Order of Ops: PEMDAS Explained w/ Examples

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In summary, PEMDAS is a common technique for remembering the order of operations in mathematical expressions. It stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. When dealing with multiple operations of the same rank, they are performed from left to right. It was not stated if P stands for Parentheses or Multiplication in PEMDAS.
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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.
 

FAQ: Order of Ops: PEMDAS Explained w/ Examples

What is PEMDAS and why is it important in math?

PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. It is the order of operations that is used in math to determine which operations should be performed first in a mathematical expression. This ensures that everyone follows the same set of rules when solving equations, making it easier to communicate and understand mathematical concepts.

How do I use PEMDAS to solve an equation?

To use PEMDAS, you must first start with the parentheses. Simplify any expressions within the parentheses first, then move on to the exponents. Next, perform any multiplication and division operations from left to right. Finally, solve any addition and subtraction operations from left to right. Remember to always follow this order to avoid any confusion or mistakes in your calculations.

Can the order of operations be changed?

No, the order of operations (PEMDAS) is a universal rule that must be followed in math. Changing the order will result in a different answer, and it is important to use the same order to ensure accuracy and consistency in solving equations.

Are there any exceptions to the PEMDAS rule?

Yes, there are some exceptions to the PEMDAS rule. For example, when there are multiple sets of parentheses, you would start with the innermost set and work your way out. Additionally, if there are operations with the same precedence (ex. multiplication and division), you would solve them from left to right. It is important to remember these exceptions and follow the order of operations accordingly.

Why is it important to learn and understand PEMDAS?

PEMDAS is a fundamental concept in math that is used in many different areas, such as algebra, geometry, and calculus. It is important to learn and understand PEMDAS because it allows us to solve complex equations and understand the order in which operations should be performed. This skill is necessary for success in higher level math courses and in many real-life situations where math is used.

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