to do with mathematics nor with the OP's problem. You have no idea when I logged off and when I logged back on and what I did in between. It was not nice of you to assume that I was indifferent to your comments. – Steven Alexis Gregory Nov 01 '16 at 04:59
  • All I was suggesting was adding one-sentence to your post. I like your post, now, with the edit. Indeed, I like it very much! (And I've deleted my comments as I promised I would. Sorry if of my comments seemed to come across as too premature. I simply wanted to alert the OP that left-to-right evaluation, all things being equal has been applied here, to. – amWhy Nov 01 '16 at 12:14