Order of Operations
September 20, 2005
Dear Student,
The Order of Operations is not one of the hardest, nor is it one of the easiest things that you will have to learn in Algebra and other mathematical classes. To begin in learning the Order of Operations, you must follow the steps, hence the "order" of the operation. To start off, the first step would be to do anything that is inside of grouping symbols ([ ], ( ), { }). Next you would have to do powers from the left to the right (9 squared). Following the Order of Operations, the next phase of a problem would be to do all of the multiplication and division from the left to the right (*, /). The final stage in the Order of Operations is to do all of the addition and subtraction from the left to the right (+, -). Now, you just have to finish by putting it altogether and finding the answer.
Example- 3*6(35-3+5)10squared
1) First do anything inside 3*6*37*10squared grouping symbols.
2) Next you do powers 3*6*37*100 from left to right.
3) Now multiplication 66,600 and division from the left to the right.
4) Lastly you would do addition and subtraction but this problem doesn't have any.
Above is an example of how the Order of Operations works. It should always be done this way. An example of someone doing it the wrong way is below:
3*6(35-3+5)10squared
1) As you can see 18(35-3+5)10squared this person decided to go from the left to the right, ignoring the steps.
2) They keep going 630-3+5*10squared this way, and calculate 622*10squared the stuff in the parentheses wrong.
3) They now do the 622*100 = square of 10, and multiply it by 622. 62,200
As you can see this answer is incorrect, because the Order of Operations was not followed.
I hope my explanation of the Order of Operations will help you understand the basic part of it, but there is much more to come in the future.
Sincerely, Andy Michaelson Andy
Dear Student,
The Order of Operations is not one of the hardest, nor is it one of the easiest things that you will have to learn in Algebra and other mathematical classes. To begin in learning the Order of Operations, you must follow the steps, hence the "order" of the operation. To start off, the first step would be to do anything that is inside of grouping symbols ([ ], ( ), { }). Next you would have to do powers from the left to the right (9 squared). Following the Order of Operations, the next phase of a problem would be to do all of the multiplication and division from the left to the right (*, /). The final stage in the Order of Operations is to do all of the addition and subtraction from the left to the right (+, -). Now, you just have to finish by putting it altogether and finding the answer.
Example- 3*6(35-3+5)10squared
1) First do anything inside 3*6*37*10squared grouping symbols.
2) Next you do powers 3*6*37*100 from left to right.
3) Now multiplication 66,600 and division from the left to the right.
4) Lastly you would do addition and subtraction but this problem doesn't have any.
Above is an example of how the Order of Operations works. It should always be done this way. An example of someone doing it the wrong way is below:
3*6(35-3+5)10squared
1) As you can see 18(35-3+5)10squared this person decided to go from the left to the right, ignoring the steps.
2) They keep going 630-3+5*10squared this way, and calculate 622*10squared the stuff in the parentheses wrong.
3) They now do the 622*100 = square of 10, and multiply it by 622. 62,200
As you can see this answer is incorrect, because the Order of Operations was not followed.
I hope my explanation of the Order of Operations will help you understand the basic part of it, but there is much more to come in the future.
Sincerely, Andy Michaelson Andy