Algebra Learning: Using the Order of Operations


Algebra is a systematic way to solve mathematical problems. Understanding the order of operations for an algebraic expression is critically important in order to find the correct answer. Follow these helpful tips, and you will be an expert when it comes to solving algebra and mathematical equations. Be careful, and follow the steps from the beginning to the end for every mathematical problem and algebraic equation.

The steps for the order of operations



1.        Always check for parenthesis.  You will need to solve the problem within the parenthesis first.


(5) 10-32   =x


   Solve any exponents or square roots.  We have an exponent in this equation, so 32needs to be solved in this equation.  Knowing the first step helps solving algebra problems.  Do as many exercises as you can to practise these rules.

WeWe can translate this to 3 x 3= 9, which means the same as 32.

(5) 10-9=x


3.       Find any expressions that need to be multiplied or divided.  The parenthesis tells us that we need to multiply the number next to it. 

(5) 10-9=x



Online help is available to expand these ideas at length, so find a tutor that can guide you further.

4.       Finally, solve any expression involving addition or subtraction. 




So the answer is x = 41.

Sometimes, you may see an equation that doesn’t use any parenthesis to show you which part of the operation to solve first.  In this case, you will need to plug in your own into the equation, and solve it using these rules for the order of operations.

Example:  10-36÷12 x 5+3= x

Use the order of operations to identify where to place the parenthesis.  

Addition and subtraction will go last.  However, it looks like we have some multiplications and divisions that need to be done, so let’s separate this equation first.

10-36÷12 x 5+3= x

10-(36÷12) 5+3= x

We may remove the multiplication sign because it is understood that the grouping symbol will require us to multiply the results obtained within the parenthesis with the number next to it.

10-(3)5 +3=x




Following the order of operations makes it easy to figure out the unknown x.  This is one of the essential rules that help us to solve any algebra problem, and online help is available to give additional help.  Get a tutor to help you check your work.  They can suggest some online resources that are available for free to help facilitate your learning.

Make sure you show your work while solving a problem so that you can track the steps that you used to solve.  Check your work!  For additional help, find an online tutor who can provide a Free Trial class to guide you with some algebra tips.

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