# Order of Operations: What is Order of Operations? Full Explain

We were never told the details of what she did. All middle schools in the U.S. will teach its students to remember this basic sentence: “Please excuse my dear Aunt Sally.” Why are we making excuses for her conduct? Did she dress in white following Labor Day or something?

The world will never be aware. “Please forgive my sweet Aunt Sally” is merely an memorizing device. It’s an educational tool to aid us in memorizing information using the use of a catchy rhyme, word, or acronym.

To give another example, we look at the field of geography “Order of Operations”. If you are unable to remember the names of the five Great Lakes, simply use the phrase “H.O.M.E.S.” Every letter of that acronym is a mnemonic for each of those lakes mentioned: Huron, Ontario, Michigan, Erie and Superior. Simple and elegant.

“Please forgive my sweet Aunt Sally” is an example of a math mnemonic. This time, what we’re supposed to remember is a crucial concept known as” the mathematical or order of operation.

If it’s the week of finals and you’re asked to work out the following problem:

**9 – (2 x 3) x 4 + 5** ^{2} **= ?**

Don’t panic. This is where an auntie can help. For each word in” Please excuse my dear Aunt Sally, “Please please excuse me dear aunt Sally,” there’s a equivalent math word that begins at the exact same letters.

**P**arentheses**E**xponents**M**ultiplication and**D**ivision**A**ddition and**S**ubtraction

Girls and boys, look out for the sequence of operations! Also called the PEMDAS for the United States, it tells us what procedure(s) to carry out first.

Before we do something else PEMDAS “Order of Operations” requires us to take a moment to ask ourselves: “Are there any parentheses?” If you answer “yes,” then our first task is to determine what’s in them.

So in the previous example we will find ” **2 x 3**” within two parentheses. Thus, we’ll begin by multiplying two times 3 and we’ll get six. The equation is now like this:

**9 – 6 x 4 + 5** ^{2} **= ?**

Cool beans. The time is now to get those exponents! When printed, experients have the form of a small number that is pressed against the upper righthand corner an even larger number. See the **5** ^{2}? That tiny “2” represents an exponent of the word “fellow..

This tiny two is telling us to multiply five times itself. Five x five equals 25, resulting in this:

**9 – 6 x 4 + 25 = ?**

What’s next? I’m glad you asked. After addressing the parentheses as well as the exponent(s) We will move on to the next two steps which are division and multiplication.

It’s important to keep in mind it’s not a statement that says that multiplying occurs *prior to* division in this case. At least, not always. Let’s suppose you’re working on an additional problem thatat this pointhas the multiplication symbol as well as the symbol for division. Your task is to carry out the two operations in a sequential order starting from the left.

The concept can be illustrated using an examples. If the equation reads : 8 4 x 3 first, you’ll divide the eight by the number 4 and you’ll get two. And only then would multiply those two times by three.

Now we return to our routinely scheduled math problem

**9 – 6 x 4 + 25 = ?**

Whoever came up with the original equation made sure that the formula was neat and straightforward; there’s not any division symbol in sight and there’s only one symbol for multiplication. Thank you, merciful exam gods.

Without further delay it is time to multiply the six times by four, which gives us 24.

**9 – 24 + 25 = ?**

Similar to division and multiplication subtraction and addition are both part of the same procedure. We’ll be performing these two tasks by arranging them from left to right. Therefore, we’ll need subtract twenty-four from nine.

If we do this, we will get negative numbers, specifically 15.

But the 25 is an integer that is positive. Therefore, in its current formula, the equation consists from a negative number 15 and positive 25. If you add the two, you’ll get an positive 10.

That’s it. The solution to our mystery.

**9 – (2 x 3) x 4 + 5** ^{2} **= 10**

Before we go on we need to know some additional points to be aware of. There is a chance that you will be facing a complicated equation that includes a myriad of operations sandwiched in two parentheses. It could be something like this:

**9 – (23 x 3 / 18) x 4 + 52 = ?**

Don’t be concerned. All you need to do is follow the PEMDAS procedure *within the parentheses* before moving on to the remainder of the issue. (In case you’re curious you can find the answer to that equation is 28.2/3 or 28.67 If you’re more into decimals.)

In the end, you may be interested in knowing that the structure of the operation that we as Americans recognize it todaywas likely officially established sometime in the 18th or beginning of the 20th century. This was also the time of the rise of the U.S. textbook industry.

In an email written by a math and science historian, Susan Grabiner states that concepts such as”order of operation” should be seen as “conventions such as red-means-stop or green-means-go, and not mathematical truths.”

“But after the convention has been set,” she says, “the analogy of traffic lights applies: Everyone has to follow with the same manner and the “same way” must be 100% without ambiguity.” Math and ambiguity can be difficult to get along with.

Different nations are able to use different acronyms but. In some parts of the world the children are taught to recall “BODMAS” which means Brackets and Orders (i.e. exponents, exponents, as well as square root) Multiplication and division Subtraction and Additionin place in place of “PEMDAS.”