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Parentheses group and give priority to operations INSIDE the symbol not outside the symbol. 2(4) is not a parenthetical priority and is mathematically the same as 2×4 When there are no OPERATIONS left INSIDE the parentheses to evaluate you can remove the parentheses and replace with an explicit multiplication symbol or leave them to represent implicit multiplication which is simply multiplication without the need for a physical multiplication sign...

P is for inside parentheses only, not outside. Otherwise you run into the 4²(3) problem. How do you do P before E here?

The order of operations like PEMDAS etc. are oversimplifications for what's really allowed when simplifying anyway. Understanding grouping and different strengths of it is more useful. Take 4 + 3²×6/2 - 4 You could follow it literally: E: 4 + 9×6/2 - 4 M: 4 + 54/2 - 4 D: 4 + 27- 4 A: 31 - 4 S: 27 However, in this example you could do: S: 0 + 3²×6/2 D: 3²×3 E: 9×3 M: 27 Same correct answer and just as valid. Shorter too in this example. + and - have the weakest grouping power. × and ÷ have stronger grouping power than + and -. Exponents have higher grouping power again. Parentheses have the highest grouping power. Depending on what you have and how they are laid out let's you simplify in different ways. Minutephysics did a short video called The Order of Operations is wrong. Worth a watch.

6 letter acronym that represents 4 levels not 6 exact steps... P E M&D equally left to right as they appear A&S equally left to right as they appear

Your comment is a joke. The correct answer when you actually understand and apply the Order of Operations and the various properties and axioms of math correctly as intended is 16 not 1

@@RS-fg5mf You do PEMDAS and continue to be mocked around the world, while I will continue to answer math equations correctly ..... Have a nice day.

@@strictlyaesthetic9202 I don't do PEMDAS but you definitely do dmba$$ ... It's not an equation, it's an expression and the only people mocking 16 are the mathematically incompetent like you...

8 -------(2+2)= 8÷2(2+2)= 16 2 8 ---------- = 8÷(2(2+2))= 1 2(2+2)

This is grade school arithmetic numpty... You're mathematically ignorant if you didn't get 16 as the correct answer.... Basic Arithmetic doesn't change after 4th grade Dunning-Kruger

The Distributive Property supports 16 not 1 .... How does it feel to be less mathematically intelligent than your average 4th grade 10 year old??

He's not wrong.... Numpty The majority of MATH BOOKS support 16 The majority of scientific calculators and online math engines support 16 Every Math Teacher I know personally, several of whom have PhDs in math and teach at Universities support 16. Stop embarrassing yourself and get a clue...

WRONG.... People confuse and conflate two different types of Implicit multiplication .... One without a delimiter and one with a delimiter.. Type 1... Implicit Multiplication between a coefficient and variable... A special relationship given to coefficients and variables that are directly prefixed i.e. juxstaposed WITHOUT a delimiter and forms a composite quantity by Algebraic Convention... Example 2y or BC This type of Implicit Multiplication is given priority over Division and most other operations but not all other operations... This can be seen in most Algebra text books or Physics book. Physics uses this type of Implicit Multiplication quite heavily.. Type 2... Implicit Multiplication between a TERM and a Parenthetical value that have been juxstaposed without an explicit operator but WITH a delimiter...The parentheses serve to delimit the two sub-expressions.. Parenthetical implicit multiplication. The act of placing a constant, variable or TERM next to parentheses without a physical operator. The multiplication SYMBOL is implicit, implied though not plainly expressed, meaning you multiply the constant, variable or TERM with the value of the parentheses or across each TERM within the parenthetical sub-expression. Parentheses group and give priority to operations WITHIN the symbol of INCLUSION not outside the symbol. Terms are separated by addition and subtraction not multiplication or division. The axiom for the Distributive Property is a(b+c)= ab+ac but what most people fail to understand is that each of those variables represents a constant value OR a set of operations that represent a constant value... A single TERM expression like 6÷2(1+2) has two sub-expressions. The single TERM sub-expression 6÷2 juxstaposed to the two TERM parenthetical sub-expression 1+2. The lack of an explicit operator implies multiplication between the TERM or TERM value outside the parentheses and the parenthetical value or across each TERM within the parenthetical sub-expression... The parentheses DELIMIT the TERM 6÷2 from the two TERMS 1+2 maintaining comparison and contrast between the two elements... Implicit multiplication is always by juxstaposition but not all juxstaposition is Implicit multiplication. Example 2½ = 2.5 not 2 times ½... There is “implicit multiplication” WITH delimiters and there is “implicit multiplication WITHOUT delimiters. Two different types of Implicit multiplication and mathematically different. 6÷2y the 2y has no delimiter.... 6÷2y=3÷y by Algebraic Convention. 6÷2(a+b) has a delimiter... 6÷2(a+b)= 3a+3b by the Distributive Property... 6y÷2y = 6y÷(2y) = 6y÷(2*y) 6y÷2(y)= (6y÷2)(y)= 6y÷2*y 6y÷2y(y)= (6y÷(2y))(y)= 6y÷(2y)*y= 6y÷(2*y)*y ÷2y the denominator is 2y ÷2(y) the denominator is 2

That doesn't prove anything as the ambiguity is caused by notation conventions. Academically, juxtaposition implies grouping and multiplication (1) Literally/programming-wise, juxtaposition implies multiplication only (16) Whichever convention you choose will put you on the path for the respective answer. You chose the academic interpretation so any "proof" of yours will of course give 1 as it's predetermined. It's called a circular argument, which can't prove anything obviously.

You fail at basic arithmetic and you fail at basic algebra... a/2(2+2)=16 a/2(4)=16 a/2=16/4 a/2=4 2×4=a a=8 a/2(2+2)=1 a/2(4)=1 a/2=1/4 2×(1/4)=a a= 1/2

​@@RS-fg5mf lol I think you are the one that fail at basic Algebra, do you know the rule of expanding bracket? 2(2+2) should be treated as whole

@@userun-j1u you FAIL to understand the Distributive Property correctly.... The Distributive Property is a PROPERTY of Multiplication NOT Parentheses and not Parenthetical Implicit Multiplication. As such it has the same priority as Multiplication and Multiplication does not have priority over Division. The Distributive Property is congruent with the Order of Operations it doesn't supercede the Order of Operations... The Order of Operations work because of the Properties and Axioms of math not in spite of them... The Distributive Property when fully applied is an act of ELIMINATING the need for parentheses by drawing the TERMS inside the parentheses out not by drawing factors in... If you can't draw a factor in and get the same result as drawing the TERMS inside the parentheses out then you haven't applied the Distributive Property correctly... The Distributive Property does NOT change or cease to exist because of parenthetical implicit multiplication... The axiom a(b+c)= ab+ac however the variable "a" represents the TERM or TERM value outside the parentheses not just a numeral next to the parentheses. In this case a = 8÷2 OR 4. People just automatically assume that "a" is a single numeral... A variable can represent a single value, a set of operations that represent a TERM that represents a single value or a solution set... 8÷2(2+2)= 8÷2×2+8÷2×2 Distributive Property.. Parentheses removed... 8÷(2(2+2))= 8÷(2×2+2×2) Distributive Property. Inner parentheses REMOVED

@@RS-fg5mf Expanding brackets means multiplying everything inside the bracket by the letter or number outside the bracket. For example, in the expression 3 ( m + 7 ) both m and 7 must be multiplied by 3: 3 ( m + 7 ) = 3 × m + 3 × 7 = 3 m + 21. in this scenerio, it is 2(2+2)=4+4=8, you don't do divsion before the expanding bracket is completed, you failed to understand this...

Wrong and willfully ignorant... 8 -----(2+2)= 8÷2(2+2)= 16 2 8 --------- = 8÷(2(2+2))= 1 2(2+2) FYI... This isn't Algebra, it's basic grade school ARITHMETIC and there is no mathematical difference between the obelus ÷ and the solidus / they both serve as equal signs of division and neither one serves as a grouping symbol. The vinculum (horizontal fraction bar) serves as a grouping symbol...

WRONG....

@@RS-fg5mf because?

@@petrkapitola2169 because when you actually understand and apply the Order of Operations and the various properties and axioms of math correctly as intended you get the only correct answer 16...

@@petrkapitola2169 The Distributive Property is a PROPERTY of Multiplication NOT Parentheses and not Parenthetical Implicit Multiplication. As such it has the same priority as Multiplication and Multiplication does not have priority over Division. The Distributive Property is congruent with the Order of Operations it doesn't supercede the Order of Operations... The Order of Operations work because of the Properties and Axioms of math not in spite of them... The Distributive Property when fully applied is an act of ELIMINATING the need for parentheses by drawing the TERMS inside the parentheses out not by drawing factors in... If you can't draw a factor in and get the same result as drawing the TERMS inside the parentheses out then you haven't applied the Distributive Property correctly... The Distributive Property does NOT change or cease to exist because of parenthetical implicit multiplication... The axiom a(b+c)= ab+ac however the variable "a" represents the TERM or TERM value outside the parentheses not just a numeral next to the parentheses. In this case a = 8÷2 OR 4. People just automatically assume that "a" is a single numeral... A variable can represent a single value, a set of operations that represent a TERM that represents a single value or a solution set... 8÷2(2+2)= 8÷2×2+8÷2×2 Distributive Property.. Parentheses removed... 8÷(2(2+2))= 8÷(2×2+2×2) Distributive Property. Inner parentheses REMOVED

@@petrkapitola2169 People confuse and conflate two different types of Implicit multiplication .... One without a delimiter and one with a delimiter.. Type 1... Implicit Multiplication between a coefficient and variable... A special relationship given to coefficients and variables that are directly prefixed i.e. juxstaposed WITHOUT a delimiter and forms a composite quantity by Algebraic Convention... Example 2y or BC This type of Implicit Multiplication is given priority over Division and most other operations but not all other operations... This can be seen in most Algebra text books or Physics book. Physics uses this type of Implicit Multiplication quite heavily.. Type 2... Implicit Multiplication between a TERM and a Parenthetical value that have been juxstaposed without an explicit operator but WITH a delimiter...The parentheses serve to delimit the two sub-expressions.. Parenthetical implicit multiplication. The act of placing a constant, variable or TERM next to parentheses without a physical operator. The multiplication SYMBOL is implicit, implied though not plainly expressed, meaning you multiply the constant, variable or TERM with the value of the parentheses or across each TERM within the parenthetical sub-expression. Parentheses group and give priority to operations WITHIN the symbol of INCLUSION not outside the symbol. Terms are separated by addition and subtraction not multiplication or division. The axiom for the Distributive Property is a(b+c)= ab+ac but what most people fail to understand is that each of those variables represents a constant value OR a set of operations that represent a constant value... A single TERM expression like 6÷2(1+2) has two sub-expressions. The single TERM sub-expression 6÷2 juxstaposed to the two TERM parenthetical sub-expression 1+2. The lack of an explicit operator implies multiplication between the TERM or TERM value outside the parentheses and the parenthetical value or across each TERM within the parenthetical sub-expression... The parentheses DELIMIT the TERM 6÷2 from the two TERMS 1+2 maintaining comparison and contrast between the two elements... Implicit multiplication is always by juxstaposition but not all juxstaposition is Implicit multiplication. Example 2½ = 2.5 not 2 times ½... There is “implicit multiplication” WITH delimiters and there is “implicit multiplication WITHOUT delimiters. Two different types of Implicit multiplication and mathematically different. 6÷2y the 2y has no delimiter.... 6÷2y=3÷y by Algebraic Convention. 6÷2(a+b) has a delimiter... 6÷2(a+b)= 3a+3b by the Distributive Property... 6y÷2y = 6y÷(2y) = 6y÷(2*y) 6y÷2(y)= (6y÷2)(y)= 6y÷2*y 6y÷2y(y)= (6y÷(2y))(y)= 6y÷(2y)*y= 6y÷(2*y)*y ÷2y the denominator is 2y ÷2(y) the denominator is 2