Well, okay, it's not incorrect, but it's flawed and by a mathematician's standards: morally wrong.

I'm sure at one point you boringly learned the order of operations. These are the set of rules that tell you whether you should do multiplication before division or addition before subtraction to get the correct answer on your math problem.

1) Parentheses (brackets)

1) Parentheses (brackets)

2) Exponents x^x

3) Multiplication 2*2

4) Division 2/2

5) Addition 2+2

6) Subtraction 2-2

7) Get the right answer :)

Except, you don't always get the right answer.

For example: 8-2+1. Is it 5 because 8-3=5? Or is it 7 because 6+1=7?

Is 6/3/3 equal to 2/3 or 6/1?

The issue here is that focusing on the order of operations can lead to ambiguity and obscures the real beauty of mathematics.

A mathematician will tell you that 8-2+1 is actually 8+(-2)+1, which is unambiguously equal to 7 even though the standard order of operations (PEMDAS) taught in the US tell you to add first and gives you 5. But in reality, if you want 5 to be your answer, then you need some parentheses like so: 8-(2+1).

But why is the ambiguity even possible? It's because fundamentally, all these operations are different procedures that start with two numbers and in some way combine them to make a single number. Each operation takes two number, no more, as an input and gives you an output. If you want to be entirely unambiguous then you would have to put parentheses around everything.

It would take something like 1+2+3+4*5-18/3 and make it look like ((1+2)+(3+((4*5)-(18/3)))).

Then, there would be no need to know any order of operations. You would just evaluate the innermost parentheses first and always get the same answer.

Then, there would be no need to know any order of operations. You would just evaluate the innermost parentheses first and always get the same answer.

But this isn't the only way. You can actually change the order of these operations by changing where the parentheses are like in (1+(2+3)) and ((1+2)+3). But the only way to do this is if you know what the underlying mathematical is.

For example, if you want to multiply the results of 3+4 by 5 or just (3+4)*5 you can either do the addition first and get 7 and multiply that by 5 and get 35. OR you can multiply first as long as you multiply the 5 by both the 3 and the 4 which would yield 15+20. The latter example is distribution and in both cases you get 35.

This even works for exponents like ((3*2)^2) which simplifies to 6^2 and ultimately 36. But you can also square both of them before you multiply which becomes 3^2 * 2^2 or 9*4 and finally 36.

So, the TRUE Order of Operations is this:

1) Parentheses first

1) Parentheses first

2) Learn Math (basically what multiplication, division, exponentiation, and the rest are really doing)

3) Do whatever you want.

3) Do whatever you want.

All this doesn't mean that we don't have a conventional order of operation in mathematics, but deciding to do multiplication before addition helps us get rid of LOTS of redundant parentheses. Also, learning things like the Associative Property(ies) of Multiplication/Addition helps get rid of a lot more. The parentheses are still there, but they're just implied.

The order of operations learned in school is very different. It's just a set of mechanical instructions that dictate just one of the MANY ways you can use algebra. It locks you in a single path in the beautiful landscape of mathematics. Like a computer, it gives you the right answer but cannot actually give you any insight on what it is that you're actually doing.

So, the order of operations isn't technically wrong, since it generally gives you the right answer, but it is morally wrong because it turns you into a robot.

*******

Text and Transcript are property of MinutePhysics Productions.

Text and Transcript are property of MinutePhysics Productions.

## Comments

I actually read this post hoping to understand what BODMAS stands for. I get that Brackets replace Parentheses, and since the division IS multiplication, just as subtraction IS addition, there can be no distinction in the order of operations, provided we recall that subtraction of a positive number is equivalent to addition of a negative number, but what does the "O" stand for, that obviously must be equivalent to an exponent?

If you can't even get 8-2+1 correct you really can't blame the order of operations for your weak math skills. (even if you add first, WHICH ISN'T what the order of operations states, -2+1=-1, this is like 1st grade math).

Secondly, you obviously haven't got a clue what you are talking about as you completely confuse the order of operations (the basis of all modern math and its rules) with the ACRONYMS created to help remember it (but way to often misunderstood as you so clearly prove here). The order of operations have 4 steps, not 6 as division is just the multiplication of fractions and subtraction the addition of negative numbers. If you actually bothered to learn it and follow it there are no ambiguities, those you imply comes only from ignorance.

You refer to distribution (something that really only applies to algebra when working with variables) and yet doesn't understand it. Distribution DOES NOT break the order of operations or give a different answer than NOt distributing, if that would happen you've made a mistake!

You can still be creative and find paths using associative and commutative properties, neither of those however ever break the order of operations, AS LONG AS YOU HAVE A CLUE WHAT YOU ARE DOING.

Order of Operationsis NOT wrong. Your Understanding ofOrder of Operationsis wrong.PEMDAS,BODMAS,BIDMAS,Punkt Vor Strich, and my own creation,GENMSall describe the exact same Rules of Math that are over 500 years old, Always apply, and are based on Logic and the History of Math.Or Simply Simplify the Terms in the Expression then Sum. If it's not a plus sign it's a Term.

You can't even get Basic Addition and Subtraction right. The rule is that the Negative Sign Sticks To The Number On Its Right! Ever heard of the Commutative Property of math? It enables us to Move the Terms around in an Expression and always arrive at the same answer. Therefore 8-2+1=8 + -2 + 1=-2 + 8 + 1=8 + 1 + -2, etc.!

Please, Everyone, Do

NOTpay an idiot like this guy to tutor you or your kid!4. Addition and subtraction (Left to Right)

(and explain why addition and subtraction share the same level in a "precedence table").(Sometimes. I'll mention tetration, but say not to worry about it!)exponents and roots

multiplication and division

addition and subtraction

This means that if a mathematical expression is preceded by one binary operator and followed by another, the operator higher on the list should be applied first.

The commutative and associative laws of addition and multiplication allow adding terms in any order, and multiplying factors in any order—but mixed operations must obey the standard order of operations.

It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse). Thus 3 ÷ 4 = 3 × ¼; in other words the quotient of 3 and 4 equals the product of 3 and ¼. Also 3 − 4 = 3 + (−4); in other words the difference of 3 and 4 equals the sum of 3 and −4. Thus, 1 − 3 + 7 can be thought of as the sum of 1, −3, and 7, and add in any order: (1 − 3) + 7 = −2 + 7 = 5 and in reverse order (7 − 3) + 1 = 4 + 1 = 5, always keeping the negative sign with the 3.

The root symbol √ requires a symbol of grouping around the radicand. The usual symbol of grouping is a bar (called vinculum) over the radicand. Other functions use parentheses around the input to avoid ambiguity. The parentheses are sometimes omitted if the input is a monomial. Thus, sin 3x = sin(3x), but sin x + y = sin(x) + y, because x + y is not a monomial. Some calculators and programming languages require parentheses around function inputs, some do not.

Symbols of grouping can be used to override the usual order of operations. Grouped symbols can be treated as a single expression. Symbols of grouping can be removed using the associative and distributive laws, also they can be removed if the expression inside the symbol of grouping is sufficiently simplified so no ambiguity results from their removal.

then, you must figure out how to pronounce those brackets

(and explain why addition and subtraction share the same level in a "precedence table")."

You are making the erroneous assumption that the mnemonic is the rule.<br>

It is not the rule - it is only a memory aid to remember the rules.<br>