The term âoperationsâ in math simply means anything to do with adding, subtracting, multiplying, dividing, etc. For most algebra equations, if itâs not a number it is probably an operation, or what you need to âdoâ to solve the problem. The âorder of operationsâ is what order you use the operations in order to solve for the answer.
If we tried to solve this problem from left to right, or right to left, we would end up with the wrong answer. To solve for X, we have to solve smaller parts of this problem in the correct order. That correct order is as follows:
Parenthesis in math problem represent groups of numbers that symbolize one number. Some examples of these are:               2(2 +7)                    or            10 /(45*2)
Do you see parenthesis in this math problem?
No, there are no parenthesis in this problem. Now we can move on to the next step!
In short, exponents are the smaller number used to explain how many times to multiple a number by itself. In the example of this expression: (5)(5)(5)Â =Â 53
The â3â is the exponent, and ittells you to simply multiply the 5 three times.
Are there any exponents in the original expression?
No, there are no exponents in the original expression. Now we can move on to the next step!
The next step in the order of operations is to solve all multiplication and division aspects of the expression.
In the above example: 16 + 9 / 3 â 11 = X Â itâs a good idea to group the type of problems that you have inside the equation.
For example, 16+ (9/3) -11=X
When you solve 9/3, that leaves the equation at: 16 +3 -11=X
When all of the other steps of the Order of Operations are done, you can Add and Subtract, just like you would any normal simplistic math problem.
In the above example: 16 +3 -11=X
It is important to remember that the Multiply/Divide and Addition/Subtract part of PEMDAS are pairs. This means if division and multiplication are in the same problem, you work the problem from left to right doing the multiplication and division, whichever comes first. The same must be done for the adding and subtracting part. Follow along with the problem below.
Remember that that Multiply and Divide are grouped together, so while you should always do the multiplication and division first before you do the adding and subtracting, you should also follow it from left to right. Since division is literally what comes first, we do that and THEN the multiplication:
16 / 8 x 3 + 2 â 5 divide before you multiply
All that is left is the adding and subtracting, which we will now do in order from left to right:
Try this one all on your own and then check back and see if you got the right answer:
If you got 16 then pat yourself on the back, you are well on your way to mastering The Order of Operations. If you are still having trouble, especially with a particular problem, try going to MathCrunch.com or downloading our app MatchCrunch straight from the app store where we have tutors standing by at any time, ready to help you with any problem you may have. Good luck!