When simplifying a numerical or algebraic expression, it is important that you complete the calculations in the correct order. If not, you may end up getting the incorrect answer! There are different tips and tricks that can be used to help you remember which operations to complete first. Operation is the term used for any addition, subtraction, multiplication, or division.
When looking at an equation with multiple operations you can follow the four steps to help you calculate the equation in the correct order:
First you can start by calculating anything that is inside grouping symbols, like brackets or parentheses.
Now you look at any powers that are in the sum, these are also known as exponents.
Next you move on to any multiplication or division, working from left to right.
Finally, you work through any addition or subtraction, again working from left to right.
There are different types of brackets that may be used;
Round brackets ( )
Curly brackets { }
Box brackets [ ]
Solve
To solve this, you can break it down into the 4 steps;
Calculate grouping symbols :
Calculate any exponents :
Multiplication/division :
Addition/subtraction :
Therefore, the answer is 42.
How to remember the rule?
In order to help you remember which order to solve a sum there is an acronym, PEMDAS;
P : Parentheses (grouping symbols)
E : Exponents (powers and roots)
MD : Multiplication and division
AS : Addition and subtraction
Order of operations examples
Simplify
Let's work through each step to solve the expression;
P :
E :
M/D : This step is not needed in this sum.
A/S :
Therefore,
Simplify
Let's work through each step to solve the expression;
P : This step is not needed in this problem.
E :
M/D :
A/S :
Therefore,
Order of operations with algebra
Sometimes when you are evaluating an algebraic expression for a given value of the variable, you will need to apply the Order of Operations to help you get the correct answer.
Evaluate when
First you can substitute 6 into the expression, then you can follow PEMDAS;
P : This step is not needed in this problem.
E :
M/D :
A/S :
Therefore when ,
Evaluate when and
To begin with, you can substitute in your variables to see the expression, then you can continue to solve it using PEMDAS;
P :
E :
M/D :
A/S :
Therefore, when and ,
Evaluate when
To begin with, you can substitute in your variable to see the expression, then you can continue to solve it usingPEMDAS;
P : This step is not needed in this problem.
E : This step is not needed in this problem.
M/D :
A/S :
Therefore, when ,
Evaluate when
To begin with, you can substitute in your variable to see the expression, then you can continue to solve it usingPEMDAS;
P :
E :
M/D :
A/S :
Therefore, when ,
Operations and Ordering - Key takeaways
It is important to evaluate numerical and algebraic expressions in a specific order to guarantee a correct answer.
There are 4 steps to follow to ensure you are calculating your operations in the right order;
Grouped terms, parentheses
Powers or exponents
Multiplication or division (in order from left to right)
Addition or subtraction (in order from left to right)
There is an acronym that can be used to help you remember the correct order of operations, it is PEMDAS.
It is also important to follow the correct order of operations when plugging in a given value for the variable in an equation.
Learn faster with the 0 flashcards about Order of Operations
Sign up for free to gain access to all our flashcards.
Frequently Asked Questions about Order of Operations
What is order of operations?
Order of operations is a correct order in which you should solve operations, operations are things such as addition, multiplication, and powers.
What are the rules of order operations?
The rules for order of operations state that you should complete a sum in the following order;
Calculate anything inside grouping symbols
Calculate any powers
Calculate any multiplication or division
Calculate any addition or subtraction
What are the importance of order of operation?
It is important to use order of operation to get the correct answer to your sum, if you simply calculate the sum from left to right you will be left with the wrong answer.
How we ensure our content is accurate and trustworthy?
At StudySmarter, we have created a learning platform that serves millions of students. Meet
the people who work hard to deliver fact based content as well as making sure it is verified.
Content Creation Process:
Lily Hulatt
Digital Content Specialist
Lily Hulatt is a Digital Content Specialist with over three years of experience in content strategy and curriculum design. She gained her PhD in English Literature from Durham University in 2022, taught in Durham University’s English Studies Department, and has contributed to a number of publications. Lily specialises in English Literature, English Language, History, and Philosophy.
Gabriel Freitas is an AI Engineer with a solid experience in software development, machine learning algorithms, and generative AI, including large language models’ (LLMs) applications. Graduated in Electrical Engineering at the University of São Paulo, he is currently pursuing an MSc in Computer Engineering at the University of Campinas, specializing in machine learning topics. Gabriel has a strong background in software engineering and has worked on projects involving computer vision, embedded AI, and LLM applications.
StudySmarter is a globally recognized educational technology company, offering a holistic learning platform designed for students of all ages and educational levels. Our platform provides learning support for a wide range of subjects, including STEM, Social Sciences, and Languages and also helps students to successfully master various tests and exams worldwide, such as GCSE, A Level, SAT, ACT, Abitur, and more. We offer an extensive library of learning materials, including interactive flashcards, comprehensive textbook solutions, and detailed explanations. The cutting-edge technology and tools we provide help students create their own learning materials. StudySmarter’s content is not only expert-verified but also regularly updated to ensure accuracy and relevance.