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How to Remember and Work on the Order of Operations

Updated on March 23, 2012

Order of Operations

Order of Operations is a universal understanding of how math is supposed to work. This simple structure ensures that we all calculate the same problem in the same way in order to get the same answer. The key here is the word 'same.'

PEMDAS is a common mnemonic device that helps us remember the Order of Operations.

Please

Excuse

My Dear

Aunt Sally

Please Excuse My Dear Aunt Sally
Please Excuse My Dear Aunt Sally

PEMDAS

The PEMDAS acronym stand for the operations in the order that they need to occur. Notice that I put Multiplication and Division on the same line. Most teachers don't teach it this way and it causes confusion. Multiplication and Division are done in order form left to right. They go together, you do not do all the multiplication and then go back and do the division. They same is true for addition and subtraction.

Problem #1
Problem #1

Put Order of Operations to use

Problem #1

(2x6) - 22 x 3 +1

When we look at this problem the first thing we should be looking at is the equation inside of the parenthesis. 2x 6 = 12

After we have taken take of the parenthesis then we need to look for any exponents. 22 = 4

We have taken care of the P & E now we are looking for any multiplication or division. The multiplication problem that we need to do is 3 x 4 = 12.

Next we are looking for all the addition and subtraction problems. 12 -12 is the first problem we see. 12-12=0

And finally 0+1=1


PEMDAS
PEMDAS

What if we are missing steps?

Problem #2

35 ÷ 5 × 3 - 4

There are no parenthesis or exponents in this problem which means that we launch directly into multiplication and division. This is where it is extremely important to note that they go hand in hand and we do the division problem first since it is the first problem we see.

We then do multiplication and follow with our subtraction problem.

The Final Challenge

This equation follows all the steps of the Order of Operations in order to show how the equation works step by step.

2×3(22+1) - 4 ~ parentheses

2×3(4 + 1) - 4 ~ (inside of the parenthesis the exponent goes first )

2×3(5) - 4 ~ inside the parenthesis the addition goes second

2×3×5-4 ~ I rewrite the problem in order to properly see the operations

6×5-4 ~ going from left to right I start the multiplication

30 - 4 ~ multiplying - subtraction last

26 - THE ANSWER


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    • Vellur profile image

      Nithya Venkat 5 years ago from Dubai

      Nicely explained. Voted up.

    • kthix10 profile image
      Author

      kthix10 5 years ago from IL

      Thanks!

    • YvetteParker profile image

      YvetteParker 5 years ago from AUGUSTA, GA

      Great lesson on order of operations; voted up!