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the question might be simple to solve but when entered in google search as:

18/3(5-4+1)

you get 12! However, If it was done using the order of operation it is solved this way:

18 ÷ 3 ( 5 - 4 + 1 ) 
18 ÷ 3 ( 2 ) 
18 ÷ 6
= 3

What is the answer? and how can I explain that the other side is wrong? I read about the order of operation but no priority is given in terms of what comes first multiplication or division. So, how is this solved?

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  • $\begingroup$ It depends on how $18/3(2)$ is interpreted: $\frac{18}{3\times 2}$ or $\frac{18}{3}\times 2$. I would personally vote for the latter one. $\endgroup$ – Matti P. May 31 '18 at 6:41
  • $\begingroup$ See Order of operations : Exceptions : "there can be ambiguity in the use of the slash symbol / in expressions such as "1/2x". With the interpretation of the division symbol as indicating multiplication by the reciprocal, 1 ÷ 2x is equal to (1 ÷ 2)x. However, in some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2x equals 1 ÷ (2x), not (1 ÷ 2)x." $\endgroup$ – Mauro ALLEGRANZA May 31 '18 at 6:41
  • $\begingroup$ Linear algebra is not the right tag for this post. $\endgroup$ – bkarthik May 31 '18 at 6:43
  • $\begingroup$ @bkarthik I do not know what kind of algebra this is and I could not add the tag "order-of-operation" can you please suggest what tags I should be putting for this? $\endgroup$ – shnisaka May 31 '18 at 6:44
  • $\begingroup$ Even if you use a calculator and write: $15/5\cdot 2$ you will get 6. This is because when using division on computer software, if you do not collect all elements in the denominator with a bracket, the software will assume that only the FIRST term after the "/" sign is in the denominator. So there is a difference between: $10/5*2$ and $10/(5*2)$ $\endgroup$ – Dylan Zammit May 31 '18 at 6:45
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The problem you face here is due to the way the equation is displayed, we have

$$ 18/3(5-4+1) $$ which usually means $$ \frac{18}{3}\cdot (5-4+1)=12. $$

The expression you evaluate is $$ \frac{18}{3\cdot(5-4+1)} $$ would be written as $$ 18/(3(5-4+1))=3. $$

Hope this helps.

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  • $\begingroup$ = 12 not 2. and you never answered the main question: The equation: 18 ÷ 3 ( 5 - 4 + 1 ) = 3 or 12? $\endgroup$ – shnisaka May 31 '18 at 6:52
  • $\begingroup$ Ohh, my bad, now corrected, thanks. The answer is $12$ as it stands now (according to me at least). You would need an extra set of brackets around $3(5-4+1)$ to ensure that it is included in the denominator. $\endgroup$ – Vinyl_cape_jawa May 31 '18 at 7:00
  • $\begingroup$ I think I found a similar question: math.stackexchange.com/questions/33215/what-is-48%C3%B7293?rq=1 and the answer is not 12 ;) $\endgroup$ – shnisaka May 31 '18 at 7:01
  • $\begingroup$ That is why I said "according to me", I would interpret it in the way as it stands in my answer. You can always use parentheses to clarify the order of the operations $\endgroup$ – Vinyl_cape_jawa May 31 '18 at 7:09

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