Order of operations rule
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 using PEMDAS;
- 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 using PEMDAS;
- 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.