# PEMDAS and BODMAS

#### cleary.not.a.geek

##### New member
Can you please help settle and ongoing argument between members of a group i am in. There seem to be Two camps.: those who pick "b" and those who insist the answer is "c"
This problem may seem very elementary... But it brought up all kinds of references to PEMDA and BODMAS

Here were some
Ok...
All the "A's" are wrong
All the "D"'s are wrong
Its either "B" or "C" depending on whether you add or subtract at the end of the equation:
3-3×0+3÷3=
3-0+1...
(can we all agree on that?)
Doing Muliplication THEN Division,
yields 3×0=0 and 3÷3=1 bring us to
3-0+1...
OR if you prefer, the BODMAS way, DIVIDE first
3÷3=1 and. THEN MULTIPLY 3×0=0,
Again yielding 3-0+1
So far, so good, either way it's 3-0+1
But then there SEEM to be two approaches:
If you say 3-0=3, and 3+1=4
You'll get 4...BUT
If you say 0+1=1, and 3-1=2
You'll get 2
BUT...Don't BOTH PEMDAS and BODMAS
say "A.S." at the end of the acronym?
and THEN the SUBTRACTION,
YOU GET 3-1=2

so i would say the "2's"
(or, the "B's") have it.
Just sayin....- lol
my thoughts:

#### Subhotosh Khan

##### Super Moderator
Staff member
Can you please help settle and ongoing argument between members of a group i am in. There seem to be Two camps.: those who pick "b" and those who insist the answer is "c"
This problem may seem very elementary... But it brought up all kinds of references to PEMDA and BODMAS

View attachment 12945 Here were some
Ok...
All the "A's" are wrong
All the "D"'s are wrong
Its either "B" or "C" depending on whether you add or subtract at the end of the equation:
3-3×0+3÷3=
3-0+1...
(can we all agree on that?)
Doing Muliplication THEN Division,
yields 3×0=0 and 3÷3=1 bring us to
3-0+1...
OR if you prefer, the BODMAS way, DIVIDE first
3÷3=1 and. THEN MULTIPLY 3×0=0,
Again yielding 3-0+1
So far, so good, either way it's 3-0+1
But then there SEEM to be two approaches:
If you say 3-0=3, and 3+1=4
You'll get 4...BUT
If you say 0+1=1, and 3-1=2
You'll get 2
BUT...Don't BOTH PEMDAS and BODMAS
say "A.S." at the end of the acronym?
and THEN the SUBTRACTION,
YOU GET 3-1=2

so i would say the "2's"
(or, the "B's") have it.
Just sayin....- lol
my thoughts:
PEMDAS and BODMAS are equivalent - P (parentheses) is replaced by B (Brackets).

However, in both rules - the unspoken rule is - that the operations are done from left right. So:

3-0+1 ...............................(3-0 is left-most operation - so it will be carried out first)

= 3 + 1 = 4

#### topsquark

##### Full Member
Can you please help settle and ongoing argument between members of a group i am in. There seem to be Two camps.: those who pick "b" and those who insist the answer is "c"
This problem may seem very elementary... But it brought up all kinds of references to PEMDA and BODMAS

View attachment 12945 Here were
Please use a more normal sized font. There is NO NEED TO YELL!!!!

#### StephenWilliams

##### New member
B - Brackets = P - Parentheses
O - Order = E - Exponents i.e. Powers
D - Division != M - Multiplication
M - Multiplication != D - Division
S - Subtraction = S - Subtraction
So we see the only difference is between the multiplication and division operators. Both are acronyms designed to be easy to remember but don’t quite tell the full story. The central idea the two acronyms try to get across is that you should do multiplication and division before addition and subtraction.

Now there are some awkward cases like 6/2*3, 6*3/2 and 6/3/2. Neither rule works for all these case. The real rule is that when the operations are of the same precedence, (like * and / ) you do the operations from left to right. Hence 6/2*3 = (6/2) * 3 = 3 * 3 = 9 and 6 * 3 / 2 = (6 * 3) / 2 = 18 / 2 = 9 and 6/3/2 = (6/3)/2 = 2/2 = 1.

The same happens with + and –. So 6 – 2 – 3 = (6 – 2) – 3.

also check PEMDAS calculator

#### Dr.Peterson

##### Elite Member
Doing Muliplication THEN Division,
yields 3×0=0 and 3÷3=1 bring us to
3-0+1...
OR if you prefer, the BODMAS way, DIVIDE first
3÷3=1 and. THEN MULTIPLY 3×0=0,
Again yielding 3-0+1
So far, so good, either way it's 3-0+1
But then there SEEM to be two approaches:
If you say 3-0=3, and 3+1=4
You'll get 4...BUT
If you say 0+1=1, and 3-1=2
You'll get 2
BUT...Don't BOTH PEMDAS and BODMAS
say "A.S." at the end of the acronym?
and THEN the SUBTRACTION,
YOU GET 3-1=2
PEMDAS and BODMAS are just reminders of the convention, which is merely "Multiplication and Division first, left to right, then Addition and Subtraction, left to right." It might be more accurately rendered as PE[MD][AS], but that's harder to pronounce.

I prefer "EMA": Exponents, then Multiplication (treating division as multiplication by the reciprocal), then Addition (treating subtraction as addition of the opposite). Parentheses aren't an operation at all, just a way to modify the order when you want to, by expressing it explicitly.

The reason, then, that we do addition and subtraction left to right is because 3-0+1 means (3) + (-0) + (1). The sign attached to the middle term doesn't affect what you do with the last term.

#### tkhunny

##### Moderator
Staff member
Keep in mind it is a convention. Not all things follow the same convention. My primary programing language interprets strictly right to left.

3 - 3 x 0 + 3 / 3
3 - 3 x 0 + 1
3 - 3 x 1
3 - 3
0

Now what do you say about all the Ds being wrong?

There is no substitute for know what it is you are doing.
There is no need to force the world to function according to your expectation.

1) Establish a rule. 2) Follow it.
Without first establishing a rule, it is very difficult to insist on compliance.