# The equation: 18 ÷ 3 ( 5 - 4 + 1 ) = 3 or 12? (order of operation) [duplicate]

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?

• 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. – Matti P. May 31 '18 at 6:41
• 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." – Mauro ALLEGRANZA May 31 '18 at 6:41
• Linear algebra is not the right tag for this post. – bkarthik May 31 '18 at 6:43
• @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? – shnisaka May 31 '18 at 6:44
• 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 $10/(5*2)$ – Dylan Zammit May 31 '18 at 6:45

$$18/3(5-4+1)$$ 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 $$18/(3(5-4+1))=3.$$
• 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. – Vinyl_cape_jawa May 31 '18 at 7:00