PEDMAS / BODMAS rule

[scott-atkinson]

Over the weekend, I was reading a post that an American had made on a social networking site about a mathematics calculation, that when summed together apparantly bought the answer of 20, yet when I summed it all together I got the answer of 320.

The poster argued that the correct way of calculating the sum, that had no Brackets whatsoever was by using the PEDMAS / BODMAS rule, to which I had never even heard of..

Apparantly according to the poster this is commom practice in Mathematics, so why have I never heard of it before???

Apparantly according to the rule, where there are brackets in a sum, these are calculated first but in the abscence of brackets you calculate the Multiplication, and Division before the Additon and Subtraction...

Is this right, or is it just rubbish...

Seems to me that whoever invented this rule was rubbish at Mathematics and just invented siomething to fit with his answer..

I cant remember the exact sum on the networking site, but it had all 4's in it, with Multiplication, Division, subtraction and addition...

 

[bob fitz]

I have heard of this before. I have vague memories of it from when I was at school, but most of those memories are now vague because it was sooooo long ago. Plenty of info if you google it though.

 

[namliam]

Yes that is "quite common" i.e. standard wihtout googling it means that you do Square roots before Division before Substraction (or their positive counter parts)

4 + 4 * 4 + 4 = 8 x 8 = 64? No wrong,
8 * 4 + 4 = 32 + 4 = 36? No wrong
4 + 16 + 4 = 24, right...
Do the multiplication first, then the adding.

Paste the calculation in Excel you get the same answer

 

[scott-atkinson]

Yes that is "quite common" i.e. standard wihtout googling it means that you do Square roots before Division before Substraction (or their positive counter parts)

4 + 4 * 4 + 4 = 8 x 8 = 64? No wrong,
8 * 4 + 4 = 32 + 4 = 36? No wrong
4 + 16 + 4 = 24, right...
Do the multiplication first, then the adding.

Paste the calculation in Excel you get the same answer

I would have calculated the answer to be 36 simply by working left to right and using each function as it appeared in order. So why is my answer incorrect and yet the third answer in your example is correct?

What purpose does the PEDMAS / BODMAS rule have? What was it created to achieve?

It appears to me that it was created in an attempt to simplify long mathematics equations, but in the attempt produced an incorrect answer..

I have used Excel before on long sums, and have always felt that the answer given was incorrect, and in an attempt to get the correct answer I have used brackets, now I know why, obviously Excel is working to this rule

 

[namliam]

I believe its main purpose is simple, to prevent the ambiguity of random ordering ....

Making sure that
4 + 4 * 4 + 4 is the same as 4+4+4*4 and 4*4+4+4 instead of getting different answers... in "your world" 36, 48 and 24.. Using BODMAS they all return 24

 

[Brianwarnock]

8 * 4 + 4 = 32 + 4 = 36? No wrong

Actually 36 is the correct answer to this.


I believe that Scot is winding us up as I'm sure that he is intelligent enough to realise that without a rule chaos would reign


Brian

 

[pbaldy]

I wouldn't have known the name, but it is common, in fact Access does it:

?4+4*4+4
24
?4*4+4+4
24
?4+4+4*4
24

 

[Brianwarnock]

We were taught BODMAS in school 50 years ago, PEDMAS. I have not come across and a google search threw up PEMDAS and it appeared to be the American version. Don't know if that's true or not, but it is the same thing.

Brian

 

[David R]

http://en.wikipedia.org/wiki/Order_of_operations#Mnemonics

 

[scott-atkinson]

Actually 36 is the correct answer to this.


I believe that Scot is winding us up as I'm sure that he is intelligent enough to realise that without a rule chaos would reign


Brian

Exactly... 36 is the correct answer if you work left to right and use each function as it is encountered in the equation.

The BODMAS and PEMDAS rules (Brian thank you for correctly my spelling on the latter) in my opinion just make the sums more complicated as you have to jump around within the sum to sum parts and then sum the latter after.

Simply working left to right each time would get the answer of 36, therefore this also negates any ambiguity in approaching the sum, so therefore BODMAS is not required.

 

[David R]

Exactly... 36 is the correct answer if you work left to right and use each function as it is encountered in the equation.

The BODMAS and PEMDAS rules (Brian thank you for correctly my spelling on the latter) in my opinion just make the sums more complicated as you have to jump around within the sum to sum parts and then sum the latter after.

Simply working left to right each time would get the answer of 36, therefore this also negates any ambiguity in approaching the sum, so therefore BODMAS is not required.

36 is correct for what namliam posted, 8 * 4 + 4 ... but that wasn't the original question. The question is, why do 4 + 4 * 4 + 4, 4 * 4 + 4 + 4, and 4 + 4 + 4 * 4 have different results in 'your world'? Under Order of Operations, they're all the same.

 

[scott-atkinson]

I believe its main purpose is simple, to prevent the ambiguity of random ordering ....

Making sure that
4 + 4 * 4 + 4 is the same as 4+4+4*4 and 4*4+4+4 instead of getting different answers... in "your world" 36, 48 and 24.. Using BODMAS they all return 24

In your example, these are three different sums, therefore they should all have a different answer, applying some rule so they all have the same answer is just plain daft.

4 + 4 = 8 * 4 = 32 + 4 = 36

4 + 4 = 8 + 4 = 12 * 4 = 48

4 * 4 = 16 + 4 = 20 + 4 = 24

Different sums, so why on earth would they all equal 24!!!!!

 

[scott-atkinson]

Did they apply the BODMAS rule in the Hitch Hikers Guide to the Galaxy to return the answer of 42 to the question of Life the Universe and Everything...

 

[scott-atkinson]

36 is correct for what namliam posted, 8 * 4 + 4 ... but that wasn't the original question. The question is, why do 4 + 4 * 4 + 4, 4 * 4 + 4 + 4, and 4 + 4 + 4 * 4 have different results in 'your world'? Under Order of Operations, they're all the same.

Working left to right and applying the functions as you encounter them in the sum returns a difference answer to each of these sums, and in my opinion so it should, as each one is a different sum in it's own right so why on earth should they all have the same answer...

 

[scott-atkinson]

I think Mr BODMAS simply created a daft rule to explain away the fact that he was simply rubbish at Mathematics...

 

[Galaxiom]

I think Mr BODMAS simply created a daft rule to explain away the fact that he was simply rubbish at Mathematics...

The rule has been around for a very long time and is routinely taught in maths class. Clearly you didn't pay enough attention at school.

Evidence of it as a convention among some authors has been seen as early as 1646. It was probably formalised in the late nineteenth or early twentieth century.

http://mathforum.org/library/drmath/view/52582.html

When hand held electronic calculators were introducded in the mid 1970s one of the tests we would perform before buying one was to ensure that it calculated according to the rule.

 

[Knildon]

I'm not sure what some of you were taught in other parts of the world but
children in the USA are taught the following in 4th grade:

The Order of Operations
When children initially learn addition, subtraction, multiplication, and division,
they begin by performing operations on two numbers.
But what happens when an expression requires multiple operations?
Over time, mathematicians have developed a set of rules called the order
of operations to determine which operation to do first.
The rules are:
1. Multiply and divide from left to right.
2. Add and subtract from left to right.

They are also taught that any operation enclosed in parentheses,
brackets or braces is done first then the rules above apply.
As the children progress they are also taught about exponents and square roots.

The term PEMDAS is not commonly used but it applies the same rules.

Order of Operations / P.E.M.D.A.S
P.E.M.D.A.S. simply means:
Parenthesis | Exponents | Multiplication | Division | Addition | Subtraction

Evaluating algebraic expressions can be a simple process,
but needs to follow an order of operations to get the right answer.
The sequence details the order you follow to
add, subtract, multiply, and divide.
The order is:
1. Perform the operations inside a parenthesis first
2. Then exponents
3. Then multiplication and division, from left to right
4. Then addition and subtraction, from left to right

You can also create a little phrase to memorize, as the sequence:
Please Excuse My Dear Aunt Sally

B.O.D.M.A.S. is just another term for the order of operation.
Brackets | Orders | Division | Multiplication | Addition | Subtraction

AKA B.E.D.M.A.S. and B.I.D.M.A.S ( E for exponents & I for indices)

I've been following these rules since I was a kid and I'm now 72.
Haven't been accused of giving wrong answers to date!!
( Of course, that will probably change today!!)

Don

 

[Knildon]

Hi again,
Let’s see if we can prove or disprove any of the posted theories.

There were 4 boys with quarters in their pockets.
The first boy had 4 quarters.
The second had twice as many as the first boy.
The third boy had 3 quarters.
The fourth boy had 3 times as many as the first boy.
How many quarters total did they have?

Try this:
4 + 4x2 + 3 + 3x4 =??
Looks a little like the original problem that was posted.

Is the answer:
88 quarters
or
27 quarters
or something else.

I think most of us know the answer, but how did we arrive at the correct answer.
Don

 

[namliam]

Hi again,
Let’s see if we can prove or disprove any of the posted theories.

There were 4 boys with quarters in their pockets.
The first boy had 4 quarters.
The second had twice as many as the first boy.
The third boy had 3 quarters.
The fourth boy had 3 times as many as the first boy.
How many quarters total did they have?

Try this:
4 + 4x2 + 3 + 3x4 =??
Looks a little like the original problem that was posted.

Is the answer:
88 quarters
or
27 quarters
or something else.

I think most of us know the answer, but how did we arrive at the correct answer.
Don

Something else, 228

 

[scott-atkinson]

The rule has been around for a very long time and is routinely taught in maths class. Clearly you didn't pay enough attention at school.

I paid attention at school, I got a whole CSE Grade 2 in Maths..

Seriously though I don't ever remember using this rule at school, i remember using brackets to seperate sums within a sum, but when there was no brackets it was a simple left to right equation

Evidence of it as a convention among some authors has been seen as early as 1646. It was probably formalised in the late nineteenth or early twentieth century.

I will have to take your word for that I wasn't around then...

http://mathforum.org/library/drmath/view/52582.html

When hand held electronic calculators were introducded in the mid 1970s one of the tests we would perform before buying one was to ensure that it calculated according to the rule.

I'm not sure what calculators you are using but when I did the 3 sums on my office calculator I got the 3 seperate answers that I was expecting to get.