# multiplication by juxtaposition and order of operations

#### Ioannes

##### Oh man, I shot Marvin in the face.
Ah, then it is incorrect since Exponentials are prioritized before brackets.
no.

• 1 person

#### Prometheus

##### Everything is mutable; nothing is sacred
Staff member
You do any math within brackets/parenthesis first. While within these brackets, you do any parenthesis in them first, then exponents, then (left to right) any multiplication or division(M and D have the same math priority!), and then (left to right) any addition or subtraction(addition and subtraction have the same math priority!). Do the same outside the brackets.

#### Samael88

##### Evil always finds a way
You do any math within brackets/parenthesis first. While within these brackets, you do any parenthesis in them first, then exponents, then (left to right) any multiplication or division(M and D have the same math priority!), and then (left to right) any addition or subtraction(addition and subtraction have the same math priority!). Do the same outside the brackets.
What part of "divisions are done from top to bottom in the old ways" don't you understand?
You are talking about from left to right as if it where the way it has always been.
I learned to calculate without fancy computers doing the math for us and that was what we learned back in the days.
And I reiterate if I where to calculate in your way in my power formulas I would get arrested for murder because of my profession.

#### Flare

##### Stops copies me!
Staff member
There seems to be some mis-teaching which said multiplication took priority over division, but in actuality they have the same priority.
Er... what does the priority of multiplication relative to the priority of division have to do with this? This post summarizes the point of the thread nicely.

Please explain those for us who does not have English as our first language.

And no, it is not mis-teaching, you have learned to calculate in a "modern" way, we who see it as the answer being one calculates with the old ways only.
If I am wrong then every formula I have learned in my occupation is wrong and many people are going to die because of it. When it comes to calculations involving power then a nine instead of a one is a big difference.
Would your equations be written in an ambiguous fashion though?
Also, some examples of these formulae you work with would be nice (just to quell my curiosity )

Ah, then it is incorrect since Exponentials are prioritized before brackets.
Source to back up your information? Every textbook and teacher/lecturer I've had prioritizes brackets before exponentials and I don't think they would all be wrong...

#### Samael88

##### Evil always finds a way
Bah, I give up this damn discussion, I am to tired for these kind of things right now.

Would your equations be written in an ambiguous fashion though?
Also, some examples of these formulae you work with would be nice (just to quell my curiosity )
I will send them to you in a PM tomorrow then.

#### Prometheus

##### Everything is mutable; nothing is sacred
Staff member
I think you're getting confused with fractions. 2 divided by 3 is the same as 2 over 3 or 2/3. When you have 2/3(4), the brackets simply mean multiplication. You'd do 2 divided by 3, and then that times 4. You only prioritize the math WITHIN the parenthesis, not its standing in the overall scheme of things.

#### Samael88

##### Evil always finds a way
I think you're getting confused with fractions. 2 divided by 3 is the same as 2 over 3 or 2/3. When you have 2/3(4), the brackets simply mean multiplication. You'd do 2 divided by 3, and then that times 4. You only prioritize the math WITHIN the parenthesis, not its standing in the overall scheme of things.
I think that you are thinking about this calculation as an equation, when you have all variables given you don't use exactly the same rules as you do when you have some none given variables.
Once again I going to tell you, if I where to calculate the way you want then I would kill people, and I am not joking.

How would you calculate this one then?
Code:
``````            133-100
75-(75-58)*--------- =
150-100``````
Calculate that one correctly using your rules and explain to me why you are correct in the way you calculate it and I will rest my case.

#### Flare

##### Stops copies me!
Staff member
I think that you are thinking about this calculation as an equation, when you have all variables given you don't use exactly the same rules as you do when you have some none given variables.
Where do you get your information from? I haven't seen anything to suggest that the order of operations changes under certain circumstances

How would you calculate this one then?
Since I'm not really bothered with trying to align numbers over a makeshift fraction bar...

75-(75-58)*(133-100)/(150-100)
75-17*33/50
75-561/50
75-11.22
63.78

How would you have done it/what answer do you get? (FWIW, Wolfram and my calculator are both giving the same result)

#### Samael88

##### Evil always finds a way
75-(75-58)*(133-100)/(150-100)
75-17*33/50
75-561/50
75-11.22
63.78
That is the correct answer. I therefore rest my case.

#### Darthfett

##### Super Mod
That is the correct answer. I therefore rest my case.
There was nothing ambiguous about that math equation, because you and Flare both presented it in a form that could not be misinterpreted.

#### Prometheus

##### Everything is mutable; nothing is sacred
Staff member
Code:
``````            133-100
75-(75-58)*---------
150-100``````
This is the same as 75 - (75-58)*(133-100)/(150-100)
75 - 17 * 33/50
75 - 17 * .66
75 - 11.22
63.78

#### Bronxernijn

##### You can change this now in User CP.
I was taught that 6 divided by 2 is not the same as 6 over 2. It is in outcome (3), but not in a formula.

6 over 2 is one number, whereas 6 divided by 2 are two. So the problem with the OP's little quiz is that 6 divided by 2 can by some people be taken as 6 over 2. In that case, the outcome of 9 is correct. If it is read as it is said, the correct outcome is 1. Multiply has priority over divide.

Only if you think 6 divided by 2 may be interpreted as 6 over 2, the answer of 9 is correct. As I have stated before, 6 divided by 2 is NOT the same as 6 over 2. By thinking so you are essentially giving the dividing operation priority over everything. Therefore, 1 can be the only correct answer.

To react to an earlier post: 3 over 4 times 2 is 1.5. Because 3 over 4 has to be interpreted as a single real number, there is no divide operation anywhere here.

Another reaction:
Code:
``````            133-100
75-(75-58)*--------- =
150-100``````
133-100
--------- is a single number and equals ((133-100)/(150-100)).
150-100

#### Flare

##### Stops copies me!
Staff member
Multiply has priority over divide.
Where do people get this idea? Multiplication and division are of equal priority - if they are both found in the expression, then they are performed in the order they are found as you read the expression left to right

http://www.mathgoodies.com/lessons/vol7/order_operations.html said:
Rule 1: First perform any calculations inside parentheses.
Rule 2: Next perform all multiplications and divisions, working from left to right.
Rule 3: Lastly, perform all additions and subtractions, working from left to right.
http://en.wikipedia.org/wiki/Order_of_operations said:
The standard order of operations, or precedence, is expressed here:
terms inside parentheses or brackets
exponents and roots
multiplication and division As they appear left to right
addition and subtraction As they appear left to right
There's also...
one
two

Sadly, I can't find anything which states that multiplication would be prioritised over a division operation that precedes it (assuming no brackets involved, of course)

• 1 person

#### Romek

##### Super Moderator
Staff member
I don't think anybody here disagrees with the fact that division and multiplication are of equal priority and are performed as they appear from left to right.
The debate is more about whether 2y takes priority over 2 * y.

#### Prometheus

##### Everything is mutable; nothing is sacred
Staff member
2y and 2*y are the exact same thing.

#### Darthfett

##### Super Mod
2y and 2*y are the exact same thing.
I think you ought to go back and take a look at Romek's earlier post, he pointed out something very interesting that actually has some evidence for it.

I still stand by my post after it, that WolframAlpha probably isn't a good source for the proper usage of the order of operations. It does try and interpret the input, instead of merely calculating it, which may or may not have some effect on the answer.

#### Prometheus

##### Everything is mutable; nothing is sacred
Staff member
The issue is that calculators will assume 2(1+2) = (2+4) as it will distribute, if you don't put the *.

#### Darthfett

##### Super Mod
The issue is that calculators will assume 2(1+2) = (2+4) as it will distribute, if you don't put the *.
I think the issue here is that only some calculators will group them into (2(1+2)) (or at least provide the same results for this case) for use in the equation. While 2(1+2) and (2+4) are equivalent, if you wish to use this value in an equation, you absolutely must put parenthesis around them for it to make sense.

I also want to point out that in my last post, I was specifically referring to the use of 2y vs 2*y in the original equation (2y/2y), and that I was not denying that 2y = 2*y.

#### Bronxernijn

##### You can change this now in User CP.
I stand corrected, and my post on multiplication before dividing is complete bullshit.

The issue with 2y or 2*y still stands on me. I had trouble explaining some stuff to a kid at work earlier today.

#### SerraAvenger

##### Cuz I can
I would personally support ab > a*b (by order of precedence) for the simple reason that I would rather introduce syntactic sugar for (a*b) than for a*b. It's just slightly more elegant.
Defining ab as a*b would just mean that we save a single character, which is usually a dot.
In most of these cases, a*b is (a*b) anyway (for reasons of associativity) and hence we will not loose much if we write ab. In those cases where there is a difference, it is still more convenient to write ab rather than (ab), especially for stuff like (a*b*c*d)/t = abcd/t.
I would also like to add that a similar notation for /+and- is missing but would make some things much more elegant to write.

Since, however, there seems to be no global convention I suggest that if you introduce such notation in your code, clearly document the precedence. Similarly, if you use such notation in your code, and you're not sure, add the parentheses.

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