Home Order of Operations: The Magical PEMDAS

# Order of Operations: The Magical PEMDAS

Order of operations may not sound like a mathematical term. What do operations have to do with math? In Mathematics,  “operations” refers to concepts like addition, subtraction, division, multiplication, and more. That means that numbers are required for something to be considered an operation. Order of operations refers to the order and set of rules in which you solve an equation. But when you see an equation like 7 x (9-4) + 2², where do you start? Left to right, right to left, or some other way?  Following the order of operations is important to ensure the equation is solved properly. If not followed, you will find a very different answer to the equation.

## PEMDAS

P–  Parentheses () first

E–  Exponents (i.e. Powers and Square Roots, etc.)

MDMultiplication and Division (left to right)

AS Addition and Subtraction (left to right)

It is important to know that Multiplication is equally ranked with Division, Addition is equally ranked with Subtraction, and both go left to right. This means that after you do “P” and “E”, go left to right and do any “M” or “D” that you find. Then go left to right and do any “A” or “S” that you find.

While the rest of PEMDAS is quite self-explanatory, let’s look at the example for a better understanding. As you go, it helps to replace the solution of each section back into the equation.

7 x (9-4) + 2²

P– means do what is in parentheses first

So that would be (9-4) which equals 5

Now the equation becomes 7 x (5) + 2²

E– means do exponents like powers next

So 2² which equals 4

Now the equation becomes 7 x (5) + 4

MD– means do the multiplication or division next

There is only multiplication in this equation

so 7 x (5) is 7 x 5 which equals 35

Now the equation becomes 35 + 4

AS– means add or subtract next

And we are left with the last part of the equation

35 + 4= 39

## Other Variations of PEMDAS

While PEMDAS is the most common acronym for this rule, you may hear about GEMS, BODMAS, or BEDMAS. All are the same concept as PEMDAS, just with slightly different names for the first two rules.

GEMS stands for:

G– Grouping () and [] first

E– Exponents (i.e. Powers and Square Roots, etc.)

M– Multiplication and Division (left to right)

S– Addition and Subtraction (left to right)

In the UK, BODMAS stands for:

B– Brackets [] first

O– Orders (i.e. Powers and Square Roots, etc.)

DM– Division and Multiplication (left to right)

AS– Addition and Subtraction (left to right)

B– Brackets [] first

E– Exponents (i.e. Powers and Square Roots, etc.)

DM– Division and Multiplication (left to right)

AS– Addition and Subtraction (left to right)

As you can see, PEMDAS, GEMS, BODMAS, and BEDMAS, are all the same but with a different name & acronyms for the Parentheses (Grouping or Brackets) and the Exponents (Orders). In U.S. mathematics education, PEMDAS is the most commonly used acronym for the order of operations.

## PEMDAS Tips & Tricks

If you need a trick to remember “PEMDAS”, you can memorize a popular phrase “Please Excuse My Dear Aunt Sally” and use the first letter from each word to complete the acronym.

Another important tip: if you find an equation that does not have any of the components within PEMDAS, it is okay to skip. Meaning, if an equation does not have “P” (parentheses), it is okay to move on to “E” (exponents). The same can be said for any of the letters in PEMDAS. Just be sure to carefully review the equation to avoid skipping a part that is there.

The order of operations is especially important to know for any testing. SAT, ACT, or even math competitions will require you to understand PEMDAS to complete equations in the right order. While this concept will be taught in middle school, it will follow a student through their high school years.

## At OMC

As we see, understanding the order of operations is important for a student’s mathematics education. While it may seem easy by itself, when combined with other math concepts, it can look a bit more complicated. It is best to have a great understanding of addition, subtraction, multiplication, division, powers, and square roots to complete the order of operations seamlessly.

At OMC, we understand topics like these may seem basic but we strive to ensure that all students leave school with a solid education of math concepts such as these and the ability to use the techniques that they’ve been taught.

Contact OMC today to make sure your child gains a solid, full understanding of the most important mathematical concepts like the order of operations by signing them up for classes that are tailored to their specific math needs.

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