MHB Order of Ops: PEMDAS Explained w/ Examples

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PEMDAS is an acronym that helps remember the order of operations in mathematics, standing for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. Parentheses take precedence over exponents, which are followed by multiplication and division (at the same level), and finally addition and subtraction. When operations of the same rank occur, they should be processed from left to right. The discussion clarifies that expressions like 6(3) and 4(4) represent multiplication, and 16/4(4) simplifies to 16/4 × 4, resulting in 16. The "P" in PEMDAS specifically denotes Parentheses as a grouping sign.
Marvin Kalngan
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The Order of Operations: PEMDAS
“A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right. For instance, 15 ÷ 3 × 4 is not 15 ÷ 12, but is rather 5 × 4, because, going from left to right, you get to the division first.”

But according to my book, 6(3) means “6 times 3”.
So,
16/4(4) = ? is the same with 16/4*4 = ?
because
4(4) means “4 times 4”
and
4*4 means “4 times 4”

It was not stated if P in PEMDAS stands for P as a sign of grouping or P as a sign of multiplication.

Sources:
The Order of Operations: PEMDAS
College Algebra by William Hart 4th edition, page 5
 
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Marvin Kalngan said:
The Order of Operations: PEMDAS
“A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right. For instance, 15 ÷ 3 × 4 is not 15 ÷ 12, but is rather 5 × 4, because, going from left to right, you get to the division first.”

But according to my book, 6(3) means “6 times 3”.
So,
16/4(4) = ? is the same with 16/4*4 = ?
because
4(4) means “4 times 4”
and
4*4 means “4 times 4”

It was not stated if P in PEMDAS stands for P as a sign of grouping or P as a sign of multiplication.

Sources:
The Order of Operations: PEMDAS
College Algebra by William Hart 4th edition, page 5

Hi Marvin! :)

That is correct.
6(3) is shorthand for $6 \times (3)$.

So:
$16/4(4) = 16 / 4 \times (4) = 4 \times 4 = 16$

And P in PEMDAS stands for Parentheses, which groups an expression.
The operation applied to it can be anything.
If no operation is specified, than multiplication is intended.
 
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